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Re: Octave Sizes
Kent Swafford #2620684 03/05/17 09:32 PM
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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... :-)

Last edited by Mark Cerisano, RPT; 03/05/17 09:32 PM.
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Re: Octave Sizes
Mark Cerisano #2620687 03/05/17 09:52 PM
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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.





Re: Octave Sizes
Gadzar #2620691 03/05/17 09:59 PM
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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)?



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Re: Octave Sizes
Kent Swafford #2620693 03/05/17 10:29 PM
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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.)


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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.



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Re: Octave Sizes
BDB #2620697 03/05/17 10:59 PM
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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

Re: Octave Sizes
Mark Cerisano #2620699 03/05/17 11:09 PM
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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.

Last edited by BDB; 03/05/17 11:14 PM. Reason: Added link to "elsewhere"!

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Re: Octave Sizes
Mark Cerisano #2620723 03/06/17 12:46 AM
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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!

Re: Octave Sizes
Mark Cerisano #2620728 03/06/17 01:15 AM
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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

Re: Octave Sizes
Mark Cerisano #2620778 03/06/17 08:24 AM
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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?


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Re: Octave Sizes
Mark Cerisano #2620788 03/06/17 08:51 AM
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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

Last edited by Mark Cerisano, RPT; 03/06/17 09:07 AM.
Re: Octave Sizes
Rick_Parks #2620802 03/06/17 10:33 AM
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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.



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Re: Octave Sizes
Mark Cerisano #2620812 03/06/17 11:16 AM
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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


Peter W. Grey, RPT
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Re: Octave Sizes
Rick_Parks #2620818 03/06/17 11:34 AM
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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...


Re: Octave Sizes
P W Grey #2620826 03/06/17 11:48 AM
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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!)

Re: Octave Sizes
Mark Cerisano #2620834 03/06/17 12:09 PM
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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.

Last edited by Mark Cerisano, RPT; 03/06/17 12:11 PM.
Re: Octave Sizes
Mark Cerisano #2620847 03/06/17 12:26 PM
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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


Peter W. Grey, RPT
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Re: Octave Sizes
Mark Cerisano #2620857 03/06/17 12:52 PM
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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.

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Re: Octave Sizes
P W Grey #2620882 03/06/17 01:35 PM
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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.


Jeff Deutschle
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Who taught the first chicken how to peck?
Re: Octave Sizes
Mark Cerisano #2620904 03/06/17 02:19 PM
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Thanks Jeff!

Pwg


Peter W. Grey, RPT
New Hampshire Seacoast
www.seacoastpianodoctor.com
pianodoctor57@gmail.com
https://www.youtube.com/watch?v=PK0T7_I_nV8
Re: Octave Sizes
Kent Swafford #2620986 03/06/17 08:06 PM
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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


Parks and Sons Piano Service
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