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#1475412 - 07/16/10 10:02 AM Re: How to tune Tempered Octaves ? [Re: pppat]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7222
Loc: France
Hello anyone ,
A little time to read you lately.

I believe that because we tuners are fighting with iH on a daily basis, we finish with a practical way that only deal with ih, and that our hearing focus more on the beats created at the partial match level, more than a listening that I would call "musical" and that imply that whatever iH level is present in a note, what a musician (or eventually a tuner) is hearing is a note with a (more or less) fixed pitch.
That pitch is tuned, if so, the tuning will be immensely more musical than any smoothing of a partial series, (this can be very evident in the medium range of pianos tuned with a smoothing of the 3d partial and thats all)


When tuning and listening to the movement produced by 2 notes of an interval as a whole, we are more near the way the interval is listened by the musician than when tuning with all those partial beat comparisons.

the beats are then produced by a mix of different partials, plus fundamental when they play a role

I believe that the common tests used are a shortcut that allow us to deal with iH in some way, but they can be misleading.

I had yet the proof that even in a thirds progression, one can have an uneven progression at 4:3 while the global beating of the thirds is progressive (as seeen with an EDT that show a kind of progressiveness, while the precedent tuner obtained a different progressivness by other ways.

Yamaha tuning practice learn to listen to some kind of 2:1 octave all along ("pure " octave. Of course , if dissected by the partial Rick Baldassin and Sanderson theory, you will find very different kind of octaves all along, but the goal and the ear training implies only somehow "pure" intervals.

I see that like just a way to listen directly to a final output which is supposed to be more musical than one only based on the iH partial theory.

I guess that one of the most respected tuners in America had put a finger on that a long time ago. But the need to have an understandeable theory (the beat's theory) and to have means to control our work , have put that method as the basis for learning.

For what I see experimented tuners often learn to directly tune intervals and listen to them in a musical way.

that 4:2 6:3 compromise is a way to have a medium octave that is stretched a little, but it have no real justification to me, it would have if that compromise allow to gain a good relation for intervals above and under there.

How is the 2:1 relation when a 4:2 6:3 octave is tuned ? it varies from piano to piano.

The coupling of near pitches in air (or whatever medium) is an effect which is laid aside in the partial theory.

This is just a method, among others.

I wish a good summer to all !










Edited by Kamin (07/16/10 10:13 AM)
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#1475502 - 07/16/10 11:56 AM Re: How to tune Tempered Octaves ? [Re: Bill Bremmer RPT]
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21286
Loc: Oakland
Originally Posted By: Bill Bremmer RPT
Originally Posted By: BDB
Well, I have explained what I do. What I get in response is people telling me that I cannot do it that way.


The story of my life.

Yes, but after people say that, I decide they do not want to hear about it and move on.

Mathematics will only take you so far. I have a degree in math, but I have learned that sometimes it is not worth obsessing over too much detail. I had a lesson in this when I was working on a budget with a group of people. I brought my computer, and had a spreadsheet with everything we were proposing. At the end, I looked at it and saw we were over by $1 million. Someone else pointed out that our budget was $400 million, so that amount of error was statistical noise.

Most of what people argue over when it comes to tuning is statistical noise. Inharmonicity is statistical noise. The difference between different octaves is statistical noise. The difference between different temperaments can be statistical noise.

In the end, I tune pianos so they sound like they are equal tempered. Maybe someone can measure them with some device and find some deviation, but that is no more guarantee that there is anything wrong with the tuning. The device may not be correct. They are subject to noise, as well.
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#1476131 - 07/17/10 02:15 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Cashley Offline
500 Post Club Member

Registered: 08/16/09
Posts: 530
Originally Posted By: UnrightTooner

So tuning ET on a piano is not about tempering all intervals types the same amount from just intonation. It is about making it seem that way by tuning so that beatrates are progressive. And by progressive, this can include getting steadily faster and then steadily slower. And it is possible to do so with many different schemes for stretching.


Does that mean if the 5ths and 4ths in the Temperament Octave are not tuned to precision, but nevertheless the M3s somehow manage to move progressively, the Temperament Octave is considered good ? Or that a series of nprogressive M3s is far more important than a series of exacting 5ths and 4ths ?

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#1476140 - 07/17/10 02:32 PM Re: How to tune Tempered Octaves ? [Re: pppat]
Cashley Offline
500 Post Club Member

Registered: 08/16/09
Posts: 530
Originally Posted By: pppat

Because you will have to deal with inharmonicity anyways in extending the temperament upwards and downwards, most tuners consider it's a good idea to make the initial temperament octave a little wider than a theoretical 2:1 octave, in order to make the transition from temperament to temperament extension as smooth as possible.


Have you just explained something in that paragraph ? There is a connection that is lost between the two statements : (1) it's a good idea; and (2) in order to make the transition from temperament to temperament extension as smooth as possible.

My question : Why is that so ? Basically you're saying we tune the temperament octave a bit wider so that when we 'duplicate' the octaves upwards and downwards the transition will be smooth.

But why would the transition be smooth just because we tuned the temperament octave wider ? You see my point ? A question seems to have been answered, but it begs the same question again. And what do you mean by smooth ???

If you tell someone to tune the octave with a slight beat and say that it will make your subsequent extension of octaves smooth, then the question that would come begging (as far as a layman is concerned) is what kind of 'roughness' would we encounter if we were to tune it beatless ?


Originally Posted By: pppat

It is, by most tuners, considered the best compromise, because the two cornerstones of harmony - 1) the unison 'echoed' 12 half steps above/below, ie the octave (2nd partial), and 2) the fifth (the 3rd partial) - sound as good as they possibly can do in the same tuning.


I'm completely lost ! I could read and understand every word, but together I just couldn't piece up the message.

Originally Posted By: pppat

Stretching is not only justified - it is desperately needed smile Just as Mark says, due to inharmonicity, if the octaves are matched on their 2:1 partials (= what Mark describes as pure), the bass is painstakingly sharp, and the treble is unbearably low. To the listener, in any musical context, they piano sounds horribly out of tune.


I'm not saying that stretching is justified or not justified. I'm saying Mark made a statement about stretching, but what is the 'explanation' that accompanies the statement made ?


Edited by Cashley (07/17/10 02:47 PM)

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#1476143 - 07/17/10 02:36 PM Re: How to tune Tempered Octaves ? [Re: Bill Bremmer RPT]
Cashley Offline
500 Post Club Member

Registered: 08/16/09
Posts: 530
Originally Posted By: Bill Bremmer RPT
Cashley, I was able to edit my post from this morning. I added some material for clarification. Please read what I wrote again before reading what I have to say now.


Mr Bremmer, I have no idea which material you're referring to. You have so many materials in so many websites confused

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#1476149 - 07/17/10 02:54 PM Re: How to tune Tempered Octaves ? [Re: Bill Bremmer RPT]
Cashley Offline
500 Post Club Member

Registered: 08/16/09
Posts: 530
Originally Posted By: Bill Bremmer RPT
Cashley, I was able to edit my post from this morning. I added some material for clarification. Please read what I wrote again before reading what I have to say now.

A piano can be tuned from a central, temperament octave that sounds "pure" to the ear. There is no argument or question about that. However, there is the inevitable dilemma that I wrote about in my previous post. Tuning a temperament octave that sounds "pure" will please the ear for music played within the central octaves. In some cases, this is what may be most appropriate.

For a person learning tuning and wishing to pass a tuning exam, this is the best approach if that person also uses an Electronic Tuning Device (ETD) and is permitted to use it to tuned the outer octaves. Making the temperament octave "slightly" wide is a technique that advanced aural tuners may use so that they can best resolve the dilemma of tuning the outer octaves. For a novice, this is often too much to comprehend and execute properly. It is therefore recommended that someone who wishes to take a tuning exam use a more conservative approach and tune the temperament octave so that it sounds "pure".

There are other circumstances where a pure sounding temperament octave is most appropriate. The pianist may only usually play within the midrange. All harmony will sound "sweeter" within octaves that are not stretched beyond the point of beatlessness. The outer octaves may sound "flat" with such a tuning but if they are not generally used, they do not matter.

On the other hand, the finest art of tuning is most often described under the circumstances of the finest pianos tuned for performing artists who utilize the entire keyboard. For those pianists, having triple octaves that are in tune is more important than the kind of "strained" harmony in the midrange that such octave stretching produces.

I digress only momentarily to say that the EBVT III with tempered octaves allows for both pleasant harmony in the midrange and the expected clarity of the outer octaves. Any of the current or future recordings on The "My piano in the EBVT III" thread will confirm that. It is a compromise that allows for both extremes to be expressed on any piano.

Early temperaments such as the 1/4 comma meantone require that M3s be pure. This cannot be maintained on a modern piano much beyond the midrange without the octaves and their multiples becoming severely narrowed. The music in that period of time does not employ the entire keyboard, so whatever narrowing of the outer octaves there may be is insignificant when performing such early music. Therefore, when tuning a piano in such early temperaments, I recommend using a temperament octave that is not stretched beyond the point of beatlessness.

Any further questions or comments are invited.


Sorry for quoting the entire post. I have scrolled up and down but I just couldn't locate the explanation about:

(1) why the temperament octave should be tuned with a slight beat; and
(2) why the slight beat in the octave, if it mirrors that of a 5th, would be an optimum compromise.

Are you saying that if we tune the temperament octave with a slight beat, the double octaves and triple octaves will have no beats ? IF so, why is that so ?

You mentioned about the 'dilemma' of tuning outer octaves. What is that dilemma ?



Edited by Cashley (07/17/10 03:34 PM)

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#1476233 - 07/17/10 06:56 PM Re: How to tune Tempered Octaves ? [Re: Cashley]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7222
Loc: France
if one tunes temperament with a sllight beat, i.e 1 beat in 3 or 5 seconds, he will have to tune the other octaves with a similar or with a progressive beat for consistency (in ET) but some may tune a different octave in temperament (a clean one, for instance),then enlarge the others to the max (meaning often : to the edge of a noticeable beat)

Different instruments will allow for more or less flexibility in octave size, the 4:2,6:3, 2:1 relations are a tentative to measure or verify that opening. it makes sence in theory, but I like to think of "acoustical intervals" , the final output, and evaluate beats for those ones, a slightly different way of listening, that allow direct tuning, as with a harpsichord.
Quieter way also
In some highly expanded tunings the octaves are beating audibly, and the double octaves much more.

To me as we look for harmony, any way that raise the natural resonance of the piano is nice to the music. But it isbSO easy to make an ET tuning that have no harmonic sence, to the point experimented pianists can miss notes in very well known pieces, by lack of reperes to phrase, lack of inspiration in the feedback received.
particularely noticeable with bland tone pianos which are not singing naturally and have a straight tone
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#1476270 - 07/17/10 07:59 PM Re: How to tune Tempered Octaves ? [Re: Cashley]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland


Originally Posted By: Cashley
Originally Posted By: pppat

Because you will have to deal with inharmonicity anyways in extending the temperament upwards and downwards, most tuners consider it's a good idea to make the initial temperament octave a little wider than a theoretical 2:1 octave, in order to make the transition from temperament to temperament extension as smooth as possible.


Have you just explained something in that paragraph ? There is a connection that is lost between the two statements : (1) it's a good idea; and (2) in order to make the transition from temperament to temperament extension as smooth as possible.

My question : Why is that so ? Basically you're saying we tune the temperament octave a bit wider so that when we 'duplicate' the octaves upwards and downwards the transition will be smooth.


Yes, that's the essence!

Originally Posted By: Cashley

But why would the transition be smooth just because we tuned the temperament octave wider ? You see my point ? A question seems to have been answered, but it begs the same question again. And what do you mean by smooth ???


It would be smooth because of the sameness of the octaves across the piano, as opposed to rough when you tune a narrow temperament and suddenly throw wide octaves into the extension of the temperament.

With "smooth" I mean no obvious beating in the octaves, no obvious jumps in ascending 3rds and 6ths, no suddenly twangy fourths aso. Smooth.

Originally Posted By: Cashley

If you tell someone to tune the octave with a slight beat and say that it will make your subsequent extension of octaves smooth, then the question that would come begging (as far as a layman is concerned) is what kind of 'roughness' would we encounter if we were to tune it beatless ?


Best test for that is to try that kind of tuning. I think it even has a descriptive name, "Schumann tuning" (others pls correct me if I'm wrong), stemming from one school of piano tuning. "Tight temperament, stretched like crazy" is pretty close to the way I remember Isaac (AKA Kamin) describe it a year ago or so.

The roughness of a tuning like that would be directly related to the way I described "smooth" in the last paragraph, but the other way around of course: Obvious beats and twanginess, jumps in ascending RBI's.

Originally Posted By: Cashley

Originally Posted By: pppat

It is, by most tuners, considered the best compromise, because the two cornerstones of harmony - 1) the unison 'echoed' 12 half steps above/below, ie the octave (2nd partial), and 2) the fifth (the 3rd partial) - sound as good as they possibly can do in the same tuning.


I'm completely lost ! I could read and understand every word, but together I just couldn't piece up the message.


Are you familiar with music and sound theory? If so, you should have no problem with this paragraph. If not, you'd just have to rely on the knowledge of those who deal with these things. The answer is given as clear as I myself can do it.

Originally Posted By: Cashley

Originally Posted By: pppat

Stretching is not only justified - it is desperately needed smile Just as Mark says, due to inharmonicity, if the octaves are matched on their 2:1 partials (= what Mark describes as pure), the bass is painstakingly sharp, and the treble is unbearably low. To the listener, in any musical context, they piano sounds horribly out of tune.


I'm not saying that stretching is justified or not justified. I'm saying Mark made a statement about stretching, but what is the 'explanation' that accompanies the statement made ?


Sorry, I don't follow you here. To me, these things have been well explained by a number of people, including Mark. Can you ask a specific question?


Edited by pppat (07/17/10 08:01 PM)
_________________________
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Senior Lecturer (jazz piano, composition, music theory, conducting) @ Novia University of Applied Sciences, Jakobstad, Finland
- - - -
Dedicated to learning the craft of tuning. Getting better.

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#1476376 - 07/18/10 02:08 AM Re: How to tune Tempered Octaves ? [Re: pppat]
Cashley Offline
500 Post Club Member

Registered: 08/16/09
Posts: 530
Originally Posted By: pppat


Originally Posted By: pppat

Stretching is not only justified - it is desperately needed smile Just as Mark says, due to inharmonicity, if the octaves are matched on their 2:1 partials (= what Mark describes as pure), the bass is painstakingly sharp, and the treble is unbearably low. To the listener, in any musical context, they piano sounds horribly out of tune.


I'm not saying that stretching is justified or not justified. I'm saying Mark made a statement about stretching, but what is the 'explanation' that accompanies the statement made ?

Originally Posted By: pppat

Sorry, I don't follow you here. To me, these things have been well explained by a number of people, including Mark. Can you ask a specific question?


I meant I used the word 'justification' in the same context as the meaning of the word 'explanation'. But you adopted my usage of the word 'justified' in a different context, and with that, my question was lost.

I admit I'm not good at music and sound theory, which is the reason for this thread. In fact, I often struggled to ask a second question, not because I was afraid to appear stupid. But I'm afraid to cause irritation to people. After all, every attempt to explain or answer is a goodwill gesture by people who are in no way obligated to me.

Basically this is how my brain works. An conclusion must always be accompanied by an explanation. Sometimes what purports to be an explanation contains many other conclusions which require further explanations. The worst scenario is of course when a question is answered not by an explanation but a conclusion.

Back to the question. Mark made a conclusion about the bass tending to sound sharp and treble, flat, if the temperament octave wasn't tuned slightly wide. But why ? And when the answer is 'due to inharmonicity', the answer begs the original question: 'How does inharmonciy cause the bass to sound sharp and treble, flat ? So we continue to move in circle.

Okay, we will put aside the issue of the bass because whatever affects the treble will inversely affect the bass. So if the treble sounds flat because of the way the temperament octave is tuned, the bass will sound sharp instead.

Now as I mentioned to Jeff earlier, I do know the if the temperament is tuned 2:1, each octave will sound pure or beatless enough, but when comparison is made beyond one octave, beats will surface. Why ? You will say is due to inharmonicty. Remember, inharmoncity is the question, not the answer. So according to my understanding, it means inharmoncity increases with partials. If the temperament octave in question is F3-F4, and if F3-F4 is tuned 'pure' or beatless, F3-F5 double octave will definitely carry a slight beating because of the increasing inharmonicity of the 4th partial of F3. By parity of reasoning, F3-F6 will beat even more because inharmoncity would have stretched the 8th partial of F3 even more. Of course, all these explanations can be summed up as 'due to inharmonicity'.

Am I correct so far ? If I'm correct, I shall venture to guess how the octave is tempered.

...to be continued.



Edited by Cashley (07/18/10 02:10 AM)

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#1476420 - 07/18/10 06:22 AM Re: How to tune Tempered Octaves ? [Re: Cashley]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Cashley
Originally Posted By: UnrightTooner

So tuning ET on a piano is not about tempering all intervals types the same amount from just intonation. It is about making it seem that way by tuning so that beatrates are progressive. And by progressive, this can include getting steadily faster and then steadily slower. And it is possible to do so with many different schemes for stretching.


Does that mean if the 5ths and 4ths in the Temperament Octave are not tuned to precision, but nevertheless the M3s somehow manage to move progressively, the Temperament Octave is considered good ? Or that a series of nprogressive M3s is far more important than a series of exacting 5ths and 4ths ?


I would say that if the M3s and the M6s are progressive then it is a good temperament octave. This is only possible when the 4ths are tempered wide and the 5ths are tempered narrow, but this does not mean that the 4ths and 5ths are precise.

Rather than use the word precise, let me use the word progressive. Since M3s are 14 cents from just intonation and 4ths and 5ths are only 2 cents from just intonation, it takes 7 times as much accuracy to tune progressive 4ths and 5ths as it does progressive M3s.

Not only "because of inharmonicity” (this phrase seems to be used to try to explain everything without explaining exactly how) but more importantly jumps in inharmonicity it can be impossible, even mathematically, to produce progressive 4ths and 5ths, or even progressive M3s and M6s.

And also, on a real piano, the condition of the pinblock and strings can often make it difficult to get both M3s and M6s progressive, let alone 4ths and 5ths!

…..

You mentioned about tuning the temperament octave and then replicating it to the rest of the piano. In practice (and in theory) adjustments are made and can only be known after the temperament octave is expanded. You could say that each octave is its own temperament octave where the tempering of intervals must be adjusted. This is true even without jumps in iH.
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#1476422 - 07/18/10 06:43 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Pat:

I understand that it is called a “Schubert”, not a Schumann, tuning. I have been moving in that direction lately, but it is more subtle than it may seems.

On a small piano 4:2 octaves will produce pure twelfths in the temperament. On a larger one they will produce pure twelfths an octave or so higher. Since there is little difference between a 4:2 and 6:3 octave on a large piano, there is even less to be gained by tuning a compromise between 4:2 and 6:3 octaves in the temperament. And once 4:2 octaves, with the help of iH, have produced pure twelfths when expanding the temperament upwards, isn’t there enough stretch by continuing pure twelfths?

And let me “beat you to the punch” and agree that a little difference can mean a lot. But I am not so sure the difference that extra wide octaves in the middle of the piano makes in the sound of the piano, provides what is needed to satisfy the ear pitch-wise as it provides what is desired to satisfy the ear contrast-wise. A piano that stands out can be heard easier.

In fact, I seriously wonder if by making the middle octaves extra wide if the ear is not indulged and expects even wider octaves on the extremes! I think there is more than what “meets the eye” in a Schubert tuning.
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Part-Time Tuner
Who taught the first chicken how to peck?

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#1476431 - 07/18/10 08:17 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
@Cashley: Good post, thanks - now I understand better what's bugging you smile I will reply ASAP.

@Jeff: You're right, and that's an interesting post you wrote. Maybe that's why so many temperament sequences just say something in the essence of "tune A3 to A4, and check with M3-M10. The upper interval should not be slower than the lower one." Thus, leaving room for octaves slightly wide of 4:2, but also for 4:2 itself. This would, just as you say, be different from instrument to instrument.

And thank you, "Schubert tuning" it is smile Now, what I've come to associate with that tuning is a very narrow temperament, then huge stretch towards the ends of the piano - some refer to this as "Carnegie Hall tuning" or use similar descriptive terms. In short, a tuning that might give sparkle to the upper end and depth to the lower end on 9 ft grands in a great hall, but that sounds VERY pitch-confused in, for example, using close-up mics on the piano (not to mention if it's a shorter grand.)

What you advocate though - using a narrower temperament octave and a more resonable stretching than I mentioned above - makes total sense. And I think you might be right about this:

Originally Posted By: UnrightTooner
In fact, I seriously wonder if by making the middle octaves extra wide if the ear is not indulged and expects even wider octaves on the extremes!


I get that feeling from a 6:3-based ET temperament. I also don't particularly like the "looseness" of the harmony in the midrange in that kind of temperament stretch. To me, it doesn't hold together that well.
_________________________
Patrick Wingren, RPT

Senior Lecturer (jazz piano, composition, music theory, conducting) @ Novia University of Applied Sciences, Jakobstad, Finland
- - - -
Dedicated to learning the craft of tuning. Getting better.

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#1476438 - 07/18/10 08:38 AM Re: How to tune Tempered Octaves ? [Re: pppat]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7222
Loc: France
Yes, I seem to agree with all that above.

good reflexions.

In Chas the medium benefit from somehow close harmony, I suggest that the sparkle is due to the raised resonance.
Chas method is something like "let the piano find it itself, the tuner is only there to push in the good direction" that is something I like and the same idea I had while tuning, as many tuners say "let the piano tell you", but the 12/15 relation is taken in account, while only octaves and multiples are in a more classical approach.
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#1476888 - 07/19/10 05:51 AM Re: How to tune Tempered Octaves ? [Re: Olek]
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1937
Loc: Pretoria, South Africa
Originally Posted By: Cashley
Back to the question. Mark made a conclusion about the bass tending to sound sharp and treble, flat, if the temperament octave wasn't tuned slightly wide.


That wasn't intended as a "conclusion". It was a statement of fact, and it actually concerned all octaves, not only the temperament octave. Right at the beginning of my post I said that any tuning must be stretched to accommodate inharmonicity. Then, later, I described what happens if inharmonicity is not accommodated: the bass will sound sharp and the treble flat.

Originally Posted By: Cashley
But why ? And when the answer is 'due to inharmonicity',


Indeed, it is the answer.

Originally Posted By: Cashley
the answer begs the original question: 'How does inharmonciy cause the bass to sound sharp and treble, flat ? So we continue to move in circle.


I don't think we're moving in circles at all. You just have to find out what harmonicity is, and then you will see why/how it causes the bass to be sharp and the treble to be flat if the octaves are not stretched.

Originally Posted By: Cashley
Remember, inharmoncity is the question, not the answer.


What do you mean by this? Inharmonicity is not a question, it is a phenomenon that can be measured, demonstrated and explained. But it seems as though you are not clear on what inharmonicity actually is?

Bill suggested earlier that one should read up on inharmonicity, e.g. on Wikipedia. Have you done so?

Originally Posted By: Cashley
If the temperament octave in question is F3-F4, and if F3-F4 is tuned 'pure' or beatless, F3-F5 double octave will definitely carry a slight beating because of the increasing inharmonicity of the 4th partial of F3.


I would rather word it like this:
If F4 is tuned beatless to the second partial of F3 (2:1 octave) and if F5 is also tuned beatless to the second partial of F4 (2:1 octave), then F5 will be lower than the fourth partial of F3. Hence, the double octave will have a slight beat.

Originally Posted By: Cashley
By parity of reasoning, F3-F6 will beat even more because inharmoncity would have stretched the 8th partial of F3 even more. Of course, all these explanations can be summed up as 'due to inharmonicity'.


Yes, they can, and they were. So where is the problem, I'm wondering?
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#1476895 - 07/19/10 06:12 AM Re: How to tune Tempered Octaves ? [Re: Mark R.]
Olek Online   content
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Registered: 03/14/08
Posts: 7222
Loc: France
To me if the temperament is enlarged, the main result is that the railsback curve is straighter and stepper.


with a close medium, one will have to add stretch in the extremes in a more abrupt way - Ih tend to give a higher pitch to the note, than the pitch of its fundamental. Then, which pitch have to be tuned ? the one we hear (mix of all partials), or the fundamental, or a partial ? or some thing dispated on a screen ?


Ih is what gives relief (?) to piano tone, largeness
low iH scale have a straighter enveloppe and saturates less.


Edited by Kamin (07/19/10 08:57 AM)
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#1476920 - 07/19/10 07:43 AM Re: How to tune Tempered Octaves ? [Re: Olek]
UnrightTooner Offline
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Registered: 11/13/08
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Mark & Cashley:

The following link is to an article that sums up the subject of octave stretch better than any I know of, but others may disagree with what it says - http://en.wikipedia.org/wiki/Piano_tuning#Stretched_octaves
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#1476947 - 07/19/10 09:15 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Bill Bremmer RPT Offline
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Registered: 08/21/02
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Loc: Madison, WI USA
Jeff, I read it and I agree that it is a good summary but that is all it is, a summary. It is like an introductory page to what would be a book on the subject. I noticed an external link at the bottom of the page that went to my website! Not that I mind but nobody ever asked me if they could put that there. The title, "Octave types and Distribution" is erroneous. The word "distribution" was only the file name I had given it in order to distinguish it from the parallel file I had made that had been edited for submission to the Journal. When I asked my webmaster to put the file on my website, he thought the word "distribution" belonged in the title. I saw that and had him take it off later but somehow it made it on to Wikipedia.

Wikipedia can be an excellent source for basic information but inevitably, it is a hodge-podge of information put up by whoever wants to put something up. I have no idea who wrote that article although it is basically fine. I noted that they used Jorgensen's book, "Tuning" and Helmholtz as sources.

At the end of the paragraph on stretching, it implies that the octaves cannot be stretched using inharmonicity enough to satisfy what the ear really wants to hear. I disagree with that because I have done it for a couple of decades now. It isn't right for every situation but the formula I used on GP's piano is one I often use: F#4-E5: octave equal beating with the 5th below the top note of the octave. F5-E6: double octave equal beating with octave-5th below the top note of the double octave. F6-B6: pure 6:1 octaves (the note being tuned is exactly in tune with the 6th partial of the note two octaves and a 5th below it). C7-E7: pure 8:1 octaves. F7-B7: pure 12:1 octaves. C8: pure 16:1 octave.

You may notice that as the scale is ascended, it keeps reaching back to the temperament octave for the reference. The partials involved at F5-E6 are 4th and 3rd. Then, they jump to 6, 8, 12 and 16. The higher the partial, the sharper the pitch. Using these partial selections for the high treble really will satisfy the ear's desire to hear those pitches much higher than they would be theoretically. When the stretched is always "pushed" as described above, the beating between single octaves in the high treble also remains in a tolerable range.
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#1476970 - 07/19/10 10:00 AM Re: How to tune Tempered Octaves ? [Re: Bill Bremmer RPT]
UnrightTooner Offline
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Hi Bill:

The reason I posted the link is because Mark and Cashley seem to be missing something very basic about stretch.

Yes, I agree that it is good as only a summation, and within the context of the stretch available with 2:1 octaves, I agree with the article: the stretch produced by inharmonic tones with 2:1 octaves is not sufficient to satisfy the ear pitch-wise in the extremes of the piano.

Of course, using higher partial matches will satisfy (or even offend such as with 8:4 octaves) the ear pitch-wise, but that would be beyond a summary article.

But when I consider the stretch scheme that you mention, there are only 6 notes (C7-E7 and C8) that use inharmonicity exclusively to obtain stretch. The remainder of the stretch scheme also uses fifths or extensions of fifths and would cause stretch even with harmonic tones because the fifths are being tempered less. This not a criticism of your scheme. I am just pointing out that it stretches by the use of more than a piano’s iH.
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#1476989 - 07/19/10 10:32 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Mark R. Offline
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Registered: 07/31/09
Posts: 1937
Loc: Pretoria, South Africa
Originally Posted By: UnrightTooner
The reason I posted the link is because Mark and Cashley seem to be missing something very basic about stretch.


I can't speak for Cashley, but what might I be missing?
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#1477003 - 07/19/10 10:49 AM Re: How to tune Tempered Octaves ? [Re: Mark R.]
UnrightTooner Offline
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Registered: 11/13/08
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Mark:

Your statement: “I don't think we're moving in circles at all. You just have to find out what harmonicity is, and then you will see why/how it causes the bass to be sharp and the treble to be flat if the octaves are not stretched.” seems odd. Are you saying that iH makes the pitch of notes sound different and that the pitch must be changed differently than harmonic tones so that they sound in-tune melodically? Actually, I have wondered about this, but it does not seem to be the question at hand.

The Topics with Cashley can be confusing because so many different conversations are going on at once. Instead of jumping into the subject that you two are discussing I thought it best to just post a link to give you two more common ground.
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#1477373 - 07/19/10 08:22 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
pppat Offline
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Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
I'd like to try to contribute with some simple charts of how inharmonicity affects octave tuning. My charts are rudimental, because they deal with inharmonicity as a standard factor, applied equally to all strings. We all know that this is not the case, some strings have more inharmonicity than others. Still, the graphs are clear enough to make the main points - much in line with what Mark described earlier.

1) Theoretically, the partials line up mathematically correct, and if this was true on the piano too, there would be no need for stretch (besides from subjective choices, of course).

Here is a graph comparing theoretical partials with partials affected by inharmonicity. Inharmonicity is due to the stiffness off the wire. Jack Stebbins thaught me to imagine the piece of wire closest to the termination points, and I agree - it really has a rough time trying to move.

The result of that stiffness is that it shrinks the actual wavelengths, and because high frequencies have shorter wavelenghts that are more sensitive to outer factors, they suffer more than the lower ones. Thus, the first partial is almost unaffected, the 2nd partial a bit more, the 3rd even more, and so on.

Here is my first graph, showing a theoretical line-up of partials vs. an actual (although exaggerated) lineup caused by IH:




This shows the piano tuner's octave dilemma right there. We can seldom, if ever, make more than one partial match.

Mark earlier described the results of theoretical tuning, ie matching the fundamental (1st partial) of the higher note in the octave with the 2nd partial of the lower octave. Let's see what happens when we do that to the octave C4-C5, when inharmonicity has come into play:



The second partial of C4 matches nicely with the 1st partial of C5, but above that we have problems. All crucial overtones (partials) above that 2:1 relationship are going to be hopelessly flat on our upper C5. Hence, C5 is going to sound flat compared to C4.

What about octaves downwards? Let's try to make a 2:1 match between C3 and C4:



... and the problem is not solved, only reversed. Again, the 2:1 match between C3 and C4 is going to sound perfectly beatless, but inharmonicity messes with the higher partials. above the 2nd partial, C3's partials are going to be higher than those of C4, causing the overall pitch perception of the listener to experience C3 as higher in pitch than it should be for a sound-wisely perfectly pure octave.

Cashley, I hope this graphs help you to see what Mark already said: a 2:1 theoretical tuning will leave the bass sharp, and the treble flat.


Edited by pppat (07/19/10 08:34 PM)
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#1477617 - 07/20/10 04:13 AM Re: How to tune Tempered Octaves ? [Re: pppat]
Mark R. Offline
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Registered: 07/31/09
Posts: 1937
Loc: Pretoria, South Africa
Many thanks, Pat, this serves very nicely to better explain my statement that Jeff questioned in the post before yours. I can't add anything more. (And I think I'll pipe down now, seeing that my posts are based on reading, not tuning (yet).)
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#1477657 - 07/20/10 07:25 AM Re: How to tune Tempered Octaves ? [Re: Mark R.]
Olek Online   content
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Registered: 03/14/08
Posts: 7222
Loc: France
Yes but we hear all the partials together, plus fundamental, and there is some attraction due to whatever effect. (the pitch is not really stable, it varies between attack and sustain, and iH of the note (not iH of the wire) varies with the voicing)

So a note can tend sharp or flat, depending of the harmonic context.

The fact that one level of partials is lined does not preclude of justness it only influence the beats produced by partials.

That approach is just to give explanations on the basis of the problem, and why pure multiples of fundamental will not give the right frequency (it does that pretty well, nice sketches, pat)

Due to that, we always try to avoid beats in octaves, while another approach (an easier one)is to accept them.

the next trouble is due to the human ear that is asking for extra high treble (due to the lack of perception of the high frequencies probably)So a piano tuning may have a way to fall in a high treble stretched in the most natural way.
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#1477659 - 07/20/10 07:38 AM Re: How to tune Tempered Octaves ? [Re: pppat]
UnrightTooner Offline
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Registered: 11/13/08
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Loc: Bradford County, PA
Originally Posted By: pppat

…..

We can seldom, if ever, make more than one partial match.

…..

Correct.

Originally Posted By: pppat

…..

Again, the 2:1 match between C3 and C4 is going to sound perfectly beatless, but inharmonicity messes with the higher partials. above the 2nd partial, C3's partials are going to be higher than those of C4, causing the overall pitch perception of the listener to experience C3 as higher in pitch than it should be for a sound-wisely perfectly pure octave.

…..


Now wait a minute! Who says that it is the higher partials that tell the ear what pitch a note is at? Someone else could say that it is the fundamental that tells the ear what pitch a note is at, and tuning to higher partials makes the higher notes too high.

So let’s take a look at what is held as a standard way to tune large pianos differently than small pianos. Large pianos are generally tuned with higher partial matches and smaller pianos with lower partial matches. This indicates that the ear does not decide what the pitch of a note is by the higher partials. Otherwise the same partial matches would be used for every size of piano.

Or we can listen to theoretical harmonic tones, such as on a common electronic organ. Play a very low note, and then a note as many octaves higher as possible. Now play the lowest note again, but this time play the note a semitone higher as many octaves as possible. If your ear determines pitch like most other ears, the note a semitone higher will sound more on pitch when compared to the lower note. If the higher partials is how the ear determines pitch, the lower note would sound more on pitch.

There are two kinds of stretch. One is due to inharmonicity and is required to make intervals harmonic (partials line up). The other is due to how the human ear perceives pitch. Tuning 2:1 octaves on a piano is perfectly sufficient for stretching the theoretical pitches for harmonic octaves, but is not enough to satisfy the pitch sense of the ear in the extremes of the piano. The article that I posted a link to explains this very simply.
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#1477704 - 07/20/10 09:16 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Mark R. Offline
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Registered: 07/31/09
Posts: 1937
Loc: Pretoria, South Africa
Jeff,

Are you saying that if you tune, for example, C5-C4 2:1, then C6-C5 2:1, ditto C7 and C8, that C7 and C8 will have no audible beat(s) with respectively the 4th and 8th partials of C4?
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1922 49" Zimmermann, project piano.
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#1477713 - 07/20/10 09:33 AM Re: How to tune Tempered Octaves ? [Re: Mark R.]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Mark R.
Jeff,

Are you saying that if you tune, for example, C5-C4 2:1, then C6-C5 2:1, ditto C7 and C8, that C7 and C8 will have no audible beat(s) with respectively the 4th and 8th partials of C4?


No, I am not saying that, but they could very well be too fast and weak to be audible. (Especially considering it would be the 8th and 16th partials, respectively wink )

But let me ask you a question. Are saying that hearing beats and perceiving pitch are the same thing?
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Who taught the first chicken how to peck?

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#1477761 - 07/20/10 10:47 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1937
Loc: Pretoria, South Africa
Originally Posted By: UnrightTooner
No, I am not saying that, but they could very well be too fast and weak to be audible. (Especially considering it would be the 8th and 16th partials, respectively wink )


OK, then let's choose another example. My understanding is that the 8th partial of a low bass string can be quite audible. From what I've heard on my piano, the 7th one is quite audible in the extreme bass, so I would expect the 8th to be audible as well.

So, what would happen if you tune contiguous 2:1 octaves all the way down from C4 to C1 - would there be no beat between C1 (partial 8) and C4 (fundamental)? If, like you say, 2:1 octaves have sufficient stretch to cater for inharmonicity, then there shouldn't be a beat. No psycho-accoustic matters, just matching of partials. So, would there be a beat or not?

Originally Posted By: UnrightTooner
But let me ask you a question. Are saying that hearing beats and perceiving pitch are the same thing?


No. That's exactly the point. I've read about the psycho-accoustics of high notes, but all my points here are directed at inharmonicity only. To wit: from what I've read hitherto, 2:1 octaves are actually not sufficiently wide to cater for inharmonicity, i.e. they are not able to prevent beats between the low bass and mid-section (or mid-section and high treble) - in other words, to put it as succinctly as I can:

My understanding hitherto was that even before the psycho-accoustics of high treble notes come into play, 2:1 octaves cannot get a piano's extremes in tune with the rest of the instrument. They will actually, physically, beat, because of mismatched parials - irrespective of my perception of pitch.

Was this understanding wrong? (Question aimed not only at Jeff.)
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#1477821 - 07/20/10 12:18 PM Re: How to tune Tempered Octaves ? [Re: Mark R.]
UnrightTooner Offline
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Registered: 11/13/08
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Loc: Bradford County, PA
Mark:

It is a two edged sword. If 2:1 octaves are not sufficiently wide to prevent beats between the low bass and mid-section ... THEN ... intervals between the low bass and midsection are not sufficiently narrow to prevent beats in the 2:1 octaves.

In your example, C1-C4 would beat about 2 bps on a typical piano when 2:1 octaves are tuned. And if C1-C4 were beatless, the 2:1 octaves could be tuned to each beat about 1/3 bps.

It is often mentioned about the need to use higher partial matches to prevent beating in large intervals such as double and triple octaves. Even if this was not the case (and I don't think it is a big deal), or if these intervals are not played, the ear still wants the stretch (or even more) to satisfy its sense of pitch not only regardless of iH or beating, but (I believe) in spite of it!

For instance, mindless octaves are often tuned, not for the sake of pure double octaves (these are deliberately stretched wide) but for the sake of satisfying the ear pitch-wise. And pure twelfths and even pure fifths are tuned for the same reason in spite of any beating that may occur in octaves or double octaves.

The reason for stretch is to satisfy the ear. Inharmonicity helps stretched intervals be more harmonious.
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#1477840 - 07/20/10 12:43 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
BDB Online   content
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Originally Posted By: UnrightTooner
The reason for stretch is to satisfy the ear. Inharmonicity helps stretched intervals be more harmonious.


I think that should be "Stretch helps inharmonic intervals be more harmonious."
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#1477853 - 07/20/10 01:04 PM Re: How to tune Tempered Octaves ? [Re: BDB]
UnrightTooner Offline
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Registered: 11/13/08
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Loc: Bradford County, PA
Not when the stretch is past the point of harmoniousness. When the purpose is to have the pitch pleasing to the ear, (regardless of the amount of inharmoniousness) the more iH, the more harmonious the interval.

"Inharmoniousness" what a word! I wonder what it could score in scrabble, if it is possible …
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