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#1477868 - 07/20/10 01:17 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
BDB Offline
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Registered: 06/07/03
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Loc: Oakland
It depends on why you believe octaves should be stretched. There are a lot of people who make octaves wider as they go up the scale because they have tin ears. Even Mozart recognized and mocked that tendency.

The whole idea of tempering octaves makes no sense. The softest possible octave is pure, so what else could you be tempering?
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#1477877 - 07/20/10 01:35 PM Re: How to tune Tempered Octaves ? [Re: BDB]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Well, 2:1 octaves make octaves go wider going up the scale cent-wise. But I know what you mean and do so delibrately with 4:2 octaves until the point that 3:1 twelfths are reached, which then produces narrowing 4:2, but wideneing 2:1 octaves. Not a trace of inharmoniousness to these tin ears, though. smile
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#1477879 - 07/20/10 01:37 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
BDB Offline
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Originally Posted By: UnrightTooner
Well, 2:1 octaves make octaves go wider going up the scale cent-wise. But I know what you mean and do so delibrately with 4:2 octaves until the point that 3:1 twelfths are reached, which then produces narrowing 4:2, but wideneing 2:1 octaves. Not a trace of inharmoniousness to these tin ears, though. smile


Whatever that means.
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#1477889 - 07/20/10 01:45 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
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Registered: 12/15/06
Posts: 1432
Loc: Mexico City
Originally Posted By: BDB
The whole idea of tempering octaves makes no sense. The softest possible octave is pure, so what else could you be tempering?


I see this fact as follows:

Problems begin when one starts measurements of frequencies. As long as we hear to tune, everybody knows what a clean octave is. But when we take measurements of the frequencies we find that fundamnetals of the two notes of an aurally clean octave are not in the ratio of 2:1 but in a greater ratio. So that clean octave is not really pure, in fact it is stretched.

Tooner will call this "natural stretch" because the octave sounds clean.

But problems do not finish here. There are in fact no pure octaves at all, that is why I talk about clean octaves.

In fact when playing the notes all pairs of nearly coincident partials are sounding simultaneously and they don't match with each other. So is iH, if you tune a 4:2 octave then 6:3 will be narrow and 2:1 will be wide, or whatever else depending on the iH of the strings involved. And you can have anything but a pure octave.

So what can we do? We do our best to make it sound good. That implies making decisions about what is the best compromise in terms of harmoniousness. That is the meaning of "tempered octave", an octave where the fundamentals of the notes are not in a 2:1 ratio but which sounds as we want.

So in fact we can only tune tempered octaves.

Now, if we accept that the perfect pure octave does not exist in piano tuning, then how much we must temper octaves? Natural stretch? Beyond natural stretch? It is a matter of priorities we give to all other intervals in our tuning.

Onlypure favors 12ths, mindless octaves tunes a balance between 15ths and 12ths, some prefer to tune double octaves and even triple octaves, some others strive to clean single octaves, etc...

But in that respect all octaves, no matter how we tune them, are stretched.


Edited by Gadzar (07/20/10 01:51 PM)
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#1477895 - 07/20/10 01:55 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
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Gadzar:

You may like this tidbit. When an octave is tuned so that it is an exact compromise between the 4:2 and 6:3 octave, the 2:1 octave also beats at the same rate! Pure enough for 'ya???
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#1477908 - 07/20/10 02:20 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
BDB Offline
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Of course, the pitch of a piano string does not remain the same as the note decays, let alone its harmonics, so none of this pseudo-physics and pseudo-math makes any sense. The beats do not remain the same, because the wave-form varies with the decay. From a practical sense, you cannot distinguish fractional beats once they beat more slowly than the note decays, and probably a lot sooner than that. So it may be that you can get an octave to be "pure" within those limitations.
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#1477912 - 07/20/10 02:25 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
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Originally Posted By: UnrightTooner
Pure enough for 'ya???


For me: Pure octave = Beatless octave.

Even in such a case where 2:1 would beat at the same rate than 6:3 and 4:2, they are beating all 3 of them, so this octave can by no means be a pure one!

And I am not so sure if 2:1 will beat at the same rate than 6:3 and 4:2. That depends on the real frequencies of partials 1, 2 and 3 of the upper string, and partials 2, 4 and 6 of the lower one. I would be surprised if they all match in such a perfect way.

Again, I am talking about real strings, made of steel (and cooper)! I am not talking about a simulation in a computer using the Young formula for estimating each partial of theoretical perfect strings, regardless of all imperfections of the real world!



Edited by Gadzar (07/20/10 02:25 PM)
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#1477914 - 07/20/10 02:30 PM Re: How to tune Tempered Octaves ? [Re: BDB]
UnrightTooner Offline
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BDB:

Seriously, you are right. Until the theory of inharmonicity was popular I do not think there was ever a mention multiple beating of octaves (although I did notice multiple beating of 5ths during my tuning lessons, which was nothing new to my instructor.)

As you say, if it sounds good, it is good.
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#1477916 - 07/20/10 02:32 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4789
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Originally Posted By: Gadzar
Originally Posted By: UnrightTooner
Pure enough for 'ya???


For me: Pure octave = Beatless octave.

Even in such a case where 2:1 would beat at the same rate than 6:3 and 4:2, they are beating all 3 of them, so this octave can by no means be a pure one!

And I am not so sure if 2:1 will beat at the same rate than 6:3 and 4:2. That depends on the real frequencies of partials 1, 2 and 3 of the upper string, and partials 2, 4 and 6 of the lower one. I would be surprised if they all match in such a perfect way.

Again, I am talking about real strings, made of steel (and cooper)! I am not talking about a simulation in a computer using the Young formula for estimating each partial of theoretical perfect strings, regardless of all imperfections of the real world!



OK, you have an ETD. Try it out and let us know. It does give frequencies of partials, doesn't it?
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#1477923 - 07/20/10 02:52 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
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Registered: 12/15/06
Posts: 1432
Loc: Mexico City
I need no ETD to know what is known by every piano tuner of our times! Every body is tuning using more or less stretch. Nobody tunes nowadays without stretch. Even if they don't notice they are doing so.

iH has existed long before
Quote:
the theory of inharmonicity was popular
and octaves were beating then as much as now at all their coincidental partials even if tuners did not speak about multiple beating octaves.

Tooner, I have a question for you:

How does your ideal simulated piano sound like if entirely tuned to balanced 6:3/4:2 = 2:1 octaves?

For what I know about the real world pianos I tune: the low bass will sound sharp, the tenor will sound good, the treble will sound sharp, too stretched, and the high treble can't be tuned that way because 6:3 octaves are not audible.

But in a computer all is possible, so how would it sound?


Edited by Gadzar (07/20/10 03:14 PM)
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#1477938 - 07/20/10 03:19 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6377
Loc: France
Hi all !

Yes older tuners did not worry about the iH theory. eventually many pianos had less iH (just a guess, but the strings where softer, out of the pre 1900 period where they harden them a lot)

so the high beats where certainly less noticeable, and in any case they did not learn to listen to them, I never see mention of 8:4 ,12:6 , etc in literature . I have to look at that again, but only basic checks where used.

Gadzar, (Zapata !) you asked about tuning with sustain pedal engaged, I had a colleague retired concert tuner who did that in the 90s he told me when he was tired, but it worked fine, and showed me that natural resonance can be used with all the piano, not only octaves doubles etc.
i like to use that when tuning Chas, in the treble because the resonant quality is easy to recognize. I use the first inversion of the minor chord and look for the resonant spot a 12th above, and it work for me. in the basses I have not find a similar trick, but Alfredo showed me the use of the M14th 2 octaves less one tone)which is a well sustained beat and have a particular "body", very useful for low basses

my colleague was mostly using 4ths in the basses, and a M third at the top of the octave for the treble, then check a sustained mix of major minor chord .
I did not find that particularly relaxing but checking major/minor against notes 2 octaves above/below is a method as another. his tunings where very lively and appreciated, the piano fall by itself in some kind of resonant spot, that is what I like with the Chas method, very similar by some aspects.

best wishes to all, dont fight !
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#1477944 - 07/20/10 03:26 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
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Registered: 12/15/06
Posts: 1432
Loc: Mexico City
Originally Posted By: BDB
So it may be that you can get an octave to be "pure" within those limitations.


I agree. In the instructions of all the ETDs that I have read, they advise to tune to the first reading when it varies in time.

Kamin also adivises to tune the attack of the unisons. I don't know if he means to avoid decay, but anyway it does avoid it.

And in general, it is considered as a good practice to repeat regularly the notes when tuning, not only because of decay but also for stability, string rendering and other issues.

But even, or mostly, if it sounds pure: it is stretched. You only have to measure the fundamentals ratio to confirm it.


Edited by Gadzar (07/20/10 03:49 PM)
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#1478294 - 07/21/10 04:02 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Mark R. Online   content
1000 Post Club Member

Registered: 07/31/09
Posts: 1866
Loc: Pretoria, South Africa
Jeff,

Earlier, you wrote (colors added by me, for clarity):

Originally Posted By: UnrightTooner
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.


But then you wrote:

Originally Posted By: UnrightTooner
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.


Now what will it be? According to the second quote, one can either have three contiguous 2:1 octaves, or a beatless 8:1 triple octave, but one can't achieve both simultaneously. Hence, I conclude that:
1) 2:1 octaves are not sufficiently wide to accommodate inharmonicity (which seems in direct contradiction with the red part of first quote), and
2) octave stretching is therefore done not only to satisfy the human ear's pitch perception (see blue part), but also to accommodate iH.

Pardon my reading if it's wrong, but this is what I conclude from the second quote, as also illustrated by Patrick's drawings.
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#1478310 - 07/21/10 05:18 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6377
Loc: France
Originally Posted By: Gadzar
Originally Posted By: BDB
So it may be that you can get an octave to be "pure" within those limitations.


I agree. In the instructions of all the ETDs that I have read, they advise to tune to the first reading when it varies in time.

Kamin also adivises to tune the attack of the unisons. I don't know if he means to avoid decay, but anyway it does avoid it.

And in general, it is considered as a good practice to repeat regularly the notes when tuning, not only because of decay but also for stability, string rendering and other issues.

But even, or mostly, if it sounds pure: it is stretched. You only have to measure the fundamentals ratio to confirm it.


The attack have to be tuned because it deals with the enveloppe, but the thick part of the decay is also tuned to "body" the tone. There, partial coupling comes in play.(in unisson)

I guess that what is addmited is that 2:1 relation cover for iH correction. and all added sech is considered "artificial" , or result of the interval ratio used.

A large temPerament octave also helps to cover for mistakes when tuning above and under. with a purer initial octave is harder to realize progressive intervals, the added strech helps the intervals to jump in the ih spectra and sound purer
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#1478342 - 07/21/10 07:29 AM Re: How to tune Tempered Octaves ? [Re: Olek]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Gadzar:

My simulation only produces numbers, not sounds.
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#1478348 - 07/21/10 07:57 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Olek Online   content
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Registered: 03/14/08
Posts: 6377
Loc: France
Thats the limit of the thing, but it is interesting anyway.

The fact is that in real word there are more parameters that comes in play than the theoretical or even real ih .
The notion of "acoustical justness" seem to describe that correctly, to me. It is the fact that the final jUstness may relate to a model. For instance "pure fifth tuning is non existent in regard to the iH theory, But acoustical pure fifth (or twelve) is a concept that can be grasped, and it have some existence .

The same apply to a pure octave, it is simply difficult to learn to recognize the good spot by ear, so the tuner is avidely asking for methods tricks, and checks to have a little control on that.

It certainly work to some point , but it also give bad habits, and lot of frustration, knowing that our tuning is only a bunch of compromises is not ve y good !

So, to me the quality of the octaves and other intervals is putting the resonance of the tuning at a more or less high level in the spectra. It is totally acoustic dependent, (room, voicing, kind of scale) unless you use a self refered ratio that auto replicates within the scale.
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#1478354 - 07/21/10 08:11 AM Re: How to tune Tempered Octaves ? [Re: Mark R.]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Hey, Mark:

I can see why what I said could be confusing because I was saying something very, very basic.

A piano tuned with 2:1 octaves have harmonically satisfying octaves. They are harmonically satisfying because they are 2:1 octaves. This is to say nothing about other intervals. But the same thing could be said about other intervals, like, “A piano tuned with pure fifths have harmonically satisfying fifths.”

So let’s look at your conclusions:

1) 2:1 octaves are not sufficiently wide to accommodate inharmonicity”

Of course they are, for 2:1 octaves. But if accommodating any other interval produces a different stretch, then it is insufficient to accommodate 2:1 octaves.

2) octave stretching is therefore done not only to satisfy the human ear's pitch perception (see blue part), but also to accommodate iH.

Well it depends on what octave you are talking about, doesn’t it? Suppose I am talking about 12:6 octaves and lets say that is too much stretch to satisfy the ear and makes other intervals unharmonious. Then I could say, “Octave compressing is therefore done not only to satisfy the human ear's pitch perception, but also to accommodate iH.” Or if by octave we mean a 2:1 frequency ratio, then when tuning 2:1 octaves we can say “Octave stretching is therefore not sufficient to satisfy the human ear's pitch perception, but is sufficient to accommodate iH.”

Consider this. Even before iH was known by tuners, octaves where stretched beyond what was harmonious to satisfy the pitch sense of the human ear. That is what is still being done. Sure there are many stretch schemes that use the sharpened partials that are an effect of iH. But iH is a tool used to stretch octaves beyond what is harmonious. Stretch is not something used to "accommodate" iH (can iH be unhappy?).
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#1478432 - 07/21/10 10:52 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6377
Loc: France
I agree with the last sentence.
What is less useful than I believed is all that partial match progression to be used for makIng a skeleton for tuning.

Facts are real, but the difference is so small that a wrong basic concept can push a tuning in a no end way easily.

I heard lately a concert on a grand piano with a not so singing tone, and a very even, but harmonically inintelegible tuning. The piano was 'just' , by evidence, but at different moments I felt the pianist where lost in their speech, to the point they played a note for another.
Then, some unisons went out of tune.!
That kind of situation does not arise with a congruent tuning, that evolve in an harmonious way even if temperature change (I have no proof for that but I strongly believe it, a piano have some form of acoustical stability availeable, hopefully)
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#1478460 - 07/21/10 11:50 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
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Registered: 12/15/06
Posts: 1432
Loc: Mexico City
Originally Posted By: UnrightTooner
Gadzar:

My simulation only produces numbers, not sounds.


That is precisely my point. We (me included) are talking about sounds and you (me excluded) are talking about numbers!

But, even if you can try to imagine how your numbers will sound when transposed to a tuning, the fact is that you don't hear them!

So we do not talk the same language!
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#1478465 - 07/21/10 12:00 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
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Registered: 11/13/08
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Fine, let’s talk about sounds.

I have never, ever heard a beating in a double or triple octave when tuning two or three stacked octaves to each sound as pure as possible. However, when tuning a triple octave this way, the upper note sounds a bit flat when compared to a chord three octaves lower.

What do you hear?
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#1478489 - 07/21/10 12:34 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Gadzar Offline
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Registered: 12/15/06
Posts: 1432
Loc: Mexico City
Tooner,

I have an ETD, which I believe is the best available nowadays.

It measures 12 partials of each string while you are tuning. So it collects iH data of more than 400 partials for each tuning.

It brings you the ability to design the tuning the way you want. You can set which type of intervals you tune at 8 different points of the scale, and for each set point you can specify the type of interval and the desired tempering in bps. You can specify, for each set point more than one interval type. And the program will accomodate the tuning to satisfy your specifications.

This is called: Style.



For example:

Built in Average Style

A0 6:3 0.33 100%
A2 6:3 0.24 100%
A3-4 4:2 0.32 100%
F5 2:1 0.30 100%
A6 4:1 0.5 100%
C8 4:1 0.00 100%


Custom made Style for studio (upright) Pianos

A0 10:5 0.00 20% 6:3 0.00 40% 4:1 0.00 40%
A1 8:4 0.00 60% 6:3 0.00 20% 4:1 0.00 20%
A3-4 6:3 0.00 20% 4:2 0.00 80%
A6 4:1 0.00 50% 3:1 0.00 50%
C8 4:1 0.00 67% 8:1 0.0 33%


You can see in the Studio style that at A6 I ask for mindless octaves by balancing 4:1 and 3:1 at 50% each.

Or in the built in Average Style the temperament octave A3-4 will be tuned as a wide 4:2 type octave beating at 0.32 bps

Or in the Studio style the low bass will be tuned as a medley of 10:5, 6:3 and 4:1 with the percentages specified.

So, you can decide how to tune the piano at the desired locations in the scale. It gives you an enormous power over the tuning you want.


It is by far much more powerfull than your simulator!

And guess what...

It has not ears! It only measures frequencies and tranlsate them to numbers and it calculs a tuning following the style you have designed.

I doesn't know if it sounds good or not! You have to hear the resulting tuning and adjust the programming if it doesn't sound good!

My ETD has very usefull features. It is great for pitch raises, for repeating a tuning you liked, it is very flexible, you can design the tunings exactly the way you want, etc...

But it has limitations.

It is extremely difficult to interpret numbers, one have to tune them and hear them to know if they are really what we thought.

That is why I prefer to do my fine tunings by ear.

So when I write here in this forum I prefer to talk about tuning and not about numbers.



Edited by Gadzar (07/21/10 12:42 PM)
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#1478497 - 07/21/10 12:46 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Gadzar:

"I see your Schwartz is as big as mine." Dark Helmut from Spaceballs.

Now are you going to talk about what you hear or not???
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Jeff Deutschle
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#1478507 - 07/21/10 01:07 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1432
Loc: Mexico City
I was writing at the same time than you.

For the tuning of stacked octaves, try this:

Tune A4 to the fork
Tune A3 to A4 as clean as possible
Tune A2 to A3 as clean as possible

Now listen to A2-A4, chances are that this double octave won't be as pure as it can be. Maybe you won't hear a noticeable beat but try and you will find a better tuning for A2 while sounding A4. So we better find a compromise in the tuning of the three intervals A3-A4, A2-A3 and A2-A4.

For the flatness of a high note compared to a lower chord this is a well documented physical phenomenom that has much to do with the way our brain deals with pitch perception. If you tune a beatless interval the high note will sound flat to our ears.

I have several singer clients who always complaint that the treble notes are flat. My tactic then is to tune one note to their taste.

"Tell me when to stop" I play the note one octave lower and then the note I am tuning while raising the pitch.

When they ask me to stop I play the two notes together and evidently the octave sounds horrible.

"Is that what you want?"

"No, never mind" is the answer.

The point here is to tune the middle as wide as possible by tempering the A3-A4 octave and tune the treble as high as possible without having too busy single octaves at the top of the scale. There are no objective limits, it is question of personal taste.


Edited by Gadzar (07/21/10 01:29 PM)
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#1478514 - 07/21/10 01:22 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
BDB Offline
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Posts: 20766
Loc: Oakland
If you are tuning octaves only by tuning octaves, that is not good enough. I do comparisons with thirds, fourths, and fifths and their octave cognates to make sure that the octave works for all intervals, not just the octave.
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#1478521 - 07/21/10 01:32 PM Re: How to tune Tempered Octaves ? [Re: BDB]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
BDB:

I do so also, now, but my point is whether beats are heard in multiple octaves when tuning single octaves aurally pure.

Gadzar:

You still have not said what you hear.
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#1478525 - 07/21/10 01:47 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Inlanding Offline
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Registered: 08/05/09
Posts: 1636
Loc: Colorado
Still reading/learning/assimilating with interest...

Glen
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#1478529 - 07/21/10 01:54 PM Re: How to tune Tempered Octaves ? [Re: Inlanding]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Hopefully it's a little entertaining, too. wink
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#1478533 - 07/21/10 01:58 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 20766
Loc: Oakland
Originally Posted By: UnrightTooner
BDB:

I do so also, now, but my point is whether beats are heard in multiple octaves when tuning single octaves aurally pure.


As far as I am concerned, they are. The area in which octaves and their multiples sound aurally pure is rather wide. Checking the other intervals narrows it down. Everything ends up in that narrow range.
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#1478536 - 07/21/10 02:04 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1432
Loc: Mexico City
Yes,

The sweet spot in tuning octaves is very large, one have to listen to other intervals to correctly tune them, always aiming to the wide side.

Tooner,

I don't follow you. I have said the way I tune. And I do it by hearing. What are you asking me?
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Rafael Melo
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1478540 - 07/21/10 02:12 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
BDB:

I have to agree that there is a wide area of where an octave sounds pure. But if I tune an octave directly, the area is very small where it sounds most harmonious. When these octaves are stacked I do not hear beats in multiple octaves. But I rarely tune octaves directly anymore. That very small area is not where I want the octaves tuned.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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