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Octave Sizes
#2618843 02/28/17 10:26 AM
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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".


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Re: Octave Sizes
Mark Cerisano #2618846 02/28/17 10:40 AM
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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

Re: Octave Sizes
Mark Cerisano #2618848 02/28/17 10:47 AM
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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?

Re: Octave Sizes
Mark Cerisano #2618852 02/28/17 11:05 AM
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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.



Last edited by Gadzar; 02/28/17 04:18 PM.
Re: Octave Sizes
RonTuner #2619015 02/28/17 08:08 PM
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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


Joe Gumbosky
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Re: Octave Sizes
Gadzar #2619088 02/28/17 11:49 PM
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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

Re: Octave Sizes
DoelKees #2619092 03/01/17 12:06 AM
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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.


Re: Octave Sizes
Gadzar #2619097 03/01/17 12:28 AM
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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

Re: Octave Sizes
Mark Cerisano #2619216 03/01/17 10:25 AM
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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?

Re: Octave Sizes
Mark Cerisano #2619223 03/01/17 10:50 AM
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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.


Jeff Deutschle
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Re: Octave Sizes
Mark Cerisano #2619257 03/01/17 12:33 PM
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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!


Ed Sutton, RPT
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Re: Octave Sizes
Ed Sutton #2619259 03/01/17 12:38 PM
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Re: Octave Sizes
Mark Cerisano #2619285 03/01/17 01:15 PM
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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?

Re: Octave Sizes
Mark Cerisano #2619299 03/01/17 01:31 PM
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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.


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Re: Octave Sizes
Mark Cerisano #2619307 03/01/17 01:44 PM
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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.


Ed Sutton, RPT
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Re: Octave Sizes
Ed Sutton #2619357 03/01/17 04:03 PM
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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!


Re: Octave Sizes
Ed Sutton #2619379 03/01/17 05:17 PM
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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."


Re: Octave Sizes
Mark Cerisano #2619430 03/01/17 07:00 PM
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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.


Jeff Deutschle
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Re: Octave Sizes
UnrightTooner #2619467 03/01/17 09:26 PM
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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!


Last edited by Rick_Parks; 03/01/17 09:29 PM.

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Re: Octave Sizes
Mark Cerisano #2619498 03/02/17 12:40 AM
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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?

Last edited by daniokeeper; 03/02/17 12:55 AM.

Joe Gumbosky
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