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Octave Sizes

Posted By: Mark Cerisano

Octave Sizes - 02/28/17 02:26 PM

I have read recently in the forum, but at other times as well, and from different people, that tuning the temperament octave somehow has something to do with the actual intervals within the temperament octave.

I have read things like:

"If you tune the octave too wide/narrow, the intervals won't fit."

And:

"If you tune the octave to one size it may have to be changed."

I have never experienced this and I'm wondering if someone can logically and clearly explain why.

Here's how I see it:

The octave can be tuned to any size and the intervals can be fit into any octave. It's like having 13 dimes. Two are placed on a table about 1 foot apart, and then the remaining 11 are fit between so they are all the same distance apart. It is possible to set the first two any distance apart and end up with the same result: equi-distant dimes.

The only empirical and musical judgement to be made is what does the octave sound like. So the logic is, if the octave is the only interval that can be judged, it should be tuned as accurately as possible from the beginning.

How do we make a judgment on the "correctness" of a bunch of intervals that are all out-of-tune? The 3/4/5/6 all beat. The octave is the only interval within the temperament that can be tuned "beatless".

Posted By: RonTuner

Re: Octave Sizes - 02/28/17 02:40 PM

I see where you are coming from and will let others chime in about the tuning within an octave making them change the octave size...

I have run into some pianos when I was designing stretch parameters for the Verituner where I found I had to move single octaves slightly away from being perceived as "pure"... Why? Because I was attempting to make an octave 'ladder', a framework of octaves first - with the best single, double, triple octaves possible.

Ron Koval
Posted By: Mark Cerisano

Re: Octave Sizes - 02/28/17 02:47 PM

Thanks Ron,

I will make another thread soon about octave stretch outside the temperament octave where we consider those larger intervals. But what I want to start with, is why some people say that within the temperament, the best sounding octave is not always the best.

I am looking for evidence that proves that when only considering the octave temperament notes, the best sounding octave may not be the best sized octave.

After that, I will ask, in a new thread, why the best sounding octave is not the best sized octave when we tune the bass and temperament.

As far as "I changed the octave because I didn't like the fourth/fifth", my question is, how can you make a judgement on an interval that is out of tune? If you are saying "I don't like the out of tuneness of this fourth/fifth", aren't you placing your own personal taste on the fourth/fifth, at the expense of an empirical interval like the octave?
Posted By: Gadzar

Re: Octave Sizes - 02/28/17 03:05 PM

It was me who posted that the best size of the octave must be determined by how the other intervals within, above and below that octave sound. So I'm going to answer.

In a piano there is not one unique kind of octave. iH of piano strings makes that there are several kinds of octave, namely 2:1, 4:2, 6:3, 8:4, etc. There is no such a thing as a beatless octave. If you tune a beatless 2:1 octave, then the other (4:2, 6:3, 8:4, ...) will be beating. No matter how wide or narrow you tune the octave, there will be always several pairs of partials beating.

So you can not tune a beatless octave and then tune the corresponding intervals that fit exactly within this octave.

In that sense octaves are also tempered. Just as fifths and fourths, and thirds etc.

So the question is how tempered my octave will be?

Well my answer is: listen to the other intervals. There are wide intervals like fourths, major thirds, major sixths, major tenths, etc. And there are narrow intervals like fifths, minor thirds, etc... Octaves are narrow or wide depending on the kind of octave (2:1, 4:2, 6:3 etc...) and the point of the scale you consider (bass, tenor, treble).

If you tune a too narrow octave then wide intervals will sound purer: you'll have nice sounding fourths, major thirds, major tenths, but narrow intervals will sound noisy: you'll have dirty fifths, too tempered minor thirds, etc...

On the contrary, if you tune a wider octave then major thirds and tenths and fourths will sound sour but narrow intervals will sound purer.

So, it's a question of how stretched you like your tuning to be. It's a balance to be made between narrow and wide intervals. It's a compromise between fifths and major thirds (tenths) so to speak.

That's why I suggest to tune fifths, fourths, thirds, ... before deciding the final and definitive size of the octave.


Posted By: daniokeeper

Re: Octave Sizes - 03/01/17 12:08 AM

Originally Posted by RonTuner
I see where you are coming from and will let others chime in about the tuning within an octave making them change the octave size...

I have run into some pianos when I was designing stretch parameters for the Verituner where I found I had to move single octaves slightly away from being perceived as "pure"... Why? Because I was attempting to make an octave 'ladder', a framework of octaves first - with the best single, double, triple octaves possible.

Ron Koval


Ron, octave ladder, that is the best way of expressing it i have ever seen smile
Posted By: DoelKees

Re: Octave Sizes - 03/01/17 03:49 AM

Originally Posted by Gadzar
It was me who posted that the best size of the octave must be determined by how the other intervals within, above and below that octave sound. So I'm going to answer.

In a piano there is not one unique kind of octave. iH of piano strings makes that there are several kinds of octave, namely 2:1, 4:2, 6:3, 8:4, etc. There is no such a thing as a beatless octave. If you tune a beatless 2:1 octave, then the other (4:2, 6:3, 8:4, ...) will be beating. No matter how wide or narrow you tune the octave, there will be always several pairs of partials beating.

So you can not tune a beatless octave and then tune the corresponding intervals that fit exactly within this octave.

In that sense octaves are also tempered. Just as fifths and fourths, and thirds etc.

So the question is how tempered my octave will be?

Well my answer is: listen to the other intervals. There are wide intervals like fourths, major thirds, major sixths, major tenths, etc. And there are narrow intervals like fifths, minor thirds, etc... Octaves are narrow or wide depending on the kind of octave (2:1, 4:2, 6:3 etc...) and the point of the scale you consider (bass, tenor, treble).

If you tune a too narrow octave then wide intervals will sound purer: you'll have nice sounding fourths, major thirds, major tenths, but narrow intervals will sound noisy: you'll have dirty fifths, too tempered minor thirds, etc...

On the contrary, if you tune a wider octave then major thirds and tenths and fourths will sound sour but narrow intervals will sound purer.

So, it's a question of how stretched you like your tuning to be. It's a balance to be made between narrow and wide intervals. It's a compromise between fifths and major thirds (tenths) so to speak.

That's why I suggest to tune fifths, fourths, thirds, ... before deciding the final and definitive size of the octave.

That's extremely clearly explained, nice post.

I'm not sure though that the infinitesimal changes in absolute beat rates of M3 m3 P4 P5 resulting from the small changes in octave size that are possible without the octave sounding bad are musically relevant or are even audible. Perhaps the P5 is an exception, at least Cordier thinks it's important.

That being said I tune octaves on my harpsichord on the narrow side of "perfect", as I care about the M10 and M17, but that's specific to my repertoire and personal taste.

Kees
Posted By: Gadzar

Re: Octave Sizes - 03/01/17 04:06 AM

Originally Posted by DoelKees
That being said I tune octaves on my harpsichord on the narrow side of "perfect", as I care about the M10 and M17, but that's specific to my repertoire and personal taste.

Kees


I hate noisy tenths. For me less stretch is better.

Posted By: DoelKees

Re: Octave Sizes - 03/01/17 04:28 AM

Originally Posted by Gadzar
Originally Posted by DoelKees
That being said I tune octaves on my harpsichord on the narrow side of "perfect", as I care about the M10 and M17, but that's specific to my repertoire and personal taste.

Kees


I hate noisy tenths. For me less stretch is better.

thumb

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/01/17 02:25 PM

My research shows an audible difference between a pure 4:2/pure 6:3 and a wide 4:2/narrow 6:3 that I judge as beatless. That is a difference of about 0.5 cents.

I am not the only one who describe octaves as beatless.

Let's just use the phrase "sound really good".

My question remains. How or why would someone tune an octave, A3A4 for example, so that it "sounds real good", and then decide to make it "not sound so good" because they don't like the sound of an interval within the temperament that is out of tune empirically. E.g. A P4 or P5.

I'm not talking about poorly scaled pianos. Maybe advocates are?
Posted By: UnrightTooner

Re: Octave Sizes - 03/01/17 02:50 PM

Originally Posted by Mark Cerisano, RPT
My research shows an audible difference between a pure 4:2/pure 6:3 and a wide 4:2/narrow 6:3 that I judge as beatless. That is a difference of about 0.5 cents.

I am not the only one who describe octaves as beatless.

Let's just use the phrase "sound really good".

My question remains. How or why would someone tune an octave, A3A4 for example, so that it "sounds real good", and then decide to make it "not sound so good" because they don't like the sound of an interval within the temperament that is out of tune empirically. E.g. A P4 or P5.

I'm not talking about poorly scaled pianos. Maybe advocates are?


You can take what is potentially the worse sounding interval on a piano and make it sound the best you can and use this as a basis for ultimately setting the octave size. On small pianos, I find this interval to be the lowest 5th on unwound strings. But to play it safer, I typically choose the one 2 semitones higher to avoid difficulties in setting the temperament.

Another way is to start with a pure or tempered 12th (as you prefer) and determine the best octave by listening to them and the resulting 5ths.

A third way, which I do not have experience with but is the beginning of the Baldassin-Sanderson sequence, is to build a ladder of CM3s spanning an M10 and adjust the octaves, if need be, to smooth out the beatrate progression of the CM3s.

Not sure if this will help, Mark. It depends if your Topic(s) are meant to open discussion or to give instruction.
Posted By: Ed Sutton

Re: Octave Sizes - 03/01/17 04:33 PM

The aural tuners whose work I most admire spend considerable time listening to the musical voice of the piano, and adjusting patiently in response to what they hear. They don't assume a one size fits all approach, and they recognize that there may be unfortunate compromises to be reconciled as best as the piano will allow.

For example, I don't know of a music theory that makes music out of long series of chromatic Major thirds, or for that matter, out of extended series of chromatic octaves.
On the other hand, 12ths and 19ths can provide a sense of stability and connectedness to the bottom side of harmonies, and 10ths can give a feeling of a warm vibrato or a nervous quivering. There is something that can make the high treble really beautiful...and I am yet to find out what that is.

[I don't get the feeling that Bach, for instance, particularly enjoys the sound of an instrument, he is more caught up in his counterpoint, and the close voicing gives a combined effect far less obvious than an individual beating third or sixth.
But Scarlatti seems to enjoy the sound of sequential diatonic 10ths, 6ths, etc., using the harpsichord more like a 19th century composer (or modern jazz composer).]

Anyway, the tuners I admire seem to have had exceptional opportunities to tune many fine pianos, developing along the way a special sensitivity to the musical possibilities of individual pianos. They don't tune a separate temperament, bass and treble, they tune the whole piano, and they spend more time listening than preaching. Perhaps I'll live long enough to get closer to that myself!
Posted By: BDB

Re: Octave Sizes - 03/01/17 04:38 PM

The tuners I admire are those who can do a good job on a bad piano!
Posted By: Mark Cerisano

Re: Octave Sizes - 03/01/17 05:15 PM

Ed,

I am always looking for the musical sound in the interval. But I also analize what the result is, so I can be more efficient, chose the most problem best size, modify if necessary, and move on.

The question is, having determined the best sounding A3A4, (my first octave tuned), why would I want to change it, barring drift?
Posted By: UnrightTooner

Re: Octave Sizes - 03/01/17 05:31 PM

Originally Posted by Mark Cerisano, RPT
Ed,

I am always looking for the musical sound in the interval. But I also analize what the result is, so I can be more efficient, chose the most problem best size, modify if necessary, and move on.

The question is, having determined the best sounding A3A4, (my first octave tuned), why would I want to change it, barring drift?


Because other intervals might sound bad. And not just the RBIs within the octave (although that is what I some across on smaller pianos.) If the A3-A4 octave is kinda narrow, but sounds great, and yet to have the A3-A5 double octave sound right, either harmonically or melodically, requires a bad sounding A4-A5 octave, this would be a reason to change the A3-A4 octave.
Posted By: Ed Sutton

Re: Octave Sizes - 03/01/17 05:44 PM

Jeff has a good answer.
Piano music usually involves complex harmonic combinations, often linked over time by pedal.
This is what gives the instrument its beauty, not the sound of one octave or third in isolation.
At the very least a two octave temperament, testing 3rds, 10ths, 4ths, 5ths and 12ths and various chord voicings will give us a framework to start from, to begin to hear what the instrument can do.
Posted By: Gadzar

Re: Octave Sizes - 03/01/17 08:03 PM

Originally Posted by Ed Sutton
The aural tuners whose work I most admire spend considerable time listening to the musical voice of the piano, and adjusting patiently in response to what they hear. They don't assume a one size fits all approach, and they recognize that there may be unfortunate compromises to be reconciled as best as the piano will allow.

For example, I don't know of a music theory that makes music out of long series of chromatic Major thirds, or for that matter, out of extended series of chromatic octaves.
On the other hand, 12ths and 19ths can provide a sense of stability and connectedness to the bottom side of harmonies, and 10ths can give a feeling of a warm vibrato or a nervous quivering. There is something that can make the high treble really beautiful...and I am yet to find out what that is.

[I don't get the feeling that Bach, for instance, particularly enjoys the sound of an instrument, he is more caught up in his counterpoint, and the close voicing gives a combined effect far less obvious than an individual beating third or sixth.
But Scarlatti seems to enjoy the sound of sequential diatonic 10ths, 6ths, etc., using the harpsichord more like a 19th century composer (or modern jazz composer).]

Anyway, the tuners I admire seem to have had exceptional opportunities to tune many fine pianos, developing along the way a special sensitivity to the musical possibilities of individual pianos. They don't tune a separate temperament, bass and treble, they tune the whole piano, and they spend more time listening than preaching. Perhaps I'll live long enough to get closer to that myself!



thumb

Nice post!

Posted By: Mark Cerisano

Re: Octave Sizes - 03/01/17 09:17 PM

Originally Posted by Ed Sutton
Jeff has a good answer.
Piano music usually involves complex harmonic combinations, often linked over time by pedal.
This is what gives the instrument its beauty, not the sound of one octave or third in isolation.
At the very least a two octave temperament, testing 3rds, 10ths, 4ths, 5ths and 12ths and various chord voicings will give us a framework to start from, to begin to hear what the instrument can do.


Hi Ed,

I have experienced having to use compromise on poorly scaled pianos, but that is only when I expand outside the temperament.

I want to know why I would change the size of my A3A4 from good to not so good if I'm just tuning an octave temperament. Just by listening to some out of tune 3/4/5/6? If one has a proclivity to the sound of a certain out of tune 4th for example, ok.

Another way to ask this is, why do some people say that the three stacked M3's within an octave can tell us the correct size of the octave? I've heard a few people say this but it just doesn't make sense. Tune the octave to a M9 and you can still set the CM3 as slow medium fast.

Unless of course one is making a subject judgement on what size they think the M3's should be. But that's not listening to the piano. That's forcing the intervals to be what you want them to be.

Is that a style of tuning? One that prioritizes interval colour over octave cleanliness?

That's the only thing that makes sense because it allows for choice instead of forcing one way of tuning onto someone else.

Example: I tune the A3A4 clean. Then I fit the progressive RBI and SBI into that best I can. I don't care if the stacked M3 are almost the same speed, or if they change a lot.

Honestly, I'm not that familiar with piano repertoire or tuning "styles" of "the greats" to be able to make an informed choice when to tune an octave less clean for the sake of matching a sound in my head. I'm doubtful there techs that do that but I sure would like to hear from one that can say, "Yes, that's exactly what I do."

Posted By: UnrightTooner

Re: Octave Sizes - 03/01/17 11:00 PM

Originally Posted by Mark Cerisano, RPT
...

I want to know why I would change the size of my A3A4 from good to not so good if I'm just tuning an octave temperament. Just by listening to some out of tune 3/4/5/6? If one has a proclivity to the sound of a certain out of tune 4th for example, ok.

...


I find there is an area, rather than a point, where an octave sounds good. There is quite a bit of "wiggle room", I would say, when expanding the temperament to make the other intervals fit better, like when the ET is less than great.

If someone doubts this, I challenge them to tune the three strings in a unison separately to the octave above or below and then listen to all 3 strings together.

For myself, a fifth has a much narrower area where it sounds right (since it is tempered, I do not use the term good). And when expanding a temperament by listening to both the 4th and the 5th I think it does become a point and I, for one, can tune a good unison by tuning each string separately.

But Mark, just because you cannot find a good reason to adjust octave width to accommodate other intervals doesn't mean others cannot, nor that their reasons are not as valid as yours.
Posted By: Rick_Parks

Re: Octave Sizes - 03/02/17 01:26 AM

Originally Posted by UnrightTooner

...But Mark, just because you cannot find a good reason to adjust octave width to accommodate other intervals doesn't mean others cannot, nor that their reasons are not as valid as yours.


I am finding that there are reasonings for just about anything to be done to an ET on this forum... Most of the people on here appear to be more interested in theory, than execution.

I do have to say though, I have learned more theory in the last week of reading certain threads- and in them I see all sorts of fatal flaws in logic.

People who say they are tuning temperaments and are able to hear what the composers of old heard as they played... That they have brought back the "color" and the original intent... Bunk!
Different days altogether--- different instruments (basic and rude), different pitch (A415; slowly increased as tension designs were improved)...

Question that doesn't perhaps belong here but:
Are you guys who advocate these endless variations of the old Temps, and theories of massive alterations to intervals thru ETA programs--- are you first setting your reference pitch to A415, adjusting the hammers to meet specs from those old world instruments...Not to mention stripping any design improvements out of the action?
Because, only then will you hear what they heard. There are "Colors" that can be truly ugly you know.

Perhaps if we did this with a piano, only then will people truly appreciate the ET with its boring rules!

I can tell you with confidence, if you could bring one of the great composers from the period of 1750-1830 and sit him/her down to a piano today they would KISS the person who allowed them to play it. And rejoice at the "color" they could create in our boring and colorless ET!

Posted By: daniokeeper

Re: Octave Sizes - 03/02/17 04:40 AM

Rick, There are multiple reasons for using UTs.

Unequal temperaments are used for novelty, the attempt to perform music with historical accuracy, or to alter the resonance/character of the piano.

UTs give the player the opportunity to explore different harmonies in the compositions he is playing.

There are also modern UTs such as EBVT3, as well as historical temperaments.

Both equal temperament and unequal temperaments have their places. String instrument players, such as guitarists, will routinely use alternative tunings and there is no controversy. Why shouldn’t pianists have the same freedom? Why impose limits on the musician?

I have customers that insist on only ET. Usually they're students and the y want their piano tuned the standard way. That's fine. I give them what they want. In fact, i always tune in ET unless the customer explicitly tells me they want to try a UT.

I also have customers that love exploring UTs. One that comes to mind is a very nice fellow who enjoys playing piano compositions by Gurdjieff-DeHartmann. He likes various meantone temperaments for this music. He dislikes well temperaments for this music. He also dislikes ET. Should I take away this option from him?

As another example, I have an elderly lady who likes playing her church hymns in a particular well tuning. Should I refuse?
Posted By: DoelKees

Re: Octave Sizes - 03/02/17 04:59 AM

Originally Posted by Rick_Parks


People who say they are tuning temperaments and are able to hear what the composers of old heard as they played... That they have brought back the "color" and the original intent... Bunk!
Different days altogether--- different instruments (basic and rude), different pitch (A415; slowly increased as tension designs were improved)...

This is utter nonsense. Pitch standards in the 18th century varied from A4=390Hz to A4=450Hz and this has nothing whatsoever to do with "improved tension designs".

Kees
Posted By: Rick_Parks

Re: Octave Sizes - 03/03/17 01:45 AM

Originally Posted by daniokeeper
Rick, There are multiple reasons for using UTs......
......As another example, I have an elderly lady who likes playing her church hymns in a particular well tuning. Should I refuse?


I don't recall every speaking against UTs. smile
I understand their place and use.

Actually what I was talking about was theoretical claims about bringing back the glorious "colors" and the emotional experiences that the composers were trying to express--- and saying that they cannot be experienced in ET, and must be experienced in some form of Meantone or Well...Yet not considering at all, when one makes such claims, that they are not reproducing any such color on our modern instruments... The way it sounded would have been completely different on such instruments as they had then. I mean, come on, the strings have changed, plate was introduced, action technological advancements all came into play with the piano since those days.
One might like the thought that they are hearing it precisely as it was meant to be by Bach or Beethoven--- but not the case.

I was also, referencing other discussions, earlier, about pure 5th theories and other such ideas...And now here, are we going to be sacrificing octaves?...
And, really I get it--- theories are all fine to have- have them-- but when people publicly insinuate that others are ignorant, or less profession, because of they disagree with or even disprove the theory- one is overstepping their place and can expect hard feelings to begin brewing toward them.

Again, IF customers want/need UTs- this was not my point-- of course you do what they need or want. smile UTs have their place.
Posted By: daniokeeper

Re: Octave Sizes - 03/03/17 02:23 AM

Rick,

No offense meant.

Usually when I hear about UTs, they are referred to as HTs.

As for historical playing, Bach's "The Well Tuned Clavier" certain seems to call for a well tuning. It also seems to call for a clavier laugh

Though a modern piano is not a fortepiano, a harpsichord, or a clavicord, a modern piano still another keyboard instrument capable of taking a well tuning.

Edit: I do agree, though. A truly historical performance should be done on instruments of the period.
Posted By: Ed Foote

Re: Octave Sizes - 03/03/17 02:49 AM

Greetings,
I don't know that Beethoven "should" be played on a well-temperament. I do know that it has a different sound in ET than in WT, but there is no way to say which is the way it "should" be heard. I have seen a lot of pianists encounter WT for the first time, and it is not uncommon for an epiphany to arise. I have often observed that his music has more emotional engagement when it is performed on a WT instead of a ET, but that is not a universal thing. The music, itself, is more harmonically complex when performed on an unequal temperament, primarily and secondarily, as there are far more harmonic relationships with a staggered series of thirds, and there is a profound introduction of texture. A bug for some, a feature for others.
Marshal McCluhan stated that "Meaning is a product of a message being received, it is not a unique quality of the message". Since the change in interval size is registered primarily in the sensual realm, how it is perceived is as subjective as individuals' sensibilities. For some listeners, regularity is important, for others, it is anathema.
Regards,
Posted By: Ed Sutton

Re: Octave Sizes - 03/03/17 06:02 PM

Two of the best aural tuners I've heard are very concerned with the fourth. David Anderson seems to have a sense of what he wants to hear, and says that when you get it, the fourths will have a similar sound over most of the piano, He's written about this in the Journal, about 10 years ago.
Another tuner I've had a chance to observe spends a careful time adjusting A4-E4-D4-A3. It's not just the octaves, it's all combinations of those notes. The thirds progress when he's done, as do the tenths, but the slow beating intervals seem more structural. He says "You can do the theoretical tests on my tunings, and they measure pretty good, but that's not how I get there," [I hope to learn more from this person, and maybe write about his approach. The result is probably close to a Perfect 12th tuning.]
I don't know the right answer. but I do know that sometimes a piano can sound so good, the whole piano can resonate wonderfully, not just with a big sound, but with a beautiful voice for playing music, and that seems to be where to look for the answers.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/03/17 07:34 PM

I'm looking for that as well.

So far I get good results by spending a lot of time on A3A4. Using checks, the precision is much higher than just tuning the octave without checks. I also choose the size depending on the Inharmonicity. I use a method of tuning a pure 4:2 and measuring the 6:3. Sometimes it's pure. Sometimes it's narrow, very narrow, or even wide. I've found some empirical sizes that sound really good within a small window, so I use them and don't want to or need to change their size. But I'm still trying to figure out why someone would want to make an octave sound not as good. The size of the octave for me sets up the stretch with pure 11/12/19/22/pure 8:6 P4. If I start messing with the octave, these larger intervals suffer.

I ask because I'm always looking for better ways to tune.
Posted By: Gadzar

Re: Octave Sizes - 03/03/17 08:21 PM

You have been given half a dozen or more answers to your question.

All of them talk about the need of compromising. Compromising the "purity of A3A4" to gain in other important aspects of piano tuning, but you seem to not want to accept their validity.

In that sense you are disqualifying us and dismissing us all as piano tuners.

All of us, who have answered your question, have given our reasons and arguments to support our point of view.

Can you tell us the reasons you have to ignore all the facts and considerations we have exposed and you cling to favor a unique isolated octave in the middle of the keyboard? Why not F3F4? Or C4C5? Or whatever other octave in the keyboard?

P.S. Question: no one person among the posters here have seconded you, doesn't this tell you something?
Posted By: UnrightTooner

Re: Octave Sizes - 03/03/17 08:51 PM

Originally Posted by Mark Cerisano, RPT
...

The size of the octave for me sets up the stretch with pure 11/12/19/22/pure 8:6 P4. If I start messing with the octave, these larger intervals suffer.

...


Are you saying you can tune a piano with pure 11th, 12th, 19th, 22nd and 8:6 4ths? That all of these intervals are aurally beatless?

That's FANTASTIC! Meaning it must be a fantasy.

Posted By: Toni Goldener

Re: Octave Sizes - 03/04/17 10:03 AM

I used to start with A4 and then tune D4 first, so it sounds best to me. Then I tune A3 to D4 as I prefer it. I now listen to the resulting octave A3 - A4. If it pleases me, I put in E4. Sometimes it needs minor corrections, mostly it is okay. So the octave is established.
Posted By: UnrightTooner

Re: Octave Sizes - 03/04/17 10:53 AM

Originally Posted by TheTuner
I used to start with A4 and then tune D4 first, so it sounds best to me. Then I tune A3 to D4 as I prefer it. I now listen to the resulting octave A3 - A4. If it pleases me, I put in E4. Sometimes it needs minor corrections, mostly it is okay. So the octave is established.


YES!

There is much to be said for forming the octaves with other intervals and using the octave as a check. Octaves can be awfully deceiving. You can think because it sounds good, that it must be best. Also when expanding a lopsided temperament, you may not notice corrections that can be made. But by tuning other intervals first, either when setting the temperament, or when expanding it, much more can be understood about the relationships of ALL intervals on THAT piano. 4ths and 5ths, I think, are the best intervals for such work because they are the ones that are closest to being pure.
Posted By: Gadzar

Re: Octave Sizes - 03/04/17 12:03 PM

Exact. All this is due to inharmonicity.

Each partial has its own individual iH and it may be lower or higher than expected. We can not know in advance where a specific partial is located. It is until we hear an interval that uses this partial that we can know where it is and how it sounds and how it lines with the other tuned notes. For example when tuning an octave we are hearing at partials 6, 4 and 2 of the lower note but we have no idea of where partials 5 and 3 are, these partials will define how the third and the fifth above will sound, if these notes are already tuned we can have a nice octave but a bad third or a bad fifth so the octave may need to be tweaked to have a better third or fifth.

In fact we do this all the time when expanding up and down the temperament: we tune the note as a pure souding octave then we hear at the fifth and adjust, then at the fourth and adjust, then at the tenth etc...

The octave A3A4 is not different from the others in that respect, so it must be checked and adjusted in the same way, hearing at the fith, fourth, etc...
Posted By: Rick_Parks

Re: Octave Sizes - 03/05/17 12:51 AM

Originally Posted by Gadzar
...In that sense you are disqualifying us and dismissing us all as piano tuners.
...Can you tell us the reasons you have to ignore all the facts and considerations we have exposed and you cling to favor a unique isolated octave in the middle of the keyboard?....

...P.S. Question: no one person among the posters here have seconded you, doesn't this tell you something?


Rafael,
You are demonstrating now, repeatedly a rude behavior that is going to get others rather angry with you...It's fine to disagree with people, even be sarcastic at times-- but you seem to want to continually insinuate that others (who happen to not agree with you) are either not professional or ignorant. A very bad approach as a professional.


As far as no one chiming in for Mark on his point-- I thought I had when I mentioned the sacrificing of octaves question... I do not at all support anyone sacrificing a "beatless" octave--- and I'm not going to stop calling it what it has been called for a long time simply because you do not like the term, or think it should be termed according to theory. smile

And, when you say that Mark is "disqualifying" you and "dismissing" you-- he did no such thing... He simply questions your reasoning, and does not take them at face value. I call that intelligent.
He has not once questioned your professionalism or knowledge, that I've seen. smile

Posted By: Beemer

Re: Octave Sizes - 03/05/17 08:49 AM

Mark,
I'm not qualified to participate in this thread, but as an aside I would like a thought of mine clarified.

The Railsback curve as shown on my ETD appears to be straight across A3-A4. However that is not the case as illustrated in the attached graphic.

https://en.m.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve

So then, if inharmonicity exists in A3-A4, and is assymetrical, why would adjusting A3-A4 not be beneficial to producing a better tuning?

Ian
Posted By: UnrightTooner

Re: Octave Sizes - 03/05/17 10:22 AM

Originally Posted by Rick_Parks
Originally Posted by Gadzar
...In that sense you are disqualifying us and dismissing us all as piano tuners.
...Can you tell us the reasons you have to ignore all the facts and considerations we have exposed and you cling to favor a unique isolated octave in the middle of the keyboard?....

...P.S. Question: no one person among the posters here have seconded you, doesn't this tell you something?


Rafael,
You are demonstrating now, repeatedly a rude behavior that is going to get others rather angry with you...It's fine to disagree with people, even be sarcastic at times-- but you seem to want to continually insinuate that others (who happen to not agree with you) are either not professional or ignorant. A very bad approach as a professional.


As far as no one chiming in for Mark on his point-- I thought I had when I mentioned the sacrificing of octaves question... I do not at all support anyone sacrificing a "beatless" octave--- and I'm not going to stop calling it what it has been called for a long time simply because you do not like the term, or think it should be termed according to theory. smile

And, when you say that Mark is "disqualifying" you and "dismissing" you-- he did no such thing... He simply questions your reasoning, and does not take them at face value. I call that intelligent.
He has not once questioned your professionalism or knowledge, that I've seen. smile



Rick, yeah, even I agree that Rafael crossed a line by being high-handed. It is "playing the man instead of the ball." I see he edited his post.

I think Rafael sees the tuners in this world as part of a somewhat heroic fellowship with an unwritten code requiring us to aspire to be worthy of all the greatest challenges of tuning. If this was the case, we would agree on certain basic tenants about tuning. I am sure it is frustrating for Rafael that this is not the case.

Myself, I find it frustrating when it is impossible to communicate when the verbiage used muddles a discussion. I sure am glad that is not happening in this Topic. smile

Posted By: Rick_Parks

Re: Octave Sizes - 03/05/17 06:34 PM

Originally Posted by Beemer
Mark,
....So then, if inharmonicity exists in A3-A4, and is assymetrical, why would adjusting A3-A4 not be beneficial to producing a better tuning?
Ian


I think an answer to this might be to ask another question:

Is the aural tuner doing anything different than what you guys are suggesting with the tuning process?... I mean, we all have our checks as we set temp and go about tuning...
NOW-- the octave must be beatless- and yes, Rafael (Gadzar) is absolutely correct in that there is a small space to play with there in the area of what is referred to as "beatless" (to toy with the other intervals before one perceives a beat in the octave)...

I don't know, but perhaps our debate here is one of perception vs machine math? BUT- if not--
IF it is a matter of a perceived beat being introduced into the temperament octave in order to fix one of the other (already beating) interval-- well then, I think that is against all basic approach to change the octave THAT MUCH!

*Was looking for a quote from an author on tuning...But, for some reason cannot find it--- she was asked what the difference was between a regular fine tuning and a concert tuning, they said her reply was simple-- "Octaves and Unisons".
I think the discussions have already been covered many times on this forum, that SOLID ("Beatless") Octaves cannot be sacrificed and it be considered possible to come away with an acceptable situation.

What is perceived is different than theoretical math produced by the machine-- if the math of an unperceivable space for adjustment is what is being debated here, I want to drop out-because there is no end to such an argument.
Since, you cannot prove something that is not perceptible smile
That must simply require faith in the unseen by the person arguing it.
Posted By: Rick_Parks

Re: Octave Sizes - 03/05/17 06:36 PM

Originally Posted by UnrightTooner
Rick, yeah, even I agree that Rafael crossed a line by being high-handed. It is "playing the man instead of the ball." I see he edited his post.......
......Myself, I find it frustrating when it is impossible to communicate when the verbiage used muddles a discussion. I sure am glad that is not happening in this Topic. smile


He edited his last post, not the one I'm speaking of (on page 1 at the bottom)... Anyway, that doesn't matter, I don't expect an edit. I think Mark, and those on our side of the argument, can cope without that LOL... Besides, we all speak out of line at times- I was just trying to point out it is unfair and puts the other person in the spot of either having to defend themselves, or not answering at all (a very irritating situation- and frustrates open discussion).

And I think it would benefit all to remember that we all are ignorant of something in this field- let's face that fact, and continue our learning... Professionals can be ignorant (not that I am saying anyone here is)...
Not knowing, and seeking the answer, is perhaps one of the most humbling aspects to being a Pro. smile

BUT- all that said, I think that Mark and I are right. LOL

Posted By: Gadzar

Re: Octave Sizes - 03/06/17 12:16 AM

I am done, this will be my last post in this thread.


An octave can not be tuned beatless!

Nobody can deny the existence of several pairs of partials beating in the octave, nor the fact that they beat all at different rates, there is no way to tune them all beatless. This is not the way i see it, this is not my opinion, this is a fact. A fact that has been proved. A fact that has been and can be measured.

So, octaves should be tempered. A3A4 is an octave exactly the same as any other octave in the piano and there is no reason to treat it differently. It must be tuned to fit in the sequence of all other octaves and its size must fit in a balanced compromise with all other intervals in the tuning.

Rick,

Before blaming me, you should make a little search on PW to find out how Mark has treated me in the past.

Posted By: BDB

Re: Octave Sizes - 03/06/17 01:00 AM

Originally Posted by Gadzar
I am done, this will be my last post in this thread.


An octave can not be tuned beatless!

Nobody can deny the existence of several pairs of partials beating in the octave, nor the fact that they beat all at different rates, there is no way to tune them all beatless. This is not the way i see it, this is not my opinion, this is a fact. A fact that has been proved. A fact that has been and can be measured.

So, octaves should be tempered. A3A4 is an octave exactly the same as any other octave in the piano and there is no reason to treat it differently. It must be tuned to fit in the sequence of all other octaves and its size must fit in a balanced compromise with all other intervals in the tuning.

Rick,

Before blaming me, you should make a little search on PW to find out how Mark has treated me in the past.



If you want to think that octaves cannot be tuned beatless, go ahead. Personally, I think that is an excuse for not learning how to tune octaves properly. Octaves can usually be tuned beatless, and with extra checks, they can be tuned better than that.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/06/17 01:44 AM

BDB, I am interested. Can you explain what you mean by "better than beatless"? Especially since you mention "with extra checks." I would like to know what they are, please.

Regards,
Posted By: Kent Swafford

Re: Octave Sizes - 03/06/17 02:24 AM

Originally Posted by Mark Cerisano, RPT
Ed,

I am always looking for the musical sound in the interval. But I also analize what the result is, so I can be more efficient, chose the most problem best size, modify if necessary, and move on.

The question is, having determined the best sounding A3A4, (my first octave tuned), why would I want to change it, barring drift?


"Analize"?

I think this must be a Freudian slip particularly common to piano techs! smile
Posted By: Mark Cerisano

Re: Octave Sizes - 03/06/17 02:32 AM

Originally Posted by Kent Swafford
Originally Posted by Mark Cerisano, RPT
Ed,

I am always looking for the musical sound in the interval. But I also analize what the result is, so I can be more efficient, chose the most problem best size, modify if necessary, and move on.

The question is, having determined the best sounding A3A4, (my first octave tuned), why would I want to change it, barring drift?


"Analize"?

I think this must be a Freudian slip particularly common to piano techs! smile


Ha ha ha. Well, some people on here do seem to think I am a bit too... :-)
Posted By: Kent Swafford

Re: Octave Sizes - 03/06/17 02:52 AM

Originally Posted by Mark Cerisano, RPT
I have read recently in the forum, but at other times as well, and from different people, that tuning the temperament octave somehow has something to do with the actual intervals within the temperament octave.

I have read things like:

"If you tune the octave too wide/narrow, the intervals won't fit."

And:

"If you tune the octave to one size it may have to be changed."

I have never experienced this and I'm wondering if someone can logically and clearly explain why.

Here's how I see it:

The octave can be tuned to any size and the intervals can be fit into any octave. It's like having 13 dimes. Two are placed on a table about 1 foot apart, and then the remaining 11 are fit between so they are all the same distance apart. It is possible to set the first two any distance apart and end up with the same result: equi-distant dimes.

The only empirical and musical judgement to be made is what does the octave sound like. So the logic is, if the octave is the only interval that can be judged, it should be tuned as accurately as possible from the beginning.

How do we make a judgment on the "correctness" of a bunch of intervals that are all out-of-tune? The 3/4/5/6 all beat. The octave is the only interval within the temperament that can be tuned "beatless".




This is a fascinating thread. It is amazing (at least to me) that there is so much common ground here at the same time that there is such strong disagreement about some relatively small details.

Mark, I like your lineup of dimes. I myself usually use as a model one of those expandable cupholders, which is inherently equal temperament regardless of how expanded or contracted it is.

You write, "How do we make a judgment on the "correctness" of a bunch of intervals that are all out-of-tune? The 3/4/5/6 all beat."

For me, the model of equal temperament is the set of relative beat rates as determined mathematically with zero inharmonicity. This model has been known longer than inharmonicity has been known, as far as I can tell. This means early tuners of equal temperament tuned using the model of ET without taking into consideration inharmonicity. To me, this means that we should do the same. Tune the model, and ignore inharmonicity to the extent that this is possible.

Inharmonicity will mess things up of course, but we will tune beatless octaves anyway. smile

Then, the correctness of the tempered intervals is determined by how well the correct pattern of beat rates is maintained. (An example of such a pattern would be tuning F3-D4 about 1 bps faster than F3-A3, and maintaining this pattern through the scale, appropriately progressed.)

There is no correct beat rate of any interval (except perhaps the unison) in isolation; in this system whole groups of intervals must be considered for whether they are forming the proper beat rate relationship among the various intervals. (An example of proper relationship would be tuning the F3-A4 faster than the F3-A3 if stretching the octave.)

I agree that equal temperament can be tuned within any size of stretched octave. In fact there is a system of "modern equal temperaments" which tightly controls different widths of the octave and tunes ET accordingly. These different widths are codified by the different pattern of beat rates that they form.

An extensive set of Piano Technician Journal articles may begin later this year on these Twenty-first Century Tuning Styles.




Posted By: Rick_Parks

Re: Octave Sizes - 03/06/17 02:59 AM

Originally Posted by Gadzar
I am done, this will be my last post in this thread.


An octave can not be tuned beatless!

Nobody can deny the existence of several pairs of partials beating in the octave, nor the fact that they beat all at different rates, there is no way to tune them all beatless. This is not the way i see it, this is not my opinion, this is a fact. A fact that has been proved. A fact that has been and can be measured.

So, octaves should be tempered. A3A4 is an octave exactly the same as any other octave in the piano and there is no reason to treat it differently. It must be tuned to fit in the sequence of all other octaves and its size must fit in a balanced compromise with all other intervals in the tuning.

Rick,

Before blaming me, you should make a little search on PW to find out how Mark has treated me in the past.


Rafael,
I don't particularly care to go beyond what I have seen here at this time (and in the recent days that I have returned to the forum)... If a person is unfair, I say it-- I'll do the same if I see Mark do that smile
I am not, nor do I want to be, the policeman of the forum LOL smile
But, it was you this time (and it was done in front of me)- so I point it out. Simple as that.

I do think it is possible that we can all disagree while still considering each other professionals. Even while expressing exasperation, humorous wit, and even sarcasm toward each other smile I like to be sarcastic.

You say this is your last post on this particular thread, and you insist octaves cannot be tuned beatless... The partials are all there, I agree - (no one here is denying partials, that I see)- but the partials have their own roles, which are secondary (in my opinion) to our obligation of keeping the temperament octave(s) solid - see I said 'solid' smile No need to be upset now cool

But, again, I will ask for clarification from people (ANYONE)-- IS IT being said (or insinuated) here that we should purposefully introduce beats into the temperament octave for the sake of other interval to be improved-- (sure sounds like it to me)? Or, is this merely theoretical debate again- where everyone is saying the same thing in different ways (the realists and the theorists see the same thing and explain it completely different)?

Posted By: Rick_Parks

Re: Octave Sizes - 03/06/17 03:29 AM

Originally Posted by Kent Swafford
......For me, the model of equal temperament is the set of relative beat rates as determined mathematically with zero inharmonicity. This model has been known longer than inharmonicity has been known, as far as I can tell. This means early tuners of equal temperament tuned using the model of ET without taking into consideration inharmonicity. To me, this means that we should do the same. Tune the model, and ignore inharmonicity to the extent that this is possible.
Inharmonicity will mess things up of course, but we will tune beatless octaves anyway. smile

Then, the correctness of the tempered intervals is determined by how well the correct pattern of beat rates is maintained. (An example of such a pattern would be tuning F3-D4 about 1 bps faster than F3-A3, and maintaining this pattern through the scale, appropriately progressed.)


thumb thumb thumb thumb
I really like it when someone shows up and says things I agree with completely smile


Originally Posted by Kent Swafford

There is no correct beat rate of any interval (except perhaps the unison) in isolation; in this system whole groups of intervals must be considered for whether they are forming the proper beat rate relationship among the various intervals. (An example of proper relationship would be tuning the F3-A4 faster than the F3-A3 if stretching the octave.)

Now THIS man I can understand!!!
Keep talking Kent! laugh


Originally Posted by Kent Swafford

I agree that equal temperament can be tuned within any size of stretched octave...

But, what does the whole end result sound like if one stretches the octave so as to favor a particular interval that they deem more preferable... Are we to begin changing the norm (the obligatory "equal temperament" (equally borrowing and adjusting, for overall results) for the sake of a preference to be served (for says pure 5ths, or really good thirds)?...
I think this is the point over which people are getting knotted up here.

Posted By: DoelKees

Re: Octave Sizes - 03/06/17 03:59 AM

Originally Posted by BDB
Originally Posted by Gadzar
I am done, this will be my last post in this thread.


An octave can not be tuned beatless!

Nobody can deny the existence of several pairs of partials beating in the octave, nor the fact that they beat all at different rates, there is no way to tune them all beatless. This is not the way i see it, this is not my opinion, this is a fact. A fact that has been proved. A fact that has been and can be measured.

So, octaves should be tempered. A3A4 is an octave exactly the same as any other octave in the piano and there is no reason to treat it differently. It must be tuned to fit in the sequence of all other octaves and its size must fit in a balanced compromise with all other intervals in the tuning.

Rick,

Before blaming me, you should make a little search on PW to find out how Mark has treated me in the past.



If you want to think that octaves cannot be tuned beatless, go ahead. Personally, I think that is an excuse for not learning how to tune octaves properly. Octaves can usually be tuned beatless, and with extra checks, they can be tuned better than that.

Generally octaves cannot be tuned beatless, let alone "even better than that", as it is generally impossible to line up the 2:1 partials as well as the 4:2 partials as well as the 6:3 partials and so on if you go down the scale.

Only when very specific conditions are satisfied by the inharmonicity curve (and on most pianos they are not) can all the audible partials be matched up.

Of course it is possible to tune octaves that sound beatless to a less sensitive ear, but have an audible beat for a more sensitive ear. One may ask who is the one that has some learning to do in that case.

Kees
Posted By: BDB

Re: Octave Sizes - 03/06/17 04:09 AM

Originally Posted by Mark Cerisano, RPT
BDB, I am interested. Can you explain what you mean by "better than beatless"? Especially since you mention "with extra checks." I would like to know what they are, please.

Regards,


Well, as I explained elsewhere , beats are approximate, and they are influenced by other things in the piano. In particular, if the beat speed is slower than the decay speed of the note, you cannot distinguish the beat from the decay.

However, if you check with other intervals, those beat faster, so you can narrow down the accuracy of the octave much better than you can just by tuning the octaves so they no longer beat. Those are the extra checks.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/06/17 05:46 AM

Originally Posted by "Kees"

Generally octaves cannot be tuned beatless, let alone "even better than that", as it is generally impossible to line up the 2:1 partials as well as the 4:2 partials as well as the 6:3 partials and so on if you go down the scale.

Only when very specific conditions are satisfied by the inharmonicity curve (and on most pianos they are not) can all the audible partials be matched up.

Of course it is possible to tune octaves that sound beatless to a less sensitive ear, but have an audible beat for a more sensitive ear. One may ask who is the one that has some learning to do in that case.

Hi Kees,

We have discussed this in other threads; the idea of measuring aurally the piano, and then deciding on a particular octave size.

The majority of pianos favour the, I can't remember what you called it, splitting the 4:2/6:3? Something like that. Meaning simply tuning exactly between the 4:2 and the 6:3.

Here are theoretical explanations as to why these octaves "seem" beatless when they may not be, mathematically:

1) The 4:2 and the 6:3 may cancel each other out.
2) If the 4:2 and 6:3 cancel each other out, perhaps the 2:1 and the 8:4 can as well.

Also, there exists the real situation where the 4:2 and the 6:3 can actually both be pure at the same time. In this situation, which I find often in nice pianos, the 8:4 and the 2:1 will be VERY close to pure.

The proof of this is in the fact that we find pianos that can be tuned as a pure 4:2, but the 6:3 tests as wide, instead of narrow like most pianos do when there is a perceivable difference.

This wide and narrow 6:3 are at opposite ends of a spectrum, and within that spectrum lies the pure 6:3. So, the presence of pianos with wide 6:3 and pure 4:2 octaves, and other pianos with narrow 6:3 and pure 4:2 octaves, proves that some pianos can have a pure 4:2/pure 6:3 mathematically!
Posted By: DoelKees

Re: Octave Sizes - 03/06/17 06:15 AM

Originally Posted by Mark Cerisano, RPT
Originally Posted by "Kees"

Generally octaves cannot be tuned beatless, let alone "even better than that", as it is generally impossible to line up the 2:1 partials as well as the 4:2 partials as well as the 6:3 partials and so on if you go down the scale.

Only when very specific conditions are satisfied by the inharmonicity curve (and on most pianos they are not) can all the audible partials be matched up.

Of course it is possible to tune octaves that sound beatless to a less sensitive ear, but have an audible beat for a more sensitive ear. One may ask who is the one that has some learning to do in that case.

Hi Kees,

We have discussed this in other threads; the idea of measuring aurally the piano, and then deciding on a particular octave size.

The majority of pianos favour the, I can't remember what you called it, splitting the 4:2/6:3? Something like that. Meaning simply tuning exactly between the 4:2 and the 6:3.

Here are theoretical explanations as to why these octaves "seem" beatless when they may not be, mathematically:

1) The 4:2 and the 6:3 may cancel each other out.
2) If the 4:2 and 6:3 cancel each other out, perhaps the 2:1 and the 8:4 can as well.

Also, there exists the real situation where the 4:2 and the 6:3 can actually both be pure at the same time. In this situation, which I find often in nice pianos, the 8:4 and the 2:1 will be VERY close to pure.

The proof of this is in the fact that we find pianos that can be tuned as a pure 4:2, but the 6:3 tests as wide, instead of narrow like most pianos do when there is a perceivable difference.

This wide and narrow 6:3 are at opposite ends of a spectrum, and within that spectrum lies the pure 6:3. So, the presence of pianos with wide 6:3 and pure 4:2 octaves, and other pianos with narrow 6:3 and pure 4:2 octaves, proves that some pianos can have a pure 4:2/pure 6:3 mathematically!

I think equal beating 4:2/6:3 is the term you're looking for.

However equal beating is not the same as not beating and IMHO there is no such thing as "beat cancellation".

While it's theoretically possible to have a pure octave at 4:2 and 6:3 I've never seen evidence that such a thing exists. I've never seen a piano which has 6:3 wide while 4:2 pure either, so even if they exist the exceptions you listed which I've called "very specific conditions" are certainly not the norm.

Kees
Posted By: Chris Storch

Re: Octave Sizes - 03/06/17 01:24 PM

Originally Posted by Mark Cerisano, RPT
Also, there exists the real situation where the 4:2 and the 6:3 can actually both be pure at the same time. In this situation, which I find often in nice pianos, the 8:4 and the 2:1 will be VERY close to pure.

Mark,

You've made this assertion several times now, in this thread and in others. This time, you indicate that you come across this situation "often".

This is baffling to me, because my experience is that I can almost always make a distinction between the 4:2 and 6:3 octave using the tests. I cannot ever recall a time that I couldn't make a distinction between the two octave types - even as a student tuner with naïve aural skills. Even on the finest pianos with low inharmonicity.

I'm with Kees on this. An octave that is simultanously beatless at the 4:2 and 6:3 partial interactions almost never happens in my experience. (When I tune aurally, I listen to single strings. Open unison tuning just muddies the waters and makes everything much more difficult to listen to.)

Makes me wonder what we're each hearing. Are you listening to single strings, or open unisons when you make these assessments of octaves?
Posted By: Mark Cerisano

Re: Octave Sizes - 03/06/17 01:51 PM

Hi Chris,

Maybe you are right. I have noticed what I can only define as "Aural Illusion". Much like an optical illusion where we think we see something that is not there.

Try this:
Play the contiguous M3's. Listen to the bottom and top one, then the three together.

I.e.
Play F3A3-C#4F4
then F3A3-A3C#4-C#4F4

I sometimes get the sensation that F3A3-C#4F4 is a lot closer when I play F3A3-A3C#4-C#4F4, than when I play F3A3-C#4F4. Sometimes I can't tell them apart.

I'm working on the math and it is not easy.

As for finding reversed octave Kees, have you been looking for them? I look for them every time I tune. I've recorded a few. I'll dig them up. If I can prove to you that reversed octaves exist, does that prove that pure 4:2/pure 6:3 can exist?

For the purpose of defining pure 4:2/pure 6:3 aurally, we only need the tests to be within 2-3%.

Found the recording. Here it is:

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)

Here is a recording of the filtered beats. I have often posted that bandpassing beat rates is a great tool. It helped me just now not to be so arrogant. (I thought the 4:2 was pure when listening to the unfiltered recording)

https://www.dropbox.com/s/xq89szaznszn0qw/A%20Filtered%20Reversed%20F3F4%20Octave.mp3?dl=0
Posted By: UnrightTooner

Re: Octave Sizes - 03/06/17 03:33 PM

Originally Posted by Rick_Parks
...

But, again, I will ask for clarification from people (ANYONE)-- IS IT being said (or insinuated) here that we should purposefully introduce beats into the temperament octave for the sake of other interval to be improved-- (sure sounds like it to me)? Or, is this merely theoretical debate again- where everyone is saying the same thing in different ways (the realists and the theorists see the same thing and explain it completely different)?



There are times I will purposely introduce a beat into octaves in the temperament, and I purposely allow beating in octaves outside the temperament.

The times I purposely introduce a beat into octaves in the temperament is in small pianos with a, um, challenging sound in their lower unwound strings. A fifth can sound really horrid and I find they sound better if the octave is narrow of 4:2 and closer to 2:1. So if you listen you can hear a slow beat at the 4:2 partial match in the middle octaves.

I usually allow beating in octaves outside the temperament in order to have the piano sound more melodically in tune, like when playing an arpeggio on one end of the piano and then playing the root note at the other end. For this to sound melodically in tune, I find it necessary to stretch the octaves more than inharmonicity requires for the piano to be harmonically in tune. In the middle of the piano the octaves don't seem to beat, but may change their tonal quality while decaying, much like an almost perfect unison might. This happens more with larger pianos. In the upper treble, yes, there is a beat if you specifically listen for it. And in the bass, well, on most pianos you can hear just about anything you want to down there...

Using the 12ths helps determine and control the amount the octaves are stretched in both situations.

As far as the theory, I find it agrees with what I hear.

Posted By: P W Grey

Re: Octave Sizes - 03/06/17 04:16 PM

Having followed this thread from the start it appears to me that there is confusion over basically two things:

1) The SCIENCE of what we do in ET, and

2) The ART of what we do in ET

My explanation:

The science behind ET is clear and well accepted as an EQUAL division of the scale. We have no choices here...

It is either equal or it is not equal...period.

And, whether we do it with an ETD or aurally, or a combination is irrelevant as long as the result is EQUAL.

The philosophy behind ET is to make everything consistent and "the same" so that any and all music can be played in any and all keys EQUALLY. Same basic tempering amount for like intervals, same basic tonality or coloration in each key, consistency from key to key, equally "pleasant" in all keys...etc.

Disclaimer: I'm limiting this to decent instruments that generally follow the "rules" and are musically tuneable...not the "dogs" that are impossible to do anything with.


The ART of what we do starts when we are able to make choices, the first of which is octave width. Everyone has an opinion (based in their experience) as to what constitutes the "best" octave width. Whether we choose to isolate the 2:1, the 4:2, the 6:3, the 8:4 or somewhere in between any of these has nothing to do with ET since we can tune true ET using ANY of these octave widths. But this is where the ART begins since we are making these decisions based on what we are hearing on this particular instrument at any given time and circumstance, and the goal is to make it sound it's best.

The ART continues as we move outside the temperament and expand to the rest of the piano. We may CHOOSE to keep the exact same octave width throughout, OR we may CHOOSE to change it as we go. Why? Because we are determining that the instrument sounds better when we do this. But we do so with due regard for our initial equal tempering of the scale so that everything is still consistent throughout the piano. (By consistent I mean no abrupt changes, but rather smooth).

There is a range of choices within which we normally need to restrict ourselves, otherwise we run the risk of creating something considered non-musical (outside the generally accepted norm for musicality). But within this range, the choice is ours to make, and that is part of the ART of what we do regularly.

Finally, we all know that it is more important to concentrate on clean unisons. If I tuned a piano concentrating on 4:2 octaves in the midrange, and someone else then came along and tuned the same piano but concentrated on 6:3 octaves in the midrange, but in each case if the unisons were clean and all intervals were consistent the piano AS A WHOLE would sound very good musically. No one could validly criticize it in either case because it is within the bounds of the SCIENCE of ET.

If you ask ten competent artists to paint a specific picture with certain details in it, you will get ten different renditions of the picture. The specified details will be there and recognizable, but each one will be a little different since they are permitted to exercise their artistic license while preserving the important details.

We get to do the same sort of thing. But arguing about what is the best octave width or whether it is or is not beatless at any particular partial level is probably not terribly constructive since it's all a matter of artistic/musical opinion, and will be judged as a whole (the whole tuning).

The bottom line IN MY OPINION is that there is no way to define the BEST octave width. Experience teaches us what is better or best under the specific circumstances.

Not looking to ruffle any feathers here. Just an observation (and opinion).

Pwg
Posted By: Kent Swafford

Re: Octave Sizes - 03/06/17 04:34 PM

Rick says:

"I really like it when someone shows up and says things I agree with completely."

I am quite sure I will say something you disagree with, probably sooner rather than later!

Rick says:

"But, what does the whole end result sound like if one stretches the octave so as to favor a particular interval that they deem more preferable... Are we to begin changing the norm (the obligatory "equal temperament" (equally borrowing and adjusting, for overall results) for the sake of a preference to be served (for says pure 5ths, or really good thirds)?... I think this is the point over which people are getting knotted up here."

This is a very difficult question to answer. I come at this from a wholly different point of view. I reject the notion that specified interval widths are desirable or undesirable, up to a point. I doubt that overall contracted octaves can be desirable; I doubt that expanded perfect fifths can be desirable.

The important thing is not which individual interval widths are most desirable (the biggest example being the "sacrosanct" beatless octave), but rather the important thing is how the overall tuning sounds when notes and intervals are combined in actual music.

For nearly a decade now, I have made it my business to tune different widths of equal temperament, and to do so in coherent and consistent fashion throughout the entire scale of the piano being tuned. If one tunes a wide octave, then in the equal temperament within that wide octave, _all_ of the intervals will be uniformly wider if ET is to be maintained.

I have recently tuned a Bösendorfer Imperial in pure 5th ET. The point isn't that individual 5ths sound good this way, but rather, a wide tuning of a low inharmonicity B'dorf' helps to establish the stretch in the high treble that is needed to satisfy our sense of high treble pitch at the same time that ET is coherently maintained through the scale.

Pure 12th ET, overall, makes the sound of many pianos sound coherent and "pure". It is not that the 12ths themselves sound good in this tuning; it is that the whole tuning sounds good.

Among electronic tuning devices, OnlyPure is still in development and working great these days tuning pure 12th ET, the default tuning in iRCT is now a beautiful version of pure 12th ET, and Verituner is currently showing promise as a device that can coherently tune many widths of ET including pure octave, pure 12th, pure 5th and widths in-between...

Posted By: Kent Swafford

Re: Octave Sizes - 03/06/17 04:48 PM

Peter, great post. Two comments:

I have greatly expanded the number of instruments that I can coherently tune in recent years; some "dogs" can actually be tuned well using the techniques of tuning without regard to inharmonicity and maintaining one width of ET throughout a scale.

Also, I downplay the change in partials tuned through the scale on given intervals. Rather than tune 4:2 versus 6:3 versus 12:6 and all the rest of the octave relationships, I check the "n:1" intervals for each note. That is, I check how each note sounds with the octave, the 12th (3:1), double octave (4:1), the 19th (6:1) and triple octave (8:1). Great compromises can often be made.

(Note that "compromise" is not a dirty word for me!)
Posted By: Mark Cerisano

Re: Octave Sizes - 03/06/17 05:09 PM

Nice post Kent,

The purpose of this thread is exactly what you state. I look for a method of tuning that produces a unified sound over the whole piano. It starts with the midrange octaves and produces the pure 11/12/19/22 I referred to earlier. (To be clear, I should say has the goal of pure 11/12/19/22, because purity is elusive.)

But the method requires the midrange octaves to be within a certain size; no beating. Within a pure 4:2 and a equal bearing 4:2/6:3.

Also, my focus is on finding a method that reduces the amount of tweaking that is implied by a method that allows one to, or even expects one to change the size of a good sounding octave.

And let's be clear here. I'm not talking about pianos that are poorly scaled, ones that need us to produce these bad sounding octaves in order to reduce the even worse sounding fourths and fifths that are present across the break.
Posted By: P W Grey

Re: Octave Sizes - 03/06/17 05:26 PM

Yes Kent, full agreement there. "Compromise" is a necessity since we are dealing with already compromised instruments to one degree or another. Even the best have idiosyncrasies that present themselves requiring us to make certain alterations in the interest of great musicality.

One area I have not spent much time on is using the 12th, so I am definitely interested in adding this to my arsenal of tests and checks. One of these days I'll experience Tunic Only-Pure and see what I think. I'd like to tune it aurally. Maybe you can help.

Actually somebody (I'm thinking it was Mark C., maybe Jeff D.) posted a proof of the 12th somewhere around here. Can't put my finger on it at the moment...help?

Pwg
Posted By: Kent Swafford

Re: Octave Sizes - 03/06/17 05:52 PM

I never know what people mean by poorly scaled pianos, given that every piano has scaling irregularities. Nor do I know how much compromise a tuning can have before someone will describe it as awful.

Taming the Wild Spinet (a playlist of 6 YouTube videos):

http://tinyurl.com/zcnqrkh
Posted By: UnrightTooner

Re: Octave Sizes - 03/06/17 06:35 PM

Originally Posted by P W Grey
...

Actually somebody (I'm thinking it was Mark C., maybe Jeff D.) posted a proof of the 12th somewhere around here. Can't put my finger on it at the moment...help?

Pwg


The RBI test for a pure 12th is the M6-M17 test. For example, when the F2-D3 M6 beats at the same rate as the F2-A4 17th, then the D3-A4 P12 is pure.
Posted By: P W Grey

Re: Octave Sizes - 03/06/17 07:19 PM

Thanks Jeff!

Pwg
Posted By: Rick_Parks

Re: Octave Sizes - 03/07/17 01:06 AM

Originally Posted by Kent Swafford
Peter, great post. Two comments......
......I check the "n:1" intervals for each note. That is, I check how each note sounds with the octave, the 12th (3:1), double octave (4:1), the 19th (6:1) and triple octave (8:1). Great compromises can often be made.
(Note that "compromise" is not a dirty word for me!)


This is basically the same checks I run up and down the scale as I go... I would think all are running these checks as we tune aurally- aren't we?!?

"Compromise" is not a dirty word for anyone in here I don't think- except, it seems, for these fast-beating-interval-people who seem to hold a specific interval as not being subject to compromise laugh (I of course am not including my octaves as an interval at this moment; but will from this point forward in the post crazy ).

I do hold the octave(s) (doubles in the extreme treble) as the most important of all the intervals smile - to try to be as close as possible to "pure" ( I use to use the term beatless, until last night- lol ).

"Sacrosanct"? Maybe.
I know some in here definitely hold "pure 5ths", and even "pure 12th" in this way... But, I just cannot see purposefully fouling up an octave (in the middle especially!-- ie. temperament) in order to specifically bring out some interval that is beating much faster... I mean, small compromises are one thing-- but this has not been the talk I've been hearing going around.

And, yes, I do think octaves are to be looked upon as more sacred than the other intervals... They should be rated a close 2nd to unisons (in my opinion). Fifths and fourths are next in line. With me, it's pretty simple: the faster the beat the more I would allow for myself to stuff the remaining math under the carpet. Some interval(s) have got to suffer somewhere to get the job done after all.

I do hold to a thought that most people (excluding tuners and classical artists) are not going to perceive whether a third- (or an even faster beating interval)- is beating slightly faster or slower than it should from its pure state... And of course- much less of the compromise you mention (which again, we are all doing, I hope?) is necessary the higher up in quality we go (size of soundboard, strings, scaling design-- it does matter)... You may like the spinet the way it sounds when you tune it a certain way-- but you gotta know there are still problems there!- there is no magic tuning that is going to be pulled out by anyone to solve that.

And, I know that the extremely cheap spinet is going to require extremes-- I haven't been referring to those either in my talk about sacrificing octaves. I guess I am just referring to my standards as I approach a piano to tune.

I'm extremely tired for some reason tonight- I don't know if I'm making any sense here (or even thinking straight enough to express what I mean).
Perhaps I shouldn't post this then?... Nah! lol
Posted By: Mark Cerisano

Re: Octave Sizes - 03/08/17 01:52 PM

Originally Posted by Mark Cerisano, RPT
Hi Chris,

Maybe you are right. I have noticed what I can only define as "Aural Illusion". Much like an optical illusion where we think we see something that is not there.

Try this:
Play the contiguous M3's. Listen to the bottom and top one, then the three together.

I.e.
Play F3A3-C#4F4
then F3A3-A3C#4-C#4F4

I sometimes get the sensation that F3A3-C#4F4 is a lot closer when I play F3A3-A3C#4-C#4F4, than when I play F3A3-C#4F4. Sometimes I can't tell them apart.

I'm working on the math and it is not easy.

As for finding reversed octave Kees, have you been looking for them? I look for them every time I tune. I've recorded a few. I'll dig them up. If I can prove to you that reversed octaves exist, does that prove that pure 4:2/pure 6:3 can exist?

For the purpose of defining pure 4:2/pure 6:3 aurally, we only need the tests to be within 2-3%.

Found the recording. Here it is:

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)

Here is a recording of the filtered beats. I have often posted that bandpassing beat rates is a great tool. It helped me just now not to be so arrogant. (I thought the 4:2 was pure when listening to the unfiltered recording)

https://www.dropbox.com/s/xq89szaznszn0qw/A%20Filtered%20Reversed%20F3F4%20Octave.mp3?dl=0


Some people have made some pretty clear accusations. Namely that a pure 4:2/pure 6:3 is not possible. And that a pure 4:2/wide 6:3 is not possible. I've offered that if I could prove a pure 4:2/wide 6:3 exists, then the pure 4:2/pure 6:3 could exist as well.

I've posted recordings that show the pure 4:2/wide 6:3 can exist, but nobody has commented. Why not?
Posted By: UnrightTooner

Re: Octave Sizes - 03/08/17 02:58 PM

Originally Posted by Mark Cerisano, RPT
...

Some people have made some pretty clear accusations. Namely that a pure 4:2/pure 6:3 is not possible. And that a pure 4:2/wide 6:3 is not possible. I've offered that if I could prove a pure 4:2/wide 6:3 exists, then the pure 4:2/pure 6:3 could exist as well.

I've posted recordings that show the pure 4:2/wide 6:3 can exist, but nobody has commented. Why not?


Well, you asked. I cannot speak for others, but I don't think you know what you are talking about and tend to hear what you want to hear. You also do not receive the views of others gracefully. So, for myself, I choose not to waste the time or experience the aggravation in following up your claims.
Posted By: DoelKees

Re: Octave Sizes - 03/08/17 03:48 PM

Originally Posted by Mark Cerisano, RPT
Originally Posted by Mark Cerisano, RPT
Hi Chris,

Maybe you are right. I have noticed what I can only define as "Aural Illusion". Much like an optical illusion where we think we see something that is not there.

Try this:
Play the contiguous M3's. Listen to the bottom and top one, then the three together.

I.e.
Play F3A3-C#4F4
then F3A3-A3C#4-C#4F4

I sometimes get the sensation that F3A3-C#4F4 is a lot closer when I play F3A3-A3C#4-C#4F4, than when I play F3A3-C#4F4. Sometimes I can't tell them apart.

I'm working on the math and it is not easy.

As for finding reversed octave Kees, have you been looking for them? I look for them every time I tune. I've recorded a few. I'll dig them up. If I can prove to you that reversed octaves exist, does that prove that pure 4:2/pure 6:3 can exist?

For the purpose of defining pure 4:2/pure 6:3 aurally, we only need the tests to be within 2-3%.

Found the recording. Here it is:

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)

Here is a recording of the filtered beats. I have often posted that bandpassing beat rates is a great tool. It helped me just now not to be so arrogant. (I thought the 4:2 was pure when listening to the unfiltered recording)

https://www.dropbox.com/s/xq89szaznszn0qw/A%20Filtered%20Reversed%20F3F4%20Octave.mp3?dl=0


Some people have made some pretty clear accusations. Namely that a pure 4:2/pure 6:3 is not possible. And that a pure 4:2/wide 6:3 is not possible. I've offered that if I could prove a pure 4:2/wide 6:3 exists, then the pure 4:2/pure 6:3 could exist as well.

I've posted recordings that show the pure 4:2/wide 6:3 can exist, but nobody has commented. Why not?

I haven't commented because I can't download the audio in those links.

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/08/17 03:54 PM

Kees,

Do you have a Dropbox account? That may be the issue. I will email you the mp3's.
Posted By: DoelKees

Re: Octave Sizes - 03/08/17 05:24 PM

Originally Posted by Mark Cerisano, RPT

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)


I get:

C#3F3 = 8.6
C#3F4 = 8.9
F3G#3 = 8.2
G#3F4 = 9.7

So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/08/17 06:03 PM

As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.
Posted By: UnrightTooner

Re: Octave Sizes - 03/08/17 06:50 PM

Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


Sure there is a proof that this can happen. It seems to be very rare. What piano was this and were any wound strings involved?
Posted By: pyropaul

Re: Octave Sizes - 03/08/17 06:52 PM

Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


No he didn't say that, he said:

Quote
So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.


Paul.
Posted By: P W Grey

Re: Octave Sizes - 03/08/17 07:01 PM

Some years ago I remember AL Sanderson talking in a class about inharmonicity and the question that someone brought up was: "Does inharmonicity essentially progress the SAME way in all piano?". He started off saying basically "yes", but then he stopped and said:"Except for the Astin-Weight...that is one weird piano, I don't exactly know how they did it but it to has reverse inharmonicity in it".

I do not measure or care much about inharmonicity, but I have had experience with three Astin-Weight Pianos and can attest to the fact that they certainly sound and behave differently from "normal".

So it is possible to engineer a piano that has a scale that could do what Mark is suggesting.

Pwg
Posted By: UnrightTooner

Re: Octave Sizes - 03/08/17 07:06 PM

Originally Posted by P W Grey
Some years ago I remember AL Sanderson talking in a class about inharmonicity and the question that someone brought up was: "Does inharmonicity essentially progress the SAME way in all piano?". He started off saying basically "yes", but then he stopped and said:"Except for the Astin-Weight...that is one weird piano, I don't exactly know how they did it but it to has reverse inharmonicity in it".

I do not measure or care much about inharmonicity, but I have had experience with three Astin-Weight Pianos and can attest to the fact that they certainly sound and behave differently from "normal".

So it is possible to engineer a piano that has a scale that could do what Mark is suggesting.

Pwg


It is only when the slope is much steeper than normal, that his can happen, not when it is "reversed", which is hard to believe.
Posted By: P W Grey

Re: Octave Sizes - 03/08/17 08:10 PM

All I am saying is that if "reverse" is possible (though very strange), it follows that almost any other combination of inharmonicity curves is theoretically possible, and probably already has been designed into some pianos. Therfore what Mark is saying probably could be in existence.

Dr. Al Sanderson was one who knew more about inharmonicity than just about anyone else on the planet, and was very deliberate to make sure he had his facts straight. I trust his judgement in the matter. He was also a REALLY nice guy.

Now, what I am about to say is probably likely to get misinterpreted so I want to make it clear that the following is not meant to be disrespectful or antagonist, or even impolite. Here goes:

Who cares? What difference does it make if an octave has pure 4:2 and 6:3 partials at the same time? Or whatever? It doesn't change the fact that we would need to figure out a way to tune the thing so that it maximizes the musicality available in that piano as a whole.

I would like to hear more expressions about what specifically is being heard in that (or any other) octave that makes you decide that that is the "best" sounding octave.

Can anyone do that? What makes you "decide" that the octave sounds better at the pure 4:2 vs pure 6:3 vs pure 8:4 OR something in between? What are YOU listening for to make that decision?

In the interest of full disclosure, I subscribe to the idea that you CANNOT tune an octave such that ALL partials are beatless (meaning pure) at the same time. You must make a choice (or two).

I would be very interested and I am sure others would be too.

Pwg
Posted By: pyropaul

Re: Octave Sizes - 03/08/17 08:39 PM

I would posit that if a string has inharmonicity (which it does) then it is mathematically impossible to tune an octave and have all partials beatless simultaneously. I don't think it matters what the inharmonicity constants are for the strings involved, unless those constants are zero. Higher partials are always proportionately sharper than lower ones so you can't have 4:2 beatless at the same time as 6:3 or any other combination. Of course, you can tune so that the sound of the inevitable beating is minimized (and with weaker upper partials, a pure 4:2 or 2:1 may sound "beatless" overall), but you can't have them all beating at the same speed (which includes zero). All bets are off, though, if different partials have different inharmoncity constants! How that works, physically, though, I'm not sure.

Paul.
Posted By: Gadzar

Re: Octave Sizes - 03/08/17 09:43 PM

Originally Posted by P W Grey
In the interest of full disclosure, I subscribe to the idea that you CANNOT tune an octave such that ALL partials are beatless (meaning pure) at the same time. You must make a choice (or two).

Pwg


thumb

Posted By: Gadzar

Re: Octave Sizes - 03/08/17 09:45 PM

Originally Posted by pyropaul
..., but you can't have them all beating at the same speed (which includes zero). All bets are off, though, if different partials have different inharmoncity constants!...

Paul.


thumb
Posted By: Mark Cerisano

Re: Octave Sizes - 03/08/17 10:18 PM

Originally Posted by pyropaul
Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


No he didn't say that, he said:

Quote
So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.


Paul.


Hi Paul,

I think you are referring to the recordings. The recordings were of a "nearly pure 4:2 and wide 6:3"

The mathematical proof that Kees made was done on a google doc I created and proves that the pure 4:2/pure 6:3 occurs when the iH of the top note is 4 times that of the lower.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/08/17 10:32 PM

Originally Posted by P W Grey
All I am saying is that if "reverse" is possible (though very strange), it follows that almost any other combination of inharmonicity curves is theoretically possible, and probably already has been designed into some pianos. Therfore what Mark is saying probably could be in existence.

Dr. Al Sanderson was one who knew more about inharmonicity than just about anyone else on the planet, and was very deliberate to make sure he had his facts straight. I trust his judgement in the matter. He was also a REALLY nice guy.

Now, what I am about to say is probably likely to get misinterpreted so I want to make it clear that the following is not meant to be disrespectful or antagonist, or even impolite. Here goes:

Who cares? What difference does it make if an octave has pure 4:2 and 6:3 partials at the same time? Or whatever? It doesn't change the fact that we would need to figure out a way to tune the thing so that it maximizes the musicality available in that piano as a whole.

I would like to hear more expressions about what specifically is being heard in that (or any other) octave that makes you decide that that is the "best" sounding octave.

Can anyone do that? What makes you "decide" that the octave sounds better at the pure 4:2 vs pure 6:3 vs pure 8:4 OR something in between? What are YOU listening for to make that decision?

In the interest of full disclosure, I subscribe to the idea that you CANNOT tune an octave such that ALL partials are beatless (meaning pure) at the same time. You must make a choice (or two).

I would be very interested and I am sure others would be too.

Pwg


Hi Peter,

You are right. We cannot have more than two partial pairs beatless.

The reason why I care about this is that tuning an octave using checks is much more precise than just tuning it directly, without checks. Theoretically there could be some techs who have great precision when tuning octaves, but I'm not one of them. :-)

I also created an online survey that shows that not many of us are.

When one can and does tune a pure 4:2/pure 6:3, it does sound very clean to me. But more importnatly, a pure 6:3 allows for pure 19ths to be tuned as well as pure 11/12/22.

Example:

When tuning pure 4:2 and pure 12, we have

M3 = M10 < M17 = M6

Add to that the pure 22

M3 = M10 < M17 = M6 = m6down

The pure 22 is at

M17 = m6down

The pure 11 is the

M6 = m6down

But with a pure 6:3, we have

m3 = M6

Using the same M6 in

M3 = M10 < M17 = M6 = m6down

We get

M3 = M10 < M17 = M6 = m6down = m3down

The pure 19 is here

m3down = M17

So, a piano that has mid range octaves that can be tuned at, or very near, the pure 4:2/pure 6:3, can have pure 11/12/19/22.


Posted By: P W Grey

Re: Octave Sizes - 03/08/17 11:39 PM

Mark,

When you say "22", are you referring to the 22nd partial? Or something else?

Pwg
Posted By: Mark Cerisano

Re: Octave Sizes - 03/09/17 12:51 AM

22 = triple octave
11 = octave plus fourth
12 = octave plus fifth
19 = two octaves plus fifth

By the way, most pianos I tune are very well scaled and I have trouble hearing the difference between the M3/M10 and the m3/M6 when I try to tune them equal. Because of human limitations in detecting beat speed differences, these are pure within 3%.

I did a study a while ago and recorded 20 or 30 piano octaves and analyzed then all. Many were pure 4:2/pure 6:3, about half.

Posted By: P W Grey

Re: Octave Sizes - 03/09/17 01:16 AM

Got it.

So, tell me how you "prove" that the triple octave is in fact pure? What RBI's do you use to confirm this, other than simply playing the triple octave and listening to it?

I admit that I have great difficulty in understanding how one can have single, double, and triple octaves all pure and beatless without having severely constricted octaves, which would sound quite flat musically, especially in an arpeggio.

Virgil Smith used to claim he could do this, but then he would turn around and say that (for instance) RCT did not have an octave stretch that could match his! They were all too narrow! I have great difficulty in accepting this rationale based on 40+ years of experience, though I am willing to be proven wrong if this can be done, which is why I am asking for more information.

Pwg

Posted By: Mark Cerisano

Re: Octave Sizes - 03/09/17 03:00 AM

If you look at the P4 window, you can see the tests. It clearly shows that you can have pure 11/12/19/22 but not pure 15 (double octave) at the same time. If we tune pure double octaves, the 11/12/19/22 will all have to be narrow.

P4 Window
M3 = M10 < M17 = M6 = m6down = m3down

The M3 < M17 proves a wide double octave.
To have a pure double octave, you need

M3 = M10 = M17

That produces a pure 2:1. I don't know why anyone advocates a pure double octave. You need a pure 2:1 and that's just too narrow imho. But even tunelab has a setting for pure double octaves.

Pure 22 triple octave test
m6down = M17

I always use beat speeds to set intervals and then check the actual intervals now and then.

Thanks for the question.
Posted By: DoelKees

Re: Octave Sizes - 03/09/17 03:30 AM

Originally Posted by Mark Cerisano, RPT
When one can and does tune a pure 4:2/pure 6:3, it does sound very clean to me. But more importnatly, a pure 6:3 allows for pure 19ths to be tuned as well as pure 11/12/22.

Example:

When tuning pure 4:2 and pure 12, we have

M3 = M10 < M17 = M6


Maybe it's me but I can't follow this and the rest. Which intervals are all these M3 m17 m6below etc?

For the last one I quoted, for C3C4G4 I understand you mean
G#2C3 = G#2C4 < D#2G4 = D#2C3
but the inequality is wrong as D#2C3 beats slower than G#2C3?

Kees
Posted By: Gadzar

Re: Octave Sizes - 03/09/17 09:47 AM

Kees,

It's easy. But I don't know where in the piano's scale it can sound right.


Take for example the octave A3A4 and the test note F3

pure 4:2 octave A3A4, M3=M10, F3A3=F3A4

wide 4:3 fourth A3D4, M3<M6, F3A3<F3D4

pure 3:1 octave plus fifth or 12th D4A5, M6=M17, F3D4=F3A5

wide 2:1 octave A4A5, M10<M17, F3A4<F3A5

wide 4:1 double octave or 15th, M3<M17, F3A3<F3A5

pure 8:3 octave plus fourth or 11th A2D4, m6down=M6, A2F3=F3D4

pure 8:1 triple octave or 22th A2A5, m6down=M17, A2F3=F3A5

pure 6:3 octave D3D4, m3down=M6, D3F3=F3D4

pure 6:1 double octave plus fifth or 19th D3A5, m3down=M17, D3F3=F3A5


This is perfectly tunable in any piano! But the question is: does it sound good?



1.- Tune A4

2.- Tune A3 to A4 as a pure 4:2 octave. Test M3=M10, F3A3=F3A4

3.- Tune D4 to A3 as a wide 4:3 fourth (slightly more tempered than usual because we are going to tune pure 12ths). Test M3<M6, F3A3<F3D4

4.- Tune A5 to D4 as a pure 3:1 twelve. Test M6=M17, F3D4=FA5

Up to this point you have a wide 4:1 double octave A3A5, M3<M17, F3A3<F3A5. You have also a wide 2:1 octave A4A5, M10<M17, F3A4<F3A5

That's where M3=M10 < M17=M6 comes from.

5.- Tune A2 to D4 as a 8:3 pure 11th (octave+fourth). Test m6down=M6, A2F3=F3D4

The test note is F3, m6down means a m6 below F3, which is A2.

To understand this test think of a wide 4:3 A3D4 fourth. You have to compare the fourth partial of A3 to the third partial of D4, to make this comparison you use the fifth partial of F3. The test is M3<M6, 5:4<5:3, F3A3<F3D4. Now to test the pure octave plus fourth A2D4 you have to compare the 8th partial of A2 to the 3th partial of D4, the test will be A2F3=F3D4, 8:5=5:3, m6down=M6.

So far we have M3=M10 < M17=M6=m6down

Notice that we have a pure 8:3 eleventh A2D4 and a pure 3:1 twelve D4A5, this builds up a pure 8:1 triple octave (22th) A2A5. The test is m6down=M17, A2F3=F3A5.

How good sounds the octave A2A3? Who knows? We know that it is a narrow 8:4 octave, because we have a wide 4:1 within a pure 8:1, so 8:4 is narrow, but does it sound good? Maybe yes, maybe not, it depends on the scaling of the piano.



6.- Tune D3 to D4 as a pure 6:3 octave. Test m3=M6 (or m3down=M6), D3F3=F3D4. And we know that F3D4=F3A5 so we have
D3F3=F3A5 or m3down=M17, this is the pure double octave plus fifth or 19th D3A5.

How good this octave D3D4 is going to sound tuned as a 6:3?

How good is the fourth A2D3? and the fifth D3A3?


Even if these pure P8, P11, P12, P19, P22 and the resulting, not explicitly tuned, intervals sound right here at A3A4 or at any other spot, what warants you that going higher or lower in the scale they will continue to sound good?

As Jeff said, it would be FANTASTIC!


I just measured the octave spread of the Centennial Steinway D I have in my shop an the result is:

pure 4:2
0.75 cents wide 2:1
0.4 cents narrow 6:3

If you tune a 0.2 cents wide 4:2 with a 0.2 narrow 6:3 you'll have a 0.95 cents wide 2:1. Is this the best sounding octave for this piano? maybe yes, maybe not, but no matter how you tune it it won't be beatless.


My August Förster studio

pure 4:2
0.1 cents wide 2:1
2.4 cents narrow 6:3

A Hamilton (Baldwin) Studio I am repairing

pure 4:2
0.2 cents wide 2:1
2.5 cents narrow 6:3


So where can I find a piano that can be tuned with a beatless A3A4 octave? Not even a high quality concert grand can have it beatless!


Posted By: UnrightTooner

Re: Octave Sizes - 03/09/17 10:26 AM

Originally Posted by Gadzar
...

So where can I find a piano that can be tuned with a beatless A3A4 octave? Not even a high quality concert grand can have it beatless!



Yes, let alone a piano with wide 6:3 with narrow 4:2. A while back Kent Swafford demonstrated such an octave on an SS-B that he had. I remember Del saying that they had some well known scaling errors but are now considered a feature instead of a fault.

As far as the example that Mark provided and Kees verified, I played with the numbers and could not come up with iH values that would produce those results, although I may be missing something. The ratio in iH would have to be WAY more than 1:4. I suspect there are wild partials on one or both notes. I asked what piano the audio was from and whether wound strings were involved, but there was no reply.
Posted By: UnrightTooner

Re: Octave Sizes - 03/09/17 01:40 PM

Originally Posted by DoelKees
...

I get:

C#3F3 = 8.6
C#3F4 = 8.9
F3G#3 = 8.2
G#3F4 = 9.7

So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.

Kees


With a freshly caffeinated mind I came up with the following possibilities for an F3-F4 octave with a 4:2 beating +0.3 bps and a 6:3 beating +1.5 bps, which is what the above RBI beatrates translate to. I used Young's equation rather than Tunelab's tabulated values. Would someone please check my math/arithmetic?

F3: iH 0.10, offset 0.0 cents
F4: iH 0.75, offset 0.0 cents
4:2 +0.3 bps
6:3 +1.5 bps
iH ratio 1:7.5

F3: iH 0.20, offset -0.3 cents
F4: iH 1.15, offset 0.0 cents
4:2 +0.3 bps
6:3 +1.5 bps
iH ratio 1:5.75

So we can't say for sure what the iH ratio might be in this case without knowing what one of the two iH values is first. Seems the higher the iH value, the less of a ratio is needed. So I expect this would happen more often in pianos with higher iH values. The problem is, pianos with higher values in the middle tend to have flatter, not steeper, iH slopes. So once again I have to wonder if this isn't a case of wild partials.

Mark, again, can you tell us what piano the recording was from and if wound strings were involved?

Posted By: Robert Scott

Re: Octave Sizes - 03/09/17 03:07 PM

Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


According to my calculations, that is only possible if the inharmonicity of the upper note is 6.40 times as high as that of the lower note. I have a PDF of those calculations I could post or send to anyone who is interested. (Is there a way to post a PDF on Piano World?) Whether it is 4 or 6.4, it is more than any one-octave jump in inharmonicity I have seen.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/09/17 03:08 PM

Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
When one can and does tune a pure 4:2/pure 6:3, it does sound very clean to me. But more importnatly, a pure 6:3 allows for pure 19ths to be tuned as well as pure 11/12/22.

Example:

When tuning pure 4:2 and pure 12, we have

M3 = M10 < M17 = M6


Maybe it's me but I can't follow this and the rest. Which intervals are all these M3 m17 m6below etc?

For the last one I quoted, for C3C4G4 I understand you mean
G#2C3 = G#2C4 < D#2G4 = D#2C3
but the inequality is wrong as D#2C3 beats slower than G#2C3?

Kees

The intervals are all from a common check note. That is why I list some as m3down, m6down.

You quoted:
"G#2C3 = G#2C4 < D#2G4 = D#2C3"
but the intervals are all from G#2. I don't know how you got D#2

So the notes would be:
G#2C3 = G#2C4 < G#2C5 = G#2F3

The pure 4:2 is C3C4
The wide double octave is C3C5
The pure 12th is F3C5
The wide 2:1 is C4C5
The wide P4 is C3F3
The narrow fifth is F3C4
All these intervals sizes are confirmed in this window.

Add the m6down (C2G#3) to confirm the pure 22 C2C5, and there are a bunch more interval sizes confirmed like the pure 11.

Add the m3down, if the 6:3 is pure (F2G#2 = G#2F3), and you get a pure 19 F2C5, and a bunch more intervals confirmed like the pure 8:6 P4

Thanks for the question Kees. You are always fair and polite and it is a pleasure conversing with you. You really could have made me feel stupid for the mistake I made when questioning your assumption in the proof you so generously did for me (in a quarter of a page when I had already written three pages and wasn't even done!) but you didn't. You are truly a gentleman and I want everyone to know. So thanks again.
Posted By: UnrightTooner

Re: Octave Sizes - 03/09/17 03:51 PM

Originally Posted by Robert Scott
Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


According to my calculations, that is only possible if the inharmonicity of the upper note is 6.40 times as high as that of the lower note. I have a PDF of those calculations I could post or send to anyone who is interested. (Is there a way to post a PDF on Piano World?) Whether it is 4 or 6.4, it is more than any one-octave jump in inharmonicity I have seen.


Thanks for chiming in, Mr. Scott. You are considered to be an authority on the subject. Is it likely, or have you seen a situation where a wild partial, perhaps from a wound string, will make it seem there is such a large jump in inharmonicity?
Posted By: DoelKees

Re: Octave Sizes - 03/09/17 05:49 PM

Originally Posted by Robert Scott
Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


According to my calculations, that is only possible if the inharmonicity of the upper note is 6.40 times as high as that of the lower note. I have a PDF of those calculations I could post or send to anyone who is interested. (Is there a way to post a PDF on Piano World?) Whether it is 4 or 6.4, it is more than any one-octave jump in inharmonicity I have seen.

Below I used Young's model, but I think if you plug in the tunelab IH model it will agree with you.
Code
Partials (n=1,2,..) are for A3  f3* n* (1+B3(n^2-1)) and for  A4  f4* n* (1+B4(n^2-1))

4:2 pure:   f3*4*(1+15*B3) = f4*2*(1+3*B4)  → f4 = 2*(1+15*B3)/(1+3*B4) * f3
6:3 wide:  f3*6*(1+35*B3) <  f4*3*(1+8*B4)

So  f3*6*(1+35*B3) < 2*(1+15*B3)/(1+3*B4) * f3 *3*(1+8*B4)
Simplify:

(1+35*B3)*(1+3*B4) < (1+15*B3)*(1+8*B4)    (K1)

We can solve K1 for B4 in terms of B3 for equality, 

B4 = 4*B3/(3*B3 + 1) ~ 4*B3 

then if we increase B4 from that value the right hand side of K1 increases faster because of factor 8*B4 on the right and 3*B4 on the left so we get wide 6:3 pure 4:2.


Kees
Posted By: DoelKees

Re: Octave Sizes - 03/09/17 06:01 PM

Thanks Raphael and Mark for explaining those checks. I thought you guys were talking about the P12 on top of a bottom note.

Kees
Posted By: pyropaul

Re: Octave Sizes - 03/09/17 07:20 PM

For what it's worth, here's pretty much the best I could do with the F3F4 octave.

F3F4.mp3

The recording is F3 then F4 followed by the part where they're together filtered at 2:1, then 4:2 and then 6:3 using a bandpass filter set at 375Hz, 700Hz and 1050Hz. The fundamental of F3 is at about 175Hz.

Both are single strings.

Piano is an 1887 Steinway A1 recently restored. Strings are Roslau.

Paul.
Posted By: DoelKees

Re: Octave Sizes - 03/09/17 07:32 PM

Originally Posted by DoelKees
Originally Posted by Robert Scott
Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


According to my calculations, that is only possible if the inharmonicity of the upper note is 6.40 times as high as that of the lower note. I have a PDF of those calculations I could post or send to anyone who is interested. (Is there a way to post a PDF on Piano World?) Whether it is 4 or 6.4, it is more than any one-octave jump in inharmonicity I have seen.

Below I used Young's model, but I think if you plug in the tunelab IH model it will agree with you.
Code
Partials (n=1,2,..) are for A3  f3* n* (1+B3(n^2-1)) and for  A4  f4* n* (1+B4(n^2-1))

4:2 pure:   f3*4*(1+15*B3) = f4*2*(1+3*B4)  → f4 = 2*(1+15*B3)/(1+3*B4) * f3
6:3 wide:  f3*6*(1+35*B3) <  f4*3*(1+8*B4)

So  f3*6*(1+35*B3) < 2*(1+15*B3)/(1+3*B4) * f3 *3*(1+8*B4)
Simplify:

(1+35*B3)*(1+3*B4) < (1+15*B3)*(1+8*B4)    (K1)

We can solve K1 for B4 in terms of B3 for equality, 

B4 = 4*B3/(3*B3 + 1) ~ 4*B3 

then if we increase B4 from that value the right hand side of K1 increases faster because of factor 8*B4 on the right and 3*B4 on the left so we get wide 6:3 pure 4:2.


Kees

Actually I get 3.2 for tunelab model. One of us is missing a factor 2.

Kees
Posted By: Chris Leslie

Re: Octave Sizes - 03/09/17 08:35 PM

Either way, it makes me wonder about the validity of any of the RBI interval checks, especially those that involve wider intervals or in areas with jumpy iH scales.
Posted By: Robert Scott

Re: Octave Sizes - 03/09/17 11:21 PM

Originally Posted by DoelKees

Code
Partials (n=1,2,..) are for A3  f3* n* (1+B3(n^2-1)) and for  A4  f4* n* (1+B4(n^2-1))

4:2 pure:   f3*4*(1+15*B3) = f4*2*(1+3*B4)  → f4 = 2*(1+15*B3)/(1+3*B4) * f3
6:3 wide:  f3*6*(1+35*B3) <  f4*3*(1+8*B4)

So  f3*6*(1+35*B3) < 2*(1+15*B3)/(1+3*B4) * f3 *3*(1+8*B4)
Simplify:

(1+35*B3)*(1+3*B4) < (1+15*B3)*(1+8*B4)    (K1)

We can solve K1 for B4 in terms of B3 for equality, 

B4 = 4*B3/(3*B3 + 1) ~ 4*B3 

then if we increase B4 from that value the right hand side of K1 increases faster because of factor 8*B4 on the right and 3*B4 on the left so we get wide 6:3 pure 4:2.


Kees

I don't see how you can write formulas for frequency in terms of inharmonicity that do not involve logs or exponentials. The inharmonicity constant applies to cents offset, which is essentially a logarithm. It does not apply linearly to frequency. Send me your e-mail by PM and I will e-mail you my PDF of the calculations. (I used Open Office Equations to write it).
Posted By: DoelKees

Re: Octave Sizes - 03/10/17 12:23 AM

Originally Posted by Robert Scott
Originally Posted by DoelKees

Code
Partials (n=1,2,..) are for A3  f3* n* (1+B3(n^2-1)) and for  A4  f4* n* (1+B4(n^2-1))

4:2 pure:   f3*4*(1+15*B3) = f4*2*(1+3*B4)  → f4 = 2*(1+15*B3)/(1+3*B4) * f3
6:3 wide:  f3*6*(1+35*B3) <  f4*3*(1+8*B4)

So  f3*6*(1+35*B3) < 2*(1+15*B3)/(1+3*B4) * f3 *3*(1+8*B4)
Simplify:

(1+35*B3)*(1+3*B4) < (1+15*B3)*(1+8*B4)    (K1)

We can solve K1 for B4 in terms of B3 for equality, 

B4 = 4*B3/(3*B3 + 1) ~ 4*B3 

then if we increase B4 from that value the right hand side of K1 increases faster because of factor 8*B4 on the right and 3*B4 on the left so we get wide 6:3 pure 4:2.


Kees

I don't see how you can write formulas for frequency in terms of inharmonicity that do not involve logs or exponentials. The inharmonicity constant applies to cents offset, which is essentially a logarithm. It does not apply linearly to frequency. Send me your e-mail by PM and I will e-mail you my PDF of the calculations. (I used Open Office Equations to write it).

These are linearly related for small inharmonicity as follows.

Partials n of note with fundamental f0 are

f(n) = f0*n*(1+B*(n^2-1))

In cent the offset from harmonic (f0*n) is

1200/log(2)*log(f(n)/f0*n) = 1200/log(2)*log(1+B*(n^2-1)) ~ 1200/log(2)*B*(n^2-1) as B is small.

So your B in cents is my 1200/log(2)*B.

You can find my email under my profile.

Kees
Posted By: P W Grey

Re: Octave Sizes - 03/10/17 12:47 AM

So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 01:03 AM

Hi Peter,

I have done a lot of research into this. I created an online survey to see what sizes tuners prefer. They choose octaves without knowing what size they were.

The following criteria covers about 90% of the pianos I tune. I use this to tune A3A4 and F3F4 and from that, I can determine the m3/M3 equality that I use for my temperament sequence. (If I didn't need to know the m3/M3 equality, I don't think I would be as interested in octave sizes.)

So, here is the procedure:

1) Tune a pure 4:2
2) Test the 6:3
- If it's pure, leave it
- If it's barely narrow, tune the octave as a wide 4:2/narrow 6:3
- If it's very narrow, leave the octave as a pure 4:2/very narrow 6:3

There are other steps that I go farther into in this flow chart, but that's basically what I do.

http://howtotunepianos.com/tuning-beatless-octaves/
Posted By: Robert Scott

Re: Octave Sizes - 03/10/17 03:58 AM

Originally Posted by Robert Scott
Originally Posted by DoelKees

Code
Partials (n=1,2,..) are for A3  f3* n* (1+B3(n^2-1)) and for  A4  f4* n* (1+B4(n^2-1))

4:2 pure:   f3*4*(1+15*B3) = f4*2*(1+3*B4)  → f4 = 2*(1+15*B3)/(1+3*B4) * f3
6:3 wide:  f3*6*(1+35*B3) <  f4*3*(1+8*B4)

So  f3*6*(1+35*B3) < 2*(1+15*B3)/(1+3*B4) * f3 *3*(1+8*B4)
Simplify:

(1+35*B3)*(1+3*B4) < (1+15*B3)*(1+8*B4)    (K1)

We can solve K1 for B4 in terms of B3 for equality, 

B4 = 4*B3/(3*B3 + 1) ~ 4*B3 

then if we increase B4 from that value the right hand side of K1 increases faster because of factor 8*B4 on the right and 3*B4 on the left so we get wide 6:3 pure 4:2.


Kees

I don't see how you can write formulas for frequency in terms of inharmonicity that do not involve logs or exponentials. The inharmonicity constant applies to cents offset, which is essentially a logarithm. It does not apply linearly to frequency. Send me your e-mail by PM and I will e-mail you my PDF of the calculations. (I used Open Office Equations to write it).

DoelKees found an arithmetic error in my calculations. It turns out the right ratio is exactly 4, as he said.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 05:23 AM

Thanks to Kees I was able to graph a beatless 4:2/6:3 octave.

I also used Parsons IH graph to find that a ratio of about
4.67 can be fit into the acceptable range for B values for F3F4

Here are the values for the differences at the partials for
A3 = 219.9013, B = 0.0003, A4 = 440, B = 0.0012 (4 times)

2:1 = 0.001Hz narrow (0.002 cents)
4:2 = 0.000 Hz (0.001 cents)
6:3 = 0.001 Hz (0.002 cents)
8:4 = 0.005 Hz (0.005 cents)

I don't think anyone can hear a beat at any of those partials.
At the 8:4 partial, it would take 3 minutes and 20 seconds for one beat!

That's a beatless octave with inharmonicity that is within the acceptable range according to Parsons and Sanderson.
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 11:25 AM

Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


Good questions! I wonder if anyone could extra the beat rates out of the F3F4 octave I posted. To my ears, there's barely a beat in 2:1 4:2 or 6:3, but I don't have the tools to measure the actual rates.

Paul.
Posted By: UnrightTooner

Re: Octave Sizes - 03/10/17 12:18 PM

Originally Posted by Robert Scott
Originally Posted by Robert Scott
Originally Posted by DoelKees

Code
Partials (n=1,2,..) are for A3  f3* n* (1+B3(n^2-1)) and for  A4  f4* n* (1+B4(n^2-1))

4:2 pure:   f3*4*(1+15*B3) = f4*2*(1+3*B4)  → f4 = 2*(1+15*B3)/(1+3*B4) * f3
6:3 wide:  f3*6*(1+35*B3) <  f4*3*(1+8*B4)

So  f3*6*(1+35*B3) < 2*(1+15*B3)/(1+3*B4) * f3 *3*(1+8*B4)
Simplify:

(1+35*B3)*(1+3*B4) < (1+15*B3)*(1+8*B4)    (K1)

We can solve K1 for B4 in terms of B3 for equality, 

B4 = 4*B3/(3*B3 + 1) ~ 4*B3 

then if we increase B4 from that value the right hand side of K1 increases faster because of factor 8*B4 on the right and 3*B4 on the left so we get wide 6:3 pure 4:2.


Kees

I don't see how you can write formulas for frequency in terms of inharmonicity that do not involve logs or exponentials. The inharmonicity constant applies to cents offset, which is essentially a logarithm. It does not apply linearly to frequency. Send me your e-mail by PM and I will e-mail you my PDF of the calculations. (I used Open Office Equations to write it).

DoelKees found an arithmetic error in my calculations. It turns out the right ratio is exactly 4, as he said.


I switched my MS Access application simulator over to Tunelab's values and found that a 1:3.2 iH ratio in an octave will result in a pure 4:2 and when 6:3 is also pure, but not 2:1 or 8:4 partial matches.
Posted By: UnrightTooner

Re: Octave Sizes - 03/10/17 12:32 PM

Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


Sure, I'll venture a comment! smile

When tuning an octave aurally, rather than setting an octave to a specific width and then listening to it, you can hear a change in timbre within the area that would be considered beatless or pure. That is the only way, I believe, you can decide what "is best", and is "What are you listening for."

But even if all the individual octaves sound "best", that does not mean the piano itself will sound "best." After all, we are tuning a piano, not tuning octaves. With experience we learn that with some octaves on some pianos it is better not to tune the "best" octaves. I find this most often in the mid treble, so that when the high treble is tuned, the pitch sounds right.

But anymore, me personally, I don't tune octaves by themselves except in the single bass strings. I tune 4ths, 5ths and 12ths and use the octaves as checks, or along with a 5th.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 02:31 PM

Originally Posted by pyropaul
Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


Good questions! I wonder if anyone could extra the beat rates out of the F3F4 octave I posted. To my ears, there's barely a beat in 2:1 4:2 or 6:3, but I don't have the tools to measure the actual rates.

Paul.


Hi Paul,

The filter was too weak. Can you resubmit the following?

Play each for 2-3 seconds

C#3F3
C#3F4
F3G#3
G#3F4
F3F4
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 02:55 PM

I took the short bit you recorded for F3 and F4,
mixed them together and filtered them using Ocenaudio.
The partials are much easier to hear now.
There may be a small beat at 8:4 but it all sounds beatless to me and looks beatless on the screen.

Here's the recording:

http://howtotunepianos.com/wp-content/uploads/2017/03/F3F4.mp3

Here's the screen shot:

http://howtotunepianos.com/wp-content/uploads/2017/03/Screen-Shot-2017-03-10-at-9.54.28-AM.png

In both files you are seeing/hearing: F3F4, 2:1 filter, 4:2 filter, 6:3 filter, 8:4 filter.

(The picture upload feature on PW doesn't seem to be working)
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 03:15 PM

Originally Posted by Mark Cerisano, RPT
I took the short bit you recorded for F3 and F4,
mixed them together and filtered them using Ocenaudio.
The partials are much easier to hear now.
There may be a small beat at 8:4 but it all sounds beatless to me and looks beatless on the screen.



Thanks Mark - I also thought all the partial pairs that I could hear were beatless.

Paul.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 04:08 PM

This shows the difference between theory
- "There is no way all the partials can be beatless at the same time"
and practice. For all intents and purposes, this octave is beatless.

If you send me the recordings I asked for, I can do some more analysis
and we can get some numbers to show what the speed of the beats are.
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 04:45 PM

Originally Posted by Mark Cerisano, RPT
This shows the difference between theory
- "There is no way all the partials can be beatless at the same time"
and practice. For all intents and purposes, this octave is beatless.

If you send me the recordings I asked for, I can do some more analysis
and we can get some numbers to show what the speed of the beats are.


I'll try and get them to you later today.

I was also guilty of saying that it was impossible to do what I actually did in practice!

Paul
Posted By: Rick_Parks

Re: Octave Sizes - 03/10/17 06:26 PM

Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


I've been following this thread, and the other two related- because I've been waiting to see what answer they would come away with... It appears the answer is always to start another thread and pick up the debate afresh there. *Shrugs*

I'll venture to answer--
After all the talk is done, you tune it to "what sounds best". This is the last word on all these conversations, because theories, and the debates surrounding them, tend to always come back to this point in the end- what does the real world require us to do?

I was recently skimming over Bill Brimmer's piece he wrote back in 2007 "Achieving 21st Century Standards of Excellence in Tuning"...
First sentence of the second paragraph:
Quote

None of these books I know of, say anything other than to make a pure octave...


Now, his whole piece is based on these theories being discussed, but I don't see the reality to it all in the realm of reality that is... We HEAR, we don't listen by plugging our ears into a machine, or by running endless math figures into our brain via ears.
Don't get me wrong- theories are fine- (and endless, as I thought to be the case)-- go for it with theory and the math, if that thrills you. But, for me, it drives me nuts reading the verbose postings, waiting for answers, waiting, waiting, all the while knowing no answers is ever coming. crazy

The old books all said tune it "to sound pure", because back in those days (before ETD/A)knowledge had not puffed us up to think that we could reasonably think that we are tuning something "better than beatless"... LOL - I liked that one. laugh
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 06:37 PM

Mark,

Here is a file that has all the intervals you asked for, together with the individual F3 and F4 notes (so you can measure the iH for them).

F3F4Intervals.mp3

Doesn't sound quite as good today as yesterday though it's still close to beatless.

Paul.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 06:43 PM

Originally Posted by Rick_Parks
Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


I've been following this thread, and the other two related- because I've been waiting to see what answer they would come away with... It appears the answer is always to start another thread and pick up the debate afresh there. *Shrugs*

I'll venture to answer--
After all the talk is done, you tune it to "what sounds best". This is the last word on all these conversations, because theories, and the debates surrounding them, tend to always come back to this point in the end- what does the real world require us to do?

I was recently skimming over Bill Brimmer's piece he wrote back in 2007 "Achieving 21st Century Standards of Excellence in Tuning"...
First sentence of the second paragraph:
Quote

None of these books I know of, say anything other than to make a pure octave...


Now, his whole piece is based on these theories being discussed, but I don't see the reality to it all in the realm of reality that is... We HEAR, we don't listen by plugging our ears into a machine, or by running endless math figures into our brain via ears.
Don't get me wrong- theories are fine- (and endless, as I thought to be the case)-- go for it with theory and the math, if that thrills you. But, for me, it drives me nuts reading the verbose postings, waiting for answers, waiting, waiting, all the while knowing no answers is ever coming. crazy

The old books all said tune it "to sound pure", because back in those days (before ETD/A)knowledge had not puffed us up to think that we could reasonably think that we are tuning something "better than beatless"... LOL - I liked that one. laugh


Hi Rick,

I have written a very specific procedure for the octave. Did you not read it? I also posted a link to a flow chart that goes into more detail. I agree with Bill. There has been no books written on this that I know of, but I have published this flow chart in the piano technicians journal and I will publish a book on the subject soon.
Posted By: Rick_Parks

Re: Octave Sizes - 03/10/17 07:15 PM

Originally Posted by Mark Cerisano, RPT
Hi Rick,
I have written a very specific procedure for the octave. Did you not read it? I also posted a link to a flow chart that goes into more detail. I agree with Bill. There has been no books written on this that I know of, but I have published this flow chart in the piano technicians journal and I will publish a book on the subject soon.


Mark,
I see (and have seen) your points, yes. But it is still (from where I'm viewing all of this-- from outside the debate) not something accepted and proven, AND applicable to the real world of pianos that we are dealing with... Perhaps I'm wrong. Even if someone comes up with some perfect tuning method- it does not mean it is something that is reasonably applicable to more than the piano they performed it upon (or a similar type)...

I'm still reading the posts though- and, I'm keeping an open mind--- even though I HATE THEORY lectures LOL smile
Posted By: UnrightTooner

Re: Octave Sizes - 03/10/17 07:31 PM

Originally Posted by Rick_Parks
...

The old books all said tune it "to sound pure", because back in those days (before ETD/A)knowledge had not puffed us up to think that we could reasonably think that we are tuning something "better than beatless"... LOL - I liked that one. laugh


Dr. White mentioned that tuners cannot resist the need to stretch the two ends of the piano. So something other than "to sound pure" was talked about in the old books. And when I listen to old records, I can hear differences in stretch, too.

Dr. White also prescribed using the M3/M10 (4:2) test for octaves in the middle, the M10/M17 (2:1) the M3/M17 (4:1) test for the treble, and the m3/M6 (6:3) test for the bass. This was also different than just "to sound pure" although, depending on the piano, it may result in sounding pure. It is interesting that these partial matches do produce different width octaves depending on iH, and are very close to the ones suggested in the present day.

What I am saying is that tuning specific octaves, rather than just "sounding good" is not something new. There is math to help understand it and describe it (and debate it...) now, that is the only real difference.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 08:07 PM

Originally Posted by Rick_Parks
Originally Posted by Mark Cerisano, RPT
Hi Rick,
I have written a very specific procedure for the octave. Did you not read it? I also posted a link to a flow chart that goes into more detail. I agree with Bill. There has been no books written on this that I know of, but I have published this flow chart in the piano technicians journal and I will publish a book on the subject soon.


Mark,
I see (and have seen) your points, yes. But it is still (from where I'm viewing all of this-- from outside the debate) not something accepted and proven, AND applicable to the real world of pianos that we are dealing with... Perhaps I'm wrong. Even if someone comes up with some perfect tuning method- it does not mean it is something that is reasonably applicable to more than the piano they performed it upon (or a similar type)...

I'm still reading the posts though- and, I'm keeping an open mind--- even though I HATE THEORY lectures LOL smile


Hi Rick,

Can you do me a favour? Can you try the procedure I listed and let me know what kind of results you get from a real piano? It is intended for tuning A3A4 and F3F4 before the temperament is tuned.

Again, the simple procedure is:

1) Tune a pure 4:2
2) Test the 6:3
- If it's pure, leave it
- If it's slightly narrow, tune it as a wide 4:2/narrow 6:3
- If it is a very narrow 6:3, leave it as a pure 4:2/very narrow 6:3.

After setting the octave like this, try to get it to sound better just but changing one note. When it sounds good, check the tests and see if they are the same as the procedure predicted.

Or you could tune an octave clean, and then preform the tests. If the octave doesn't agree with the tests, change it. Does it sound better?

The advantage to this kind of approach is precision. There is a wide window for an acceptable octave when we tune without checks. With checks as the criteria, the window is much smaller.
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 08:08 PM

I just had a thought - given the unlikeliness of being able to tune an octave where 2:1 4:2 6:3 and 8:4 are beatless (since this would require a magic pair of iH numbers), I was wondering if there's some kind of coupling taking place that locks the partials together, even if they are not truly equal? This, of course, is what you're doing aurally when listening for a "beatless" octave - maybe it really does become beatless, even though, in theory, it shouldn't be?

Probably goes to show that how things sound is more important than sets of numbers.

Paul.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 08:19 PM

Originally Posted by pyropaul
I just had a thought - given the unlikeliness of being able to tune an octave where 2:1 4:2 6:3 and 8:4 are beatless (since this would require a magic pair of iH numbers), I was wondering if there's some kind of coupling taking place that locks the partials together, even if they are not truly equal? This, of course, is what you're doing aurally when listening for a "beatless" octave - maybe it really does become beatless, even though, in theory, it shouldn't be?

Probably goes to show that how things sound is more important than sets of numbers.

Paul.


Waves can not be added or subtracted. It would have to happen at the source. But the piano is a truly amazing instrument. Maybe.
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 08:22 PM

Originally Posted by Mark Cerisano, RPT
Originally Posted by pyropaul
I just had a thought - given the unlikeliness of being able to tune an octave where 2:1 4:2 6:3 and 8:4 are beatless (since this would require a magic pair of iH numbers), I was wondering if there's some kind of coupling taking place that locks the partials together, even if they are not truly equal? This, of course, is what you're doing aurally when listening for a "beatless" octave - maybe it really does become beatless, even though, in theory, it shouldn't be?

Probably goes to show that how things sound is more important than sets of numbers.

Paul.


Waves can not be added or subtracted. It would have to happen at the source. But the piano is a truly amazing instrument. Maybe.


Yes but the coupling of strings (in a unison) is a well documented phenomenon, so maybe it happens with other intervals too. Really an octave is no different than a unison as there are matches for all partials except the fundamental of the lower note.

Paul.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 08:55 PM

Agreed.

Did you get my PM about the F3F4 recording?
Posted By: Chris Leslie

Re: Octave Sizes - 03/10/17 09:03 PM

Originally Posted by pyropaul
Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


Good questions! I wonder if anyone could extra the beat rates out of the F3F4 octave I posted. To my ears, there's barely a beat in 2:1 4:2 or 6:3, but I don't have the tools to measure the actual rates.

Paul.


I hear a nice octave. The filtered frequencies have a more noticeable slow roll, and then when relistening to the whole octave are then more noticeable. Certainly well within the bounds of an acceptable octave. However, taken out of isolation and relating to the whole piano, do either notes sound reasonable with other double or triple octaves octaves?
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 09:25 PM

Originally Posted by Chris Leslie
Originally Posted by pyropaul
Originally Posted by P W Grey
So...the numbers are all "interesting", but how does that translate into what you hear? In other words, let's say you start out tuning a pure 4:2 A4-A3 octave (with your ETD so you KNOW it's right and you confirm it with RBI tests). Now you listen to it. What are you listening FOR to decide whether you feel that's the "best" octave width or not?

Suppose you now decide to widen it a bit, perhaps to a 6:3 octave and you play it and listen, then you slightly narrow that and listen...at what point, and what criteria are you using to decide that THAT (whatever it is) octave width is "the best"? What are you listening for?

Anyone want to venture a comment or two?

Pwg


Good questions! I wonder if anyone could extra the beat rates out of the F3F4 octave I posted. To my ears, there's barely a beat in 2:1 4:2 or 6:3, but I don't have the tools to measure the actual rates.

Paul.


I hear a nice octave. The filtered frequencies have a more noticeable slow roll, and then when relistening to the whole octave are then more noticeable. Certainly well within the bounds of an acceptable octave. However, taken out of isolation and relating to the whole piano, do either notes sound reasonable with other double or triple octaves octaves?


This seems to be the issue.

If we purposely tune this octave so that it has more roll in it, in order to appease some other relationship of fourths/fifths within the temperament, we can be sure that that roll will be present in the larger octaves that you refer to, plus any roll due to the interval itself. Where's the logic in this?
Posted By: DoelKees

Re: Octave Sizes - 03/10/17 09:30 PM

Originally Posted by pyropaul
I just had a thought - given the unlikeliness of being able to tune an octave where 2:1 4:2 6:3 and 8:4 are beatless (since this would require a magic pair of iH numbers), I was wondering if there's some kind of coupling taking place that locks the partials together, even if they are not truly equal? This, of course, is what you're doing aurally when listening for a "beatless" octave - maybe it really does become beatless, even though, in theory, it shouldn't be?

The fact that if you tune a pure 4:2 you can detect the non-zero beatrate of for example 6:3 and 2:1 with the usual tests shows that this does not happen.

Generally if you tune say 4:2 pure, there can be a value for the relative inharmonicity where one (and only one) other partial match becomes also pure, for example a 3.2 ratio for 6:3.

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/10/17 09:57 PM

Originally Posted by DoelKees
Originally Posted by pyropaul
I just had a thought - given the unlikeliness of being able to tune an octave where 2:1 4:2 6:3 and 8:4 are beatless (since this would require a magic pair of iH numbers), I was wondering if there's some kind of coupling taking place that locks the partials together, even if they are not truly equal? This, of course, is what you're doing aurally when listening for a "beatless" octave - maybe it really does become beatless, even though, in theory, it shouldn't be?

The fact that if you tune a pure 4:2 you can detect the non-zero beatrate of for example 6:3 and 2:1 with the usual tests shows that this does not happen.

Generally if you tune say 4:2 pure, there can be a value for the relative inharmonicity where one (and only one) other partial match becomes also pure, for example a 3.2 ratio for 6:3.

Kees


Yes, mathematically, but there is a range where the aural tests sound equal. This range can produce very slow beating partials. Slower than the decay. This is how I use it in the real world.

For example, Paul's F3F4 "sounds" beatless, but when we analyze it, we may discover slow beating at the 4:2 and 6:3. But the beating may be so slow as to not be audible or detectable.
Posted By: pyropaul

Re: Octave Sizes - 03/10/17 10:00 PM

Originally Posted by DoelKees
Originally Posted by pyropaul
I just had a thought - given the unlikeliness of being able to tune an octave where 2:1 4:2 6:3 and 8:4 are beatless (since this would require a magic pair of iH numbers), I was wondering if there's some kind of coupling taking place that locks the partials together, even if they are not truly equal? This, of course, is what you're doing aurally when listening for a "beatless" octave - maybe it really does become beatless, even though, in theory, it shouldn't be?

The fact that if you tune a pure 4:2 you can detect the non-zero beatrate of for example 6:3 and 2:1 with the usual tests shows that this does not happen.

Generally if you tune say 4:2 pure, there can be a value for the relative inharmonicity where one (and only one) other partial match becomes also pure, for example a 3.2 ratio for 6:3.

Kees


I was just curious as Mark's filtered analysis seemed to indicate that all of 2:1 4:2 6:3 and possibly 8:4 were pure. I just wondered if the iH numbers were "close" to the magic value that maybe a few more partial pairs could lock, rather than the one and only one your analysis proves.

Paul.
Posted By: DoelKees

Re: Octave Sizes - 03/10/17 11:43 PM

Originally Posted by pyropaul
Mark,

Here is a file that has all the intervals you asked for, together with the individual F3 and F4 notes (so you can measure the iH for them).

F3F4Intervals.mp3

Doesn't sound quite as good today as yesterday though it's still close to beatless.

Paul.

F3 has false beat at partial 8, 6bps. Partial 8 is also very weak.
F4 has false beat at partial 4, 0.7 bps.

Looking at spectrogram for F3F4:
2:1 no beats
4:2 0.5 bps
6:3 0.5 bps
8:4 0.7 (could be false beat)

Tests bps:
F3G#3 8.9
G#3F4 9.5
F3C#4 10.5 (hard to see)
C#4F4 10.5

There were no 2:1 and 4:2 tests.

Kees
Posted By: pyropaul

Re: Octave Sizes - 03/11/17 02:05 AM

Thanks for the analysis Kees. I had a feeling today's recording was a tad worse than yesterday's. I wonder if any of the false beats came from the mutes? Nevertheless, it was interesting to see the same bps for the 4:2 and 6:3 partials. I don't suppose you could extract the iH values? I only have the entropy tuner and the iH values seem to be in quite different units to those used by Tunelab (which I don't have access to anymore).

Paul
Posted By: P W Grey

Re: Octave Sizes - 03/11/17 04:02 AM

Originally Posted by Mark Cerisano, RPT
Hi Peter,

I have done a lot of research into this. I created an online survey to see what sizes tuners prefer. They choose octaves without knowing what size they were.

The following criteria covers about 90% of the pianos I tune. I use this to tune A3A4 and F3F4 and from that, I can determine the m3/M3 equality that I use for my temperament sequence. (If I didn't need to know the m3/M3 equality, I don't think I would be as interested in octave sizes.)

So, here is the procedure:

1) Tune a pure 4:2
2) Test the 6:3
- If it's pure, leave it
- If it's barely narrow, tune the octave as a wide 4:2/narrow 6:3
- If it's very narrow, leave the octave as a pure 4:2/very narrow 6:3

There are other steps that I go farther into in this flow chart, but that's basically what I do.



Mark,

You bravely ventured into my question. Nice procedure and makes perfect sense...HOWEVER you didn't actually answer my question which was "just what are you listening for to decide THAT is where you want to leave it"? Can you describe the sound of the terms "pure", "barely narrow", and "very narrow". In my experience the only way to determine any of these terms is by using the RBI tests to "prove" them from the "outside"...M3-M10 to start with. Simply listening to the octave alone doesn't tell me it's relative width except in extreme circumstances. Can you be more specific? If not, that's fine, as I understand your process. It's good.


Sure, I'll venture a comment! smile

When tuning an octave aurally, rather than setting an octave to a specific width and then listening to it, you can hear a change in timbre within the area that would be considered beatless or pure. That is the only way, I believe, you can decide what "is best", and is "What are you listening for."

But even if all the individual octaves sound "best", that does not mean the piano itself will sound "best." After all, we are tuning a piano, not tuning octaves. With experience we learn that with some octaves on some pianos it is better not to tune the "best" octaves. I find this most often in the mid treble, so that when the high treble is tuned, the pitch sounds right.

But anymore, me personally, I don't tune octaves by themselves except in the single bass strings. I tune 4ths, 5ths and 12ths and use the octaves as checks, or along with a 5th.



Jeff,

You too were willing to give it a shot. I like that: "a change in timbre within the area that would be considered beatless or pure." We're getting a little closer but I'd be interested in even more description of your final decision to accept THAT octave sound (initially of course, and subject to change as circumstances dictate).


Rick,

You too made some interesting comments about "real world tuning", etc. Very true.

Does anyone ever have a circumstance when they would accept an actual "beating" octave in midsection of the piano? Just curious.

Very few seem to want to go out on a limb here on this subject. Interesting.

Pwg
Posted By: DoelKees

Re: Octave Sizes - 03/11/17 04:40 AM

Originally Posted by pyropaul
Thanks for the analysis Kees. I had a feeling today's recording was a tad worse than yesterday's. I wonder if any of the false beats came from the mutes? Nevertheless, it was interesting to see the same bps for the 4:2 and 6:3 partials. I don't suppose you could extract the iH values? I only have the entropy tuner and the iH values seem to be in quite different units to those used by Tunelab (which I don't have access to anymore).

Paul

Doesn't the entropy tuner measure each individual partial rather than fitting them to a one parameter model (the one parameter being the IH "constant")? Anyways the ratio of F4/F3 inharmonicity is independent of units and the is the determining factor.

Having pure 2:1 and 8:4 (according to test) and equal beating 4:2 and 6:3 is impossible with the usual model. You can get 2:1 and 8:4 to be both pure if IH ratio of F4 and F3 is 16.6 which is not realistic.

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/11/17 04:53 AM

Originally Posted by P W Grey
Originally Posted by Mark Cerisano, RPT
Hi Peter,

I have done a lot of research into this. I created an online survey to see what sizes tuners prefer. They choose octaves without knowing what size they were.

The following criteria covers about 90% of the pianos I tune. I use this to tune A3A4 and F3F4 and from that, I can determine the m3/M3 equality that I use for my temperament sequence. (If I didn't need to know the m3/M3 equality, I don't think I would be as interested in octave sizes.)

So, here is the procedure:

1) Tune a pure 4:2
2) Test the 6:3
- If it's pure, leave it
- If it's barely narrow, tune the octave as a wide 4:2/narrow 6:3
- If it's very narrow, leave the octave as a pure 4:2/very narrow 6:3

There are other steps that I go farther into in this flow chart, but that's basically what I do.



Mark,

You bravely ventured into my question. Nice procedure and makes perfect sense...HOWEVER you didn't actually answer my question which was "just what are you listening for to decide THAT is where you want to leave it"? Can you describe the sound of the terms "pure", "barely narrow", and "very narrow". In my experience the only way to determine any of these terms is by using the RBI tests to "prove" them from the "outside"...M3-M10 to start with. Simply listening to the octave alone doesn't tell me it's relative width except in extreme circumstances. Can you be more specific? If not, that's fine, as I understand your process. It's good.


Sure, I'll venture a comment! smile

When tuning an octave aurally, rather than setting an octave to a specific width and then listening to it, you can hear a change in timbre within the area that would be considered beatless or pure. That is the only way, I believe, you can decide what "is best", and is "What are you listening for."

But even if all the individual octaves sound "best", that does not mean the piano itself will sound "best." After all, we are tuning a piano, not tuning octaves. With experience we learn that with some octaves on some pianos it is better not to tune the "best" octaves. I find this most often in the mid treble, so that when the high treble is tuned, the pitch sounds right.

But anymore, me personally, I don't tune octaves by themselves except in the single bass strings. I tune 4ths, 5ths and 12ths and use the octaves as checks, or along with a 5th.



Jeff,

You too were willing to give it a shot. I like that: "a change in timbre within the area that would be considered beatless or pure." We're getting a little closer but I'd be interested in even more description of your final decision to accept THAT octave sound (initially of course, and subject to change as circumstances dictate).


Rick,

You too made some interesting comments about "real world tuning", etc. Very true.

Does anyone ever have a circumstance when they would accept an actual "beating" octave in midsection of the piano? Just curious.

Very few seem to want to go out on a limb here on this subject. Interesting.

Pwg


Hi Peter,

I wasn't sure how or who wrote the post quoted. I'll assume it was you.

I'll be more specific. I think we agree re:RBI tests. I think you thought I was implying just listen to the 6:3. No. We have to use the RBI tests. Those are what are more precise than just tweaking the octave by ear, like you said.

1) Tune a pure 4:2 (M3 = M10)
2) Test the 6:3 (m3 and M6)
- If the 6:3 is pure, leave it. (m3 = M6)
- If the 6:3 is barely narrow, tune it as a wide 4:2, narrow 6:3. (M3 < M10 and m3 > M6)
- If the 6:3 is very narrow, leave it as a pure 4:2, very narrow 6:3. (M3 = M10 and m3 >> M6)

= means "beats the same speed as"
< means "beats slower than", barely noticeable.
> means "beats faster than", barely noticeable.
>> means "beats much faster than", obvious.

I hope that is clearer.

P.S. I would leave a slow beat in an octave in the low midrange if the beatless octave would sacrifice the octave + fifth, octave + fourth, two octaves + fifth, and triple octave.
Posted By: DoelKees

Re: Octave Sizes - 03/11/17 05:46 AM

Here are some theoretical plots of the beat rates of the F3F4 octave at various partials, when 4:2 is tuned pure as a function of the inharmonicity ratio of F4 and F3.
[Linked Image]

Here's a zoom into the interesting region:

[Linked Image]

There seems to be a critical region near the ratio of 3.15 where 2:1, 4:2 and 6:3 are aurally pure. So on a piano which such a steep curve aurally pure octaves at 2:1 4:2 and 6:3 are possible. Other close match is Steinway D with ratio 2.7.

Kees
Note added: Looking at the IH data I have from various sources I only found a Mason&Hamlin which has an IH ratio close to that, 3.14, usually it is 2 or less. Other close one is Steinway D at 2.7.

Posted By: Chris Leslie

Re: Octave Sizes - 03/11/17 06:25 AM

Originally Posted by P W Grey


Does anyone ever have a circumstance when they would accept an actual "beating" octave in midsection of the piano? Just curious.

Very few seem to want to go out on a limb here on this subject. Interesting.

Pwg


This is my simple answer: I tune octaves as beatless as possible while also ensuring that other perfect expanded intervals are simultaneously as beatless as possible. Tuning is all compromises. Such is life. Nothing is perfect.
Posted By: UnrightTooner

Re: Octave Sizes - 03/11/17 12:08 PM

Originally Posted by P W Grey
...


Jeff,

You too were willing to give it a shot. I like that: "a change in timbre within the area that would be considered beatless or pure." We're getting a little closer but I'd be interested in even more description of your final decision to accept THAT octave sound (initially of course, and subject to change as circumstances dictate).


...


Um, I think I gave the answer:


Originally Posted by UnrightTooner
...

But anymore, me personally, I don't tune octaves by themselves except in the single bass strings. I tune 4ths, 5ths and 12ths and use the octaves as checks, or along with a 5th.


I don't tune so an octave sounds like THAT. I tune for pure 12ths by listening to the ratio of the 4ths and 5ths. It is the pure 12ths that decide how an octave sounds, and they always sound great!

But perhaps you are asking about the FIRST octave that is tuned. THAT octave is the result of tuning up a 5th from the initial pure 12th. And if I don't care for the sound, I may adjust the 5th. I may use RBI tests to see what is going on, like is there a large difference between the 2:1 and 4:2. But it isn't about a precise sound of the octave. It is about the best sound of the 5th. the 5ths are much more "touchy".

And the same thing goes as the original 5th temperament is expanded until a full 12th is available: I will listen to the resulting octaves and use them to point out errors in the temperament and judge how the ratio between the beating of the 4ths and 5ths should progress. Generally the 5th need to progress faster. Experience is a great teacher, and I know that when I complete the first full 12th I'll be very close to the proper 4th and 5th ratio.

Peter, I am sure it is foreign to think of the temperament octave being made of 4ths and 5ths rather than the temperament octave being divided into 4ths and 5ths (and other intervals). But when you really consider the "old books", such as Dr. White's, that is what they proscribe: using SBIs to create an octave. If the resulting octave is good, the SBIs are correct.

So I gues MY answer to you question of how I decide to accept THAT octave is: it is the one that is acceptable with a pure 12th and a good sounding 5th.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/11/17 02:28 PM

Re: Kees graph showing pure 2:1/4:2/6:3 at iH ratio 3.15.

Quick calculations from Tremaine Parsons scale collection.
http://www.goptools.com/gallery.htm

Mason and Hamelin 6'4": 3.33
Steinway Upright: 2.65
Kimball Upright: 2.86
Bluthner 5'7": 2.55
Baldwin 9": 3.16
Posted By: P W Grey

Re: Octave Sizes - 03/11/17 03:46 PM

Mark, Chris, Jeff:

BINGO! Those are real world, practical descriptions of what we are required to do in tuning.

In other words would you all agree that what we are really doing is evaluating the MUSICAL qualities of ALL the intervals involved in order to make our decisions on octave width?

This is what I mean by the ART of what we do. Those who use ETDs (if they have not already learned to do so) need to incorporate this aspect into their work. They need to go beyond the numbers and LISTEN.

I am saying this for the benefit of those new or less experienced who are reading all this stuff. I know already that the seasoned pros know how to do it and do so regularly. But its important for newer ones to more fully understand the depth that we are trying to achieve here in tuning. This could be difficult for a complete non-musician, but it must become part of our MO if we are to truly succeed.

Also, I would suggest that we all go back to the very beginning of this thread and read it again before it morphed into a lot of technical stuff that is really hard to apply in reality. Some very good comments were made right at the outset.

I hope others will have the courage to also put in to words exactly what the are listening for so as DECIDE what to do with both octaves and other intervals. IOW What makes you smile and say "yes, I like that," and move on? And, what sacrifices are you willing to make if things don't seem to be working the way you envision?

Pwg
Posted By: DoelKees

Re: Octave Sizes - 03/11/17 08:02 PM

Originally Posted by Mark Cerisano, RPT
Re: Kees graph showing pure 2:1/4:2/6:3 at iH ratio 3.15.

Quick calculations from Tremaine Parsons scale collection.
http://www.goptools.com/gallery.htm

Mason and Hamelin 6'4": 3.33
Steinway Upright: 2.65
Kimball Upright: 2.86
Bluthner 5'7": 2.55
Baldwin 9": 3.16


In those plots I posted I randomly fixed the lower IH (in tunelab units) to 1. 0.3 is more realistic, so all those beat rates on the vertical axis should be divided by 3 for a more realistic ballpark.

This will of course extend the "aurally pure" window around the 3.15 ratio.

So it seems there are plenty of pianos where those octaves can indeed be pure!

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/11/17 08:58 PM

In my experience this should be a great move forward in understanding piano tuning and Inharmonicity. This is not the only forum where professional technicians have argued...well no, they didn't argue. This is argument. There was no place for arguement in some of the other discussions I have had with other professional piano technicians. In their opinion, it was just not possible to have pure 4:2 and pure 6:3 in a piano. End of story. I am happy that there are people like you Kees who are interested in advancing knowledge and not just keeping the status quo.
Posted By: Mark Cerisano

Re: Octave Sizes - 03/11/17 09:01 PM

Yes, my numbers are for F3F4. The ratio increases as we move up, so more pianos would be tuneable as pure 4:2/6:3 if we looked at A3A4. It is not uncommon for me to find small octave spread (pure 4:2/6:3) for A3A4 and medium octave spread (wide 4:2/narrow 6:3) for F3F4.
Posted By: Gadzar

Re: Octave Sizes - 03/11/17 11:41 PM

Originally Posted by DoelKees
In those plots I posted I randomly fixed the lower IH (in tunelab units) to 1. 0.3 is more realistic, so all those beat rates on the vertical axis should be divided by 3 for a more realistic ballpark.

This will of course extend the "aurally pure" window around the 3.15 ratio.

So it seems there are plenty of pianos where those octaves can indeed be pure!

Kees



I completely disagree. I think you are doing a big error. Not in your calculations. I'm sure your maths are OK. But you make an error when thinking that you can take B values to calculate beat rates of specific intervals.

I guess this is why I do not like the tunings I get from TuneLab while I like the tunings of Verituner. TuneLab computes a B value for a string by measuring its actual partials, and uses this B value to estimate the B values for other strings and finally to compute a tuning curve. Verituner measures each partial of each string and computes the tuning targets for all notes. It uses the actual measured partials to calculate the tuning.

I have a lot of troubles trying to express my ideas in english, so I'll illustrate this concept with a concrete example.


Here are the B's I've just measured of three pianos which are now at my shop:

August Förster Studio

[Linked Image]

[Linked Image]


Hamilton (Baldwin) Studio

[Linked Image]

[Linked Image]


Steinway & Sons Concert Grand

[Linked Image]

[Linked Image]


Ratios for these 3 pianos are:

August Förster = 2.18
Hamilton = 2.24
S&S = 2.56

Maybe these ratios are in the desired range to make it possible, theoretically speaking, to tune beatless 4:2 and beatless 6:3 octaves. But, and this is a big but, the actual partials as measured by TuneLab and showed in the pictures above give the following widths for the 6:3 octave when 4:2 is tuned pure:

August Förster

4:2 = 0 cents
6:3 = 2.90-4.24+5.96-8.69 = -4.07 cents

4:2 pure, 6:3 narrow by 4.1 cents



Hamilton

4:2 = 0 cents
6:3 = 3.02-3.08+4.91-7.49 = -2.64

4:2 pure, 6:3 narrow by 2.6 cents



Steinway & Sons

4:2 = 0 cents
6:3 = 2.38-2.71+4.19-5.27 = -1.41 cents

4:2 pure, 6:3 narrow by 1.4 cents


None of these pianos can be tuned with pure 4:2 and pure 6:3 octaves, despite their B values may be in an appropriate ratio range.

I've measured with Verituner the octave spread of these pianos for A3A4 with similar conclusions.

And more important: I've tuned these pianos, not once, but several times, the August Förster many times, and there is no way to tune them with pure 4:2 and pure 6:3 octaves in the temperament area.


We are faced here to the fact that theory is using a mathematical model that may work fine in general, to calculate a tuning curve that can make the piano to sound in tune, but which can not be applied to specifical isolated pairs of partials, i.e. 4:2 and 6:3 of the F3F4 octave. This mathematical model works fine for a tuning aid such as TuneLab, but is not adequate to conclude that:

"there are plenty of pianos where those octaves can indeed be pure!"

Irregularities in the distribution of partials can not be ignored by using a B value which represents the inharmonicity of a string as a whole and is no other than a "mean amount of iH" assumed for all partials of this string.


When tuning an octave at a piano you won't hear the calculated partials from estimated or computed B values.


To make such a study and take such a conclusion, you should use actual measured partials because that's what you hear when tuning an octave, this is obvious, for me at least.


Posted By: DoelKees

Re: Octave Sizes - 03/12/17 12:54 AM

Originally Posted by Gadzar
Originally Posted by DoelKees
In those plots I posted I randomly fixed the lower IH (in tunelab units) to 1. 0.3 is more realistic, so all those beat rates on the vertical axis should be divided by 3 for a more realistic ballpark.

This will of course extend the "aurally pure" window around the 3.15 ratio.

So it seems there are plenty of pianos where those octaves can indeed be pure!

Kees


I completely disagree. I think you are doing a big error. Not in your calculations. I'm sure your maths are OK. But you make an error when thinking that you can take B values to calculate beat rates of specific intervals.


I could be wrong but I think you making a sign error. For the S&S example we have from your post:

S&S
IH(F3) = 0.232
IH(F3) = 0.596
ratio = 2.56

Partial offsets:
F3_4 2.71
F3_6 5.27
F4_2 2.38
F4_3 4.19

To make 4:2 match raise F4 by (2.71-2.38).
So now F4_3 is at 4.19 + (2.71-2.38).
F3_6 - F4_3 = 5.27 -4.19 -2.71+2.38 = 0.75 cent.

Taking F3 at 174.6Hz, 6:3 bps is 6*174.6Hz*log(2)/1200*0.75 = 0.45bps.

Calculating just from the tunelab IH model I get bps=0.4bps which is very close.

On another note I did an extensive analysis of Prout's data set quite a while ago and concluded the partials fit the usual IH model very accurately with almost no exceptions.

Kees
Posted By: UnrightTooner

Re: Octave Sizes - 03/12/17 01:42 AM

Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
Re: Kees graph showing pure 2:1/4:2/6:3 at iH ratio 3.15.

Quick calculations from Tremaine Parsons scale collection.
http://www.goptools.com/gallery.htm

Mason and Hamelin 6'4": 3.33
Steinway Upright: 2.65
Kimball Upright: 2.86
Bluthner 5'7": 2.55
Baldwin 9": 3.16


In those plots I posted I randomly fixed the lower IH (in tunelab units) to 1. 0.3 is more realistic, so all those beat rates on the vertical axis should be divided by 3 for a more realistic ballpark.

This will of course extend the "aurally pure" window around the 3.15 ratio.

So it seems there are plenty of pianos where those octaves can indeed be pure!

Kees


Wouldn't the 1:3.15 ratio hold true only if the Tremaine Parsons iH curves were determined using Tunelab's equations? If he used Young's equations, which I think likely, then wouldn't the ratio need to be 1:4?
Posted By: DoelKees

Re: Octave Sizes - 03/12/17 03:04 AM

Originally Posted by UnrightTooner
Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
Re: Kees graph showing pure 2:1/4:2/6:3 at iH ratio 3.15.

Quick calculations from Tremaine Parsons scale collection.
http://www.goptools.com/gallery.htm

Mason and Hamelin 6'4": 3.33
Steinway Upright: 2.65
Kimball Upright: 2.86
Bluthner 5'7": 2.55
Baldwin 9": 3.16


In those plots I posted I randomly fixed the lower IH (in tunelab units) to 1. 0.3 is more realistic, so all those beat rates on the vertical axis should be divided by 3 for a more realistic ballpark.

This will of course extend the "aurally pure" window around the 3.15 ratio.

So it seems there are plenty of pianos where those octaves can indeed be pure!

Kees


Wouldn't the 1:3.15 ratio hold true only if the Tremaine Parsons iH curves were determined using Tunelab's equations? If he used Young's equations, which I think likely, then wouldn't the ratio need to be 1:4?

Good point. Tunelab IH values and Young IH values approximately differ by a constant, though the constant varies somewhat over the scale. If you accept that the tunelab model is more accurate then you could simply take the Young ratio as an approximation to the tunelab IH ratio and 3.15 will still be the best estimate.

Kees
Posted By: Gadzar

Re: Octave Sizes - 03/12/17 03:08 AM

Originally Posted by DoelKees
I could be wrong but I think you making a sign error.


You are right, I made a sign error. The correct widths for the 6:3 octaves are:

August Förster 6:3 = -1.66 cents
Hamilton 6:3 = -2.52 cents
S&S = - 0.75 cents

None of these octaves can be considered as beatless.



Posted By: DoelKees

Re: Octave Sizes - 03/12/17 03:23 AM

Originally Posted by Gadzar
Originally Posted by DoelKees
I could be wrong but I think you making a sign error.


You are right, I made a sign error. The correct widths for the 6:3 octaves are:

August Förster 6:3 = -1.66 cents
Hamilton 6:3 = -2.52 cents
S&S = - 0.75 cents

None of these octaves can be considered as beatless.


As is correctly predicted by the tunelab inharmonicity model, as the IH ratios are not close enough to 3.15. Though the S&S 6:3 beat rate of 0.45 is pretty good.

So I consider your point that these IH models can't predict beat rates correctly and that the individual partials need to be considered refuted.

Kees
Posted By: P W Grey

Re: Octave Sizes - 03/12/17 03:33 AM

I'm going to go down as saying that I do not want a totally beatless octave. I want to hear movement in it. I believe that from a musical perspective that is something that the pianist can sense and work with. A totally beatless octave sounds dead...lifeless to me both as a tech AND as a musician.

I will consciously expand the octave to get as much movement as I think that piano can stand. Not a repeating beat, but a beat that starts but doesn't finish in the amount of time I estimate it is likely anyone is actually going to play that octave.

This is what my ear and musical sense requires.

Feel free to disagree. I just wanted to go ahead and answer my own question.

Pwg
Posted By: Gadzar

Re: Octave Sizes - 03/12/17 03:55 AM

Originally Posted by DoelKees
On another note I did an extensive analysis of Prout's data set quite a while ago and concluded the partials fit the usual IH model very accurately with almost no exceptions.


Correct me if I am wrong but the differences I find between the calculated versus the measured iH for these 3 pianos in the partials of F3 and F4 are as follows:

iH(n) = B*[C(n)-1]

C(2) = 4
C(3) = 8.45
C(4) = 13.18
C(6) = 27.27

[Linked Image]


Differences between calculated vs measured partials range from -3.48 cents to +12.32 cents.

Am I right?

Posted By: Mark Cerisano

Re: Octave Sizes - 03/12/17 03:59 AM

I like the math but I have to agree that what the piano says in the matter is what counts. I.e. we need to take real notes, real F3, F4, A3, A4, for example, and try to tune it as a pure 4:2/pure 6:3 on every piano we tune, and then get an idea of how many pianos make this possible. That's what I have done for about three years now. That's where I get my opinion that there are many pianos where this is aurally possible within 3% for the check intervals.

Peter's comments are the first comments that actually answer my OP. Why would someone want to purposely detune a beatless octave? Answer: to create a roll that adds life to the piano. That I can understand. Tuning an octave to match the sound of an out-of-tune fourth/fifth just doesn't make any sense to me. But maybe I'm just a lightweight in the world of great tuners.

But that's ok. Having a solid procedure that allows beginners to tune solid, but lifeless, tunings is ultimately more powerful than teaching a method that produces beating imprecise octaves that contribute to the whole piano sounding out of tune, which is the way I learned, and had to unlearn.
Posted By: DoelKees

Re: Octave Sizes - 03/12/17 04:18 AM

Originally Posted by Gadzar
Originally Posted by DoelKees
On another note I did an extensive analysis of Prout's data set quite a while ago and concluded the partials fit the usual IH model very accurately with almost no exceptions.


Correct me if I am wrong...
Am I right?

You have mixed up lower and upper inharmonicities.

Kees
Posted By: DoelKees

Re: Octave Sizes - 03/12/17 04:24 AM

Originally Posted by P W Grey
I'm going to go down as saying that I do not want a totally beatless octave. I want to hear movement in it. I believe that from a musical perspective that is something that the pianist can sense and work with. A totally beatless octave sounds dead...lifeless to me both as a tech AND as a musician.

I will consciously expand the octave to get as much movement as I think that piano can stand. Not a repeating beat, but a beat that starts but doesn't finish in the amount of time I estimate it is likely anyone is actually going to play that octave.

This is what my ear and musical sense requires.

Feel free to disagree. I just wanted to go ahead and answer my own question.

Pwg

I agree. Not that I like an impure octave but in real music there are so many beating intervals anyways that you can easily sneak in a small roll in the octaves without detrimental effects. This is why I like to tune my octaves on the narrow side on my harpsichord to improve M10 and M17, but this is particular to the kind of music I like to play.

On the piano there may be different motivations such as larger stretch and wider octaves. It really depends on what the player likes.

Kees
Posted By: Rick_Parks

Re: Octave Sizes - 03/12/17 04:30 AM

Originally Posted by P W Grey
I'm going to go down as saying that I do not want a totally beatless octave. I want to hear movement in it. I believe that from a musical perspective that is something that the pianist can sense and work with. A totally beatless octave sounds dead...lifeless to me both as a tech AND as a musician.

I will consciously expand the octave to get as much movement as I think that piano can stand. Not a repeating beat, but a beat that starts but doesn't finish in the amount of time I estimate it is likely anyone is actually going to play that octave.

This is what my ear and musical sense requires.

Feel free to disagree. I just wanted to go ahead and answer my own question.

Pwg


I disagree profoundly - but respectfully smile

Again I'll say, tuning solid octaves is a basic principle to a concert tuning- supposed to be on par to tuning solid unisons.

To purposefully- willy-nilly add randomly thought up beats to octaves is what I would call "chaotic", and is not according to any proven tuning standards I was trained in...Perhaps I'm ignorant of 21st century (new-age) tuning; completely possible.
Again, I note that we are talking mid-range piano here--- not upper octaves or extreme bass... This is our temperament!

Where these ideas have come from is beyond my ability to fathom.

The professional aural tuner has always founded themselves on solidity and purity-- not fluidity of beat ratios, opinions of which interval I like best, and imposing beats of my own calculations.
Is this the 21st century world of tuning?
I'll stick with my ignorant 20th century, thank you.
Posted By: DoelKees

Re: Octave Sizes - 03/12/17 04:47 AM

Originally Posted by Mark Cerisano, RPT
I like the math but I have to agree that what the piano says in the matter is what counts. I.e. we need to take real notes, real F3, F4, A3, A4, for example, and try to tune it as a pure 4:2/pure 6:3 on every piano we tune, and then get an idea of how many pianos make this possible.


Agreed of course, and if theory disagreed we'd have to revise theory, but it seems theory is still mostly agreeing with reality here.

For example look at the data on the S&S Raphael posted here. With a pure 4:2 the 6:3 bps is 0.45, so if you slightly widen 4:2 to make them equal beating (as you advocate) they will beat at 0.23 which is probably aurally pure.

Kees
Posted By: Mark Cerisano

Re: Octave Sizes - 03/12/17 05:05 AM

Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT
I like the math but I have to agree that what the piano says in the matter is what counts. I.e. we need to take real notes, real F3, F4, A3, A4, for example, and try to tune it as a pure 4:2/pure 6:3 on every piano we tune, and then get an idea of how many pianos make this possible.


Agreed of course, and if theory disagreed we'd have to revise theory, but it seems theory is still mostly agreeing with reality here.

For example look at the data on the S&S Raphael posted here. With a pure 4:2 the 6:3 bps is 0.45, so if you slightly widen 4:2 to make them equal beating (as you advocate) they will beat at 0.23 which is probably aurally pure.

Kees


I would like to add another beautiful use of check intervals to tune precise octaves.

I have stated that the human ear's capability to hear beat speed differences is 3%, but when trying to tune a wide 4:2/narrow 6:3, we can decrease that window significantly.

Take your S&S example.

Suppose I were to come to that piano and tune the F3F4 octave, but hear it as a pure 4:2 and barely narrow 6:3. I hear the 6:3 as narrow because the M6 is more than 3% slower than the m3.

It is quite possible that, in order to tune the octave as a wide 4:2/narrow 6:3, that I raise the F4 and that I now hear the 4:2 as still pure, but the 6:3 has now become pure.

We can conclude that the 4:2 changed size, but is still beyond my 3% limit, so I didn't hear it change. However, the 6:3 did indeed change size from a narrow 6:3 to within the 3% limit of perception.

We could assume that this is a wide 4:2/narrow 6:3, but it is way more precise than we could have tuned just listening to the 4:2 or the 6:3. By listening to both the 4:2 and the 6:3 (using RBI tests) we have increased our precision greatly beyond the 3% limit.

Does this makes sense? I have some graphics that may explain better.
Posted By: BDB

Re: Octave Sizes - 03/12/17 08:05 AM

To add to the process of comparing octaves to other intervals, consider the multiple of the overtone that coincides with the octave that you are comparing. The more remote the interval, that is, the more you multiply by, the bigger the difference there is with a small variation in the pitch. So for instance, if you listen to the beat of the major third F to A, that will theoretically* be the same speed as the beat to the next higher A, as well as the next higher A, which is where the fifth (if I have that number right) overtone of the F coincides with the fundamental frequency of the A. That is, five times the frequency of that F is approximately that A, so that making those beats coincide requires the accuracy of the A to be much more accurate than just tuning to the A an octave below. In this case, a change in the frequency of 1 Hz in the top A would change the beat speed of the octave by 1 bps, while the change with that lower F would be 5 beats per second.

*or in actuality, depending on what you think the theory is.
Posted By: P W Grey

Re: Octave Sizes - 03/12/17 07:27 PM

Rick,

I thoroughly understand your viewpoint, and also appreciate your way of expressing it. Very nice! Let me explain some of what brought me to this viewpoint.

For years I felt exactly like you, but the first thing that got me started thinking differently was exposure to UTs through Owen Jorgensen (who I initially viewed as a NUT CASE!). However, my general open-mindedness and curiosity pushed me explore and to give it a try. I got the big book, read the background, was not yet convinced, but gave it a try. I had two nice uprights side by side in the shop, tuned one in ET as usual, then did my best at following his instructions for Thomas Young's 1799 WT "according to personal taste". Wasn't perfect, but not too bad.

Then I sat down to play...and it was basically an OMG moment. I remember thinking to myself as I was tuning it (WT)..."no way...there is no way anyone would accept noisy 5ths like this, some 3rds so slow as almost pure, some so fast they make your teeth grind...no way".

But...as I played I found that IN THE CONTEXT OF THE MUSIC, I didn't even notice it (unless I tried real hard to purposely notice it). Then of course I repeated the music in ET and found it so different (it was OK, but now it seemed to lack something)...back and forth WT...ET...WT...ET.

Then I started playing some of my own music (in WT) which tends toward the simpler keys (and therefore less dissonant than with many sharps and flats) and I started liking it more and more all the time, and liking ET less and less.

So, as time went by and I got better at tuning WT, I started offering it to certain clients who played exclusively pre-1850 repertoire. What I saw surprised me. It was the fact that these musicians (not only did they love it) they gravitated towards the more complicated keys with the fast beating RBI's (exactly the opposite of what I gravitated toward) but I would hear them "oohing and ahhing" over these sounds they had never heard before. At first I thought it was weird, but eventually realized that they were simply hearing things differently from me. They were hearing the MUSIC, not the piano per se (perhaps somewhat closer to the way it originally sounded). They liked it. So I eventually got to thinking...(always a dangerous thing).

The next step was Lucas Mason's book "The New Tuning" which we have all discussed in a different thread. My general open-mindedness made me check this out too. In this case I did not like what I heard when I tried his ideas...HOWEVER there is a chapter on psycho-acoustics that I thought was very interesting and had some food for thought. This was where I started thinking about expanding my octaves STARTING in the middle (which I previously had thought..."never"). I thought: "Hmmm, if my ear will tolerate WT 5ths and 4ths that would be considered HORRIBLE in ET, I wonder if I can tolerate wider octaves in ET (and everything else that goes along with that, as we all know) and would it sound good?". So I started experimenting.

What was interesting was that, not only did I like the sound of ET better this way (obviously when playing music specifically designed for ET) I started getting unsolicited positive comments from clients that their pianos sounded better. I wasn't influencing them in any way, simply playing with octave width, eventually finding a balance between too little and too much "stretch".

I eventually also learned that I could vary the "stretch" amount on certain pianos beyond what I would normally consider appropriate simply because the instrument "asked" me to do so to make it sound better. (NO, I AM NOT HAVING CONVERSATIONS WITH PIANOS!) You know what I'm talking about.

Still, some pianos "talk" better with a conservative approach, but I try to let the piano tell me what it wants to satisfy both my technical ear and my musical ear. Like the Verituner, sometimes it takes a second try after getting more information to get it where I think it should be.

I recognize that not everyone will agree with this MO, but my musical background forces me to be open-minded about it. I don't get it right every single time but I keep trying till I think it is. If the client/artist agrees, BINGO!

This is a SHORT history of how I arrived here. I hope you can understand (but you're not required to agree).

Pwg
Posted By: Bosendorff

Re: Octave Sizes - 03/12/17 08:34 PM

Originally Posted by P W Grey
They were hearing the MUSIC, not the piano...

Glad to read that coming from a pro tech about UTs. I use my own UT since 1990.

An analogy is piano teachers listening to a live performance. Many of them have a hard time appreciating the music, because they can't turn off their "analysis mode" while listening. I can have the same problem as well when I hear pieces that I play differently from the person I hear.
Posted By: P W Grey

Re: Octave Sizes - 03/12/17 10:57 PM

Currently my UT of choice to ease people into it is Bill Bremmer's EBVT.

Incidentally, there is at least one brand of piano I can speak of specifically that I know I must tune close, pure, clean octaves. That is the Charles Walter studio upright. Also, EBVT sounds great on this piano too, depending on the type of music they play.

At least this is my opinion.

I'm interested in other's viewpoints on UT but I assume that would be another thread entirely.
May have already discussed and I don't know about it.

Pwg
Posted By: Chris Leslie

Re: Octave Sizes - 03/13/17 01:20 AM

Yes, it has been argued ad infinitum over the years. Mostly the opponents have agreed to disagree and kissed and made up.

Start a new thread though and stand back.
Posted By: P W Grey

Re: Octave Sizes - 03/13/17 02:16 AM

That's ok
Posted By: Toni Goldener

Re: Octave Sizes - 03/13/17 07:01 PM

What do you think about these octaves? The octaves start at 2.09

https://vimeo.com/ondemand/27507/115504806?autoplay=1
Posted By: Rick_Parks

Re: Octave Sizes - 03/14/17 02:26 AM

Originally Posted by P W Grey
Rick,
I thoroughly understand your viewpoint, and also appreciate your way of expressing it. Very nice! Let me explain some of what brought me to this viewpoint......

That was quite some testimony, Peter (plenty of passion)... smile
Almost ye persuade me to be a Theorist. laugh

But, I'm not ready to be "open-minded". I know I used the phrase to express that I was keeping my mind open to Mark's ideas, but I try no to be "open-minded" for everything.
Mind really is just another word for spirit-- being open spirited technically means any spirit can wonder in--- (scary thought)-- the results can be devastating, and work irreversible damage!
Now, apply that to our profession, and you'll understand my approach to these ideas (it's just a lesser form - and can work the same sort of damage to my professional attitude).

I am glad for the story you tell, since it shows me your progressive approach and how it has led you to your current reasoning.

I do have a problem however with these attitudes toward theory and experiments, and what it has (and will) lead to--- I noticed something you said:
Originally Posted by P W Grey

......So I started experimenting.
What was interesting was that, not only did I like the sound of ET better this way (obviously when playing music specifically designed for ET) I started getting unsolicited positive comments from clients that their pianos sounded better. I wasn't influencing them in any way, simply playing with octave width, eventually finding a balance between too little and too much "stretch".
Pwg


I hope I am misunderstanding-- but thie appears to come accross to me as an example of something that I've been talking about all along in these forum debates-- when speculations, and theories get out of hand, people begin thinking they can (must!- because the piano is asking them to) toy with the tuning on customers' pianos without approval!...
The profession I am apart of, requires me to stand up and protest such a thing---- again- IF this is what you mean... I'm not quite clear as to that being what you meant.

For one thing-- had they not liked your unkown experiment, wouldn't your reputation have pretty much been hurt?

But the more important point that I do think that our profession dictates that at the least we do the standard ET (with no funny manipulations)- unless the customer is educated about, and wishes otherwise. It would never even come into my head to experiment with a customer's tuning without their being aware of it!

These are the exact things I fear happening from people who allow theory to become "truth".
It happens (and has happened over the ages) in many other realms of life throughout the world- not just here.
And I stand on guard against it in my own life- not to let my own ideas carry me away.

AND, there was one more thing that I simply do not agree with---- this dea that the music can sound better, while the way the instrument sounds placed in an altogether different category. confused
Blame will be placed on the standard issue ET for the dull sound of the music (yet the great lack of offensive intervals), by the same people who say these things about the color-filled UT (or ET stretched octave, altered pure 5ths, etc).
The temperament IS the instrument's voice is it not?! Either the voice sounds good or it doesn't. Either it is in tune or it is not. If I have a interval that is a "wolf"- (or in some of these ideas multiple wolves)- the voice is cracking in the attempt to sing-- I.e. there's a fault(s)... While, IF I have a voice that is pretty much solid, and no offensiveness in any song sung-- I am sure to win the contest smile

Again- there are places for UT's - this is not my argument.

My fear here is that there is a great push to REDEFINE "tuning"... Traditional standards turned into chaotic opinions will destroy your profession. Just as sure as endless debates on theories and unproven (unprovable) ideas will only lead to devouring one another.

My thoughts on the matter. I think I'm done with these kind of debates.


It just strikes me in all of this (even more after this post- thank you Peter smile ) that the artists' emotions are getting in the way of the professional's reasoning of standard practices... Perhaps it is just me- as I am adverse to going on my emotional momentary experience (I am not a musical artist) rather than established truths (I am a firmly grounded realist- and a 'proven standards' torchbearer).
Posted By: P W Grey

Re: Octave Sizes - 03/14/17 02:31 AM

No contest there. I understand.

Pwg
Posted By: Mark Cerisano

Re: Octave Sizes - 03/14/17 03:24 AM

I read your post with interest Rick. And I agree with your concern.

Let me tell you the story of how I got here.

When I started teaching tuning, I was challenged by trying to find descriptions to help people get good results. "Tune it so it sounds good" is pointless if the student has no idea what sounds good.

So I started to analyze my own tunings. I measured beat rates, calculated differences, and recorded intervals. I began to find a pattern that developed from my measuring of octaves that I tuned as pure as possible.

Note, I was not trying to find a new way to tune, only trying to quantify what I was already doing.

It is often the same arguement when it comes to music theory. The composers first wrote the music, and then the theorists write the theory about it. The composers didn't write the theory first and then compose.

So I hope you see that my interest in theory is to facilitate a student's learning curve, and not to redefine what a good tuning is.

Great post.
Posted By: P W Grey

Re: Octave Sizes - 03/14/17 02:54 PM

Rick,

I just re-read your post and I guess I should clarify a thing or two.

It would appear that I used a less-than-ideal expression when I wrote "simply playing with octave width"... I can see how you (and others) might see this as toying willy-nilly with clients pianos without their permission. IMO this is not what I do (or have done).

Since I also have a reasonably long musical background (50 years at this point), when I tune a piano, I KNOW (within 95% accuracy) if it sounds good or not. I have a pretty good understanding of ET, scaling issues, inharmonicity (although in an analog way rather than digital), I know what's "clean" and what isn't. However, I am not afraid to make adjustments in the tuning if my "musical ear" registers that my "technical ear" is not getting the job done to my satisfaction.

Now before someone starts to say: "But you are being paid to tune for the client...their interests come first...not your opinon...blah, blah, blah..."

I KNOW THAT! I didn't fall off the turnip truck yesterday!

But the fact is that the vast majority of our clients leave the decision making in OUR hands to make (or try to make) their piano sound the BEST IT CAN BE. If that requires (in my judgement) some deviation from what I was originally taught, I feel it is my responsibility to do that. No, I am not going to bring them over to the piano and explain in detail what "the book" says, and why their piano has one thing or another about it that causes me to do this or that and ask: "Can I please have your permission to do this?" No...what they want is for me to use my skill and experience to make their piano sound as good as possible. And that is what I do. I happen to know that 99% of the time IF I AM HAPPY with the result, they will be too.

I do not tune every instrument exactly the same. I will not tune the performance piano the same as the recording studio piano. I will not tune the chamber music piano the same as I will tune the jazz pianist's piano. I will not tune the spinet the same way as the glorious Steinway B. If ET is being tuned on all of these instruments, I will apply my skills to tune ET on each one, but there will be some differences. It is not a one-size-fits-all profession we are in, nor is it a matter of "obeying the law" vs. "dis-obeying the law". (How many of us have ever driven 55 or 60 mph in a 50 mph zone?) THIS IS JUST AN ILLUSTRATION!

Let's carry that illustration a little further... As we travel down a main road we have to our left a double yellow line (for instance), and on our right a white line. Between these markers is a certain amount of space in which we are allowed to drive (assuming we have a license and are not DUI). Generally speaking, travel anywhere in between these lines is permitted and appropriate. We are not required to rigidly adhere to X feet from the yellow line and Y feet from the white line. No, there is flexibility for obvious reasons. However, CROSSING either of these lines is going to have ramifications, and under normal circumstances we should not do it.

Similar with tuning. Certain parameters must be adhered to in tuning ET, however reality dictates that we also have a certain amount of flexibility within those parameters (boundaries) to make the "musical driving experience" safe and pleasant. I don't need a backseat or passenger seat driver second-guessing every single move I make while I'm driving. That will prove to be a trip I don't want to make again. If though, I'm acting recklessly, that's a different story.

I don't think you are actually accusing me of "driving recklessly", though there is a slight hint of that in your post. You can be assured that I stay within the proper bounds of accepted ET tuning practice. I am not "inventing" anything new, nor changing the rules or theories to fit any wacked out ideas of tuning. But if I read something or observe something (tuning related) that I hadn't been taught, or hadn't occurred to me, I'm usually willing to give it a try. Some of this I have accepted and use, some of it doesn't seem to work for me so I don't practice it.

Finally, one case in point. Just last week I had to tune a 60's Chickering (Aeolian) grand. Temperament section worked out surprisingly well (I say surprisingly because my experience tells me that similar pianos have problems in that area). Bass...not too bad...pretty much followed the rules. But as I got going past the tenor/treble break it quickly became apparent that if I left it TECHNICALLY correct (as some would define it), the treble was going to sound seriously flat (partly an IH issue and partly a soundboard condition issue. Therefore, (IMO) I was going to need to stretch octaves (as it turned out) ACTUALLY WIDER THAN I AM NORMALLY COMFORTABLE WITH. I tried one thing and I tried another and finally I said: "Okay, if this is what it wants (to be musical), this is what it's going to get". In the end it sounded quite good (for what it was), I was happy, owner was happy, piano was "happy". And I'll see it again in a few months and maybe I can do an even better job with it.

I am not even going to go into UT because that's a "whole 'nother ball game".

But I hope you will understand that I am not taking liberties and creating anything "new under the sun". Of course you are still free to disagree (of course without being disagreeable). :-)

Pwg
Posted By: rysowers

Re: Octave Sizes - 03/14/17 08:53 PM

As someone who has been involved with administering the tuning exam for the Piano Technicians Guild for over 20 years I can tell you beyond the shadow of a doubt that many tuners are not achieving great ET in their everyday work. The PTG tuning exam allows an accumulation of 13 errors in the midrange between C3 and B4. An error is defined as any note that deviates a cent or more from our master tuning. A note that deviates 2 cents or more is considered two errors, and a note that is 3 cents off is considered 3 errors.

Theoretically, adjusting C4 and A# upwards by 2.9 cents in the temperament octave will change an ET tuning to a well tuning by making the CE third and the A#-D third a little sweeter and the A#-C and F#-A# thirds a little more dissonant, yet if all the other notes are within tolerance a temperament such as this will score a 90%, which is considered a very good score.

I just think we need to be realistic about how precise actual practice is. And this is just the midrange area - the tolerance for the low bass and high treble is 6 cents, meaning you can be 5.9 cents sharp or flat and have the note count as "perfect".

Granted, that some feel the PTG exam is not picky enough, but when it was created Dr. Sanderson and Jim Coleman spent a lot of time studying and measuring the tunings of working professionals to create a baseline.

So yes, there is certainly leeway in what is considered a professional level tuning. The old tuners have always said that stability, unisons and octaves are the most important aspects of a tuning. As long as the temperament is somewhat even, it will be extremely unusual for a client to complain.
Posted By: UnrightTooner

Re: Octave Sizes - 03/14/17 09:32 PM

Originally Posted by rysowers
As someone who has been involved with administering the tuning exam for the Piano Technicians Guild for over 20 years I can tell you beyond the shadow of a doubt that many tuners are not achieving great ET in their everyday work. The PTG tuning exam allows an accumulation of 13 errors in the midrange between C3 and B4. An error is defined as any note that deviates a cent or more from our master tuning. A note that deviates 2 cents or more is considered two errors, and a note that is 3 cents off is considered 3 errors.

Theoretically, adjusting C4 and A# upwards by 2.9 cents in the temperament octave will change an ET tuning to a well tuning by making the CE third and the A#-D third a little sweeter and the A#-C and F#-A# thirds a little more dissonant, yet if all the other notes are within tolerance a temperament such as this will score a 90%, which is considered a very good score.

I just think we need to be realistic about how precise actual practice is. And this is just the midrange area - the tolerance for the low bass and high treble is 6 cents, meaning you can be 5.9 cents sharp or flat and have the note count as "perfect".

Granted, that some feel the PTG exam is not picky enough, but when it was created Dr. Sanderson and Jim Coleman spent a lot of time studying and measuring the tunings of working professionals to create a baseline.

So yes, there is certainly leeway in what is considered a professional level tuning. The old tuners have always said that stability, unisons and octaves are the most important aspects of a tuning. As long as the temperament is somewhat even, it will be extremely unusual for a client to complain.


Thanks Ryan, for questioning the accuracy in our tunings. It makes me wonder just how much of what has been posted in this Topic is irrelevant. Kinda like when you buy a box of paper clips that says "100 count." It maybe be 95, it may be 105. So too with the octaves we think we are tuning. They may be 4:2, they may be 6:3. And so too with any particular temperament. It may be ET, it may be UT.

Furthermore, if a tuner was to change how he tunes for whatever reason and decides that since he only hears positive feedback, it must be an improvement, can be very deceptive. What piano owner is likely to question a tuning he isn't sure is all that pleasing? More likely the owner will "trust the expert" rather than risk embarrassing himself. But the few that DO hear an improvement and mention it may create a very biased feedback.
Posted By: P W Grey

Re: Octave Sizes - 03/14/17 09:43 PM

In addition to what Ryan pointed out, the aural verification portion of the test clearly shows whether an applicant UNDERSTANDS ET, understands how to achieve it, and whether or not he/she has the skills to find and correct errors.

It is a very fair test, with reasonable latitude.

Furthermore, the applicant is informed that he/she is being asked to tune the piano in a specific way (NOT necessarily the BEST way, nor the way THEY would normally tune it), octave widths are specified, guidelines are given. This tests whether the applicant has the skills to cooperate and actually achieve something that they may not ordinarily do. If they can do this then they probably have the skills to satisfy just about anyone in the real world.

I took my test under Dr. Sanderson. He was a swell guy, and humble too. A rare quality these days.

Pwg
Posted By: rysowers

Re: Octave Sizes - 03/15/17 04:48 AM

Peter,

That is AWESOME that you were tested by the one and only Dr. Sanderson! What a great memory that must be.
Posted By: Rick_Parks

Re: Octave Sizes - 03/15/17 11:28 AM

Originally Posted by P W Grey
Rick,

I just re-read your post and I guess I should clarify a thing or two.

It would appear that I used a less-than-ideal expression when I wrote "simply playing with octave width"... I can see how you (and others) might see this as toying willy-nilly with clients pianos without their permission. IMO this is not what I do (or have done)...

Pwg


Peter,
Thanks for clarifying that... You have to understand my position here-- I'm watching a debate on opinions and ideas and a lot of theories, and someone says they "started experimenting...". That (to me) means a person is trying something he never has done before-- and you mentioned doing this on the customers' pianos... I'm glad it was a mistake in understanding what you meant smile --- as you see, I don't let anyone get by if I think they have gone off the deep end LOL... Signs of a true friend is it not? grin

It is impressive experience-- yet IF you had been doing what I took it to mean, I still would have called you out...Only, had I realized your position over me in age and background I would have been more respectful in my approach... Sorry.

That said, I do understand your points. I don't think any of us tune EQ the same for every piano we come up against; this has not been my point at all...Since it does indeed require borrowing from different areas for each unique instrument to come out good... BUT, again I must stress my position to people of a solid temperament octave- (at the least)-- and as solid octaves as possible from then forward! PLEASE! lol

My position hasn't change from 3 threads back in these debates...One should not take it upon themselves to install theory and self-opinionated ideas "wily-nilly" (yes I used that word) into the standard practices of the profession... At least and expect to be viewed (at least by me) as having a professional mindset toward this field of work.



As far as the PTG tuning test---
A full 1-cent margin is a lot of room before being corrected on it in points... And I would think that 3 cents off from the "Master Tuning" on any mid-range note should disqualify a tuning altogether.
If a WT can pass grades as an ET, then in my opinion there's a change in grading needed. This is not to even mention how far out the bass is allowed to be before correction is applied.

It would appear to me easy to keep between the yellow line and the solid white line-- IF the road on which you have been placed is 3 lanes on each side!

But, IF it is a matter of getting more cars on the road--- watch out! don't mind that driver there!--- (each with a license requiring yearly dues)--- by increasing that road's width? Well then, there is another matter altogether that should be discussed.
* This is not meant as a knock on anyone who holds a PTG membership-- just food for thought about the process and the why it might actually be that way... If you are going to have a test-- don't dumb it down (public school for tuners?).
Posted By: P W Grey

Re: Octave Sizes - 03/15/17 03:25 PM

Agreed on all counts!


In reference to the PTG exam...it is actually more difficult than some would think. A lot of thought went into it. And, there are many misconceptions about it, particularly due to the "tolerances" allowed in the actual tuning part.

First, the "master" tuning applied to the test piano is not intended to be the "best" of all possible tunings for that piano. It is to be the BEST VERIFIABLE tuning (via aural testing) that can be applied to that instrument. So the examiners (3 altogether) follow exactly the same instructions that are given to the applicant, and create as perfect (as they believe possible) a temperament within a 4:2 (perfect) octave, expanding with clean octaves (no stretching beyond IH requirements), then clean 2:1 octaves in the high treble. Then it is recorded electronically.

The intention here is to make it objective, eliminating the subjective preferences that any tuner might have. Aural tests are clear and concise, and verifiable with standard, accepted practice. No funny business!

Second, the applicant is given these exact instructions (same as examiners) and then tunes the piano (middle strings only). If the applicant doesn't understand the instructions then we have a problem right out of the gate. Usually they do...but again no funny business, don't try to impress anyone with your ability to make the piano sound great! Just do it as instructed.

Third, (and I think this is the best part of the exam) is the aural verification portion, where the applicant sits at the piano, listens to notes that MAY be in question and is asked to determine whether that note is sharp or flat in relation to the others (according to standard accepted ET requirements). This is (as AL Sanderson would put it): "Time to prove the examiners wrong!". The applicant uses all the tests he/she knows, to determine if the temperament would be improved by moving it. If the tests agree that the note "should" be moved then a point is scored in error. However (and this is the fun part), if the applicant did a good job of fitting things in (although perhaps slightly askew from the master tuning), the aural tests may very well show that note to be in the best place possible already, and that moving it would be detrimental to the temperament. Then, (as the Doc would say): "We get to throw that one out!". No adverse score. (He made it fun and showed that he was with you, not against you).

And it goes on like that for the rest of the piano. This process is extremely important and very often opens the eyes of the applicant to themselves, their tuning, and their attitude. It quickly becomes clear to the examiners if this person really understands what they are doing and how to improve it. If the tuner has the skills, the process can take as little as 10-15 minutes for the whole piano. If though, the applicant doesn't quite get it, or is argumentative, it can turn into a grueling process.

But it truly shows up whether they know what they are doing or not...very objectively in my experience. And that was the crux of what Doc Sanderson (and Jim Coleman, I believe) was trying to get at with test.

Finally, unisons and stability are tested, again very objectively with standardized procedures.

Yes, there are some extreme "if's" and "coulds" that theoretically could slip through, but again as Dr. Sanderson eloquently said: "Tuners don't normally tune that way". He knew what he was talking about and was quite careful to try to eliminate MOST variable factors.

Ryan may also be able to update my accounting here with other relevant data. Please feel free to do so.

I have to go finish cleaning up after the blizzard of 2017 here.

Pwg
Posted By: rysowers

Re: Octave Sizes - 03/16/17 02:12 AM

Nice description of the exam process, Peter. I agree with your sentiments on aural verification. It really legitimizes the whole exam and it can be an educational experience for the examinee.

Rick: If you think the exam standards are not high enough, I suggest you give it a shot. You might find it a snap, or you find that its more challenging than you thought! It's really a great deal for $180: You get 3 experienced tuners spending 4 hours evaluating your tuning skills. It should be a lot more expensive when you consider the money they could have all made tuning a couple of pianos during that time. The PTG is generally a very giving and generous group.

The exam is not supposed to test for high end skills. Its goal is to set a realistic bar for entry level skills in our industry. It's really a starting point.
Posted By: Rick_Parks

Re: Octave Sizes - 03/16/17 02:30 PM

Originally Posted by rysowers
...Rick: If you think the exam standards are not high enough, I suggest you give it a shot. You might find it a snap, or you find that its more challenging than you thought! It's really a great deal for $180: You get 3 experienced tuners spending 4 hours evaluating your tuning skills. It should be a lot more expensive when you consider the money they could have all made tuning a couple of pianos during that time. The PTG is generally a very giving and generous group.

The exam is not supposed to test for high end skills. Its goal is to set a realistic bar for entry level skills in our industry. It's really a starting point.


I was offered to get PTG membership back during my first years of employment with a company in MD... I chose not to for some fundamental differences of approach, which I believe in professionally. I can give the reasons if people wish, but I prefer to keep it to myself, since it tends to cause arguments.
I still could not consciously join, being aware of certain aspects and practices.

I do very much appreciate many things that the PTG has made possible (I do not argue its benefits to our profession)- for one, is the great share and wealth of info, data, findings and such...
I do not very much appreciate the way many PTG members tend to behave toward (about) me for my not being (or wishing to become) a member-- both privately to the face, and publicly behind my back (with suggestions to clients about my abilities, or rather a possible lack thereof).

While I am an outsider- I do see many things, and have many thoughts for improvement that would benefit the organization... One for instance is structural: if the PTG were to have standard tests other than entrance level. For example, Entry Level, Professional, Master Tuner. While, yes this might be a source of hesitation, and even of possible loss of some members who would be intimidated by the process- it would give a united sense of purpose and a common goal to shoot for, for all its members. The Master Tuner level would be something all would strive to achieve to become, as members (the purpose of the guild if you would). More like the educational structure of the school system (k - college, and doctorate)- only without dumbing down anything.
I would think the end result would be more money for the PTG anyway.
The way it is set up right now- strikes me as more of a union...Pass the basic test, pay your dues, and we are all RPT now! (kind of thing)...Again, this isn't to ridicule or put down, just basic thinking for improvements.


I might also say that this would shape a better piano tuning market out there-- with customers aware of what they were paying for (an entry level tuner would not going to be charging master-tuner prices). The customer could then be more openly informed as to what exactly they are getting under the PTG brand.

LOL But this is all very much off topic-- why doesn't someone start a thread for PTG critiquing and improvement suggestions laugh
I DARE YOU! LOL
Posted By: P W Grey

Re: Octave Sizes - 03/16/17 03:48 PM

Back to the topic of octave sizes, since Jeff (and I think Rick) wrote down the specific test for a perfect 12th (partly at my request):

1) It turns out that yes, I already knew this test, but not specifically as relating to the 12th but rather as a barometer for double octave width (as espoused by Rick Butler and others).

2) My general MO has long been to use the M17>M3rd test (which is essentially the same test) to determine the width of my double octaves.

3) The main difference (as I see it) is that one compares identical beat speeds (showing purity) whereas the other compares relative beat speeds (showing expansion).

4) So what I found in analyzing my general tendency to expand octaves is that, in general, my practice is to have the 12th JUST BARELY shy of pure, so that the 3rd-17th test shows about one beat difference, or slightly less.

So, just in case anyone reading all of this has been under the impression that I am out there stretching octaves into outer space...no...my practice is well within the realm of normal professional practice.

Part of the reason this seems to work for me is that since part of my musical training is as a percussionist, I am much better at comparing relative beat rates than I am at judging purity of an interval. IOW I come to it more from the "outside" than from the "inside" if that makes sense to anyone.

I rarely (if ever) actually TUNE a 5th for instance (I'll listen to it briefly), but I'll almost always use the 6th-10th test to check it's width. My ear has difficulty in judging at face value whether it is pure, contracted, or expanded, so I prove it with the tests. Same with octaves, so I always rely on the outside tests.

I know everyone else does this too, but I think some techs are actually better at hearing the slow beating intervals, or even pure. I just see this as a difference between people and the way we hear things.

I want to thank the forum members for helping me refine my tuning even more!

Pwg
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