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#1485682 - 08/01/10 05:54 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4904
Loc: Bradford County, PA
Gadzar:

Verituner, from what I understand, must use some calculations not just measured partials. Otherwise, you would have to sample all the notes before tuning.

As I said before, what got me started on all this originally is the difference between what I hear and what “modern iH tuning theory” calls for especially the behavior of the beat rates of 4ths and 5ths.

If a tuner is skilled, Dr. White’s method is more than adequate including the stretch necessary for both iH and the human ear. It was not until Dr. Sanderson tried to use theoretical pitches to tune a piano that he had a problem and had to make allowances for iH.

The effect of iH on beat rates is largely self-correcting on well scaled pianos. On poorly scaled pianos ETDs, even the Verituner, have problems from what you have said. So not only is “modern iH tuning theory” inadequate, but an ETD measuring actual, individual partials is also.

Thinking more about the error in using Young’s equations rather than a lookup table made me realize that the error is not as great as I first thought. The results from my analyses are still valid. Since I produced my own iH curves from (hopefully) raw data using Young’s equations and predicted beat rates using the same equation, I did not compare “apples to oranges.” And the general behavior of beat rates is still as predicted, is what I hear, and agrees more closely to what Dr. White predicts than what “modern iH tuning theory” predicts. If you doubt this, learn to set the temperament and expand it upwards by using 4ths and 5ths.

Rather than refer to CHAS and OnlyPure I prefer to use the terms mindless octaves and pure 12ths. It is not clear what either CHAS or OnlyPure exactly is. Stepping back from the details I realize that these stretch schemes are untempering fifths, which results in stretching octaves. They do not temper octaves directly. IH need not come into play when discussing the way a tuning is stretched unless actual frequencies are calculated even when using octave types instead of untempering fifths: The choice of octave type is a practical matter of using the most appropriate tests as Dr. White proscribed: 6:3 in the bass, 4:2 in the middle, 4:1 in the treble and give a little extra stretch on the ends to satisfy the human ear if desired. When discussing widening the middle octaves to 6:3 or to a 4:2/6:3 compromise the next comment always is the slight beat that is heard when the octave is played. In practice the octaves are stretch wider than aurally pure – end of story. And although SBIs do not double in beat rate each octave, the important fact that they do increase in beat rate does not change, unless of course they are deliberately tuned otherwise. I am still confused that others do not hear this.
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#1485697 - 08/01/10 07:13 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Olek Online   content
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Registered: 03/14/08
Posts: 7156
Loc: France
It is SO complicated ! researches have also shown than the "aurally pure" octave is not a 2:1 but a little larger, and that not only on the piano.

Other show that appreciation of pitch is due to the spacing between partials more than the "fundamental"

I seriously question the ability of Edt to "hear", even if som come pretty close , as the first dedicated version of the Verituner, the VT100.

Due to the definition level of the ear all that can well pass unperceived.

I Suggest that a software based on a predetermined ratio, as 3:1, may well provide some kind of coherent result without any iH appreciation, as what is checked is a coupling of frequencies, a simple effect than little pocket goodies may be able to check.
Now how are the first notes evaluated? can a list of frequencies suffice as a start ? if the expected result is a pure ratio between for instance 220hz and 660hz, no need to compute iH.
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#1485805 - 08/01/10 11:00 AM Re: How to tune Tempered Octaves ? [Re: Olek]
Gadzar Offline
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Registered: 12/15/06
Posts: 1589
Loc: Mexico City
Tooner,

Verituner does measure iH. Every partial needed for calculation is measured in advance. And yes it makes a lot of calculations with these measured partials. In fact it measures partials as you are tuning. So you don't need to do a measure pass. Though there are tuners who like to do a little measure before the actual tuning. Ron Koval for instance advises to do so.

I personaly make always two passes, the first one is a rough tuning to put piano at pitch and the second, aural or electronic, a fine tuning.

It is not the same to talk about the size of an interval, for example a pure 12th, than to talk about a way of tuning, for example CHAS and Onlypure.


A tuning involves the stretching of all the intervals all along the scale, which may and do change from one point to the other. I don't know what Onlypure does in the low bass, but If I tune pure 12ths I get busy 6:3 octaves, too narrow to be acceptable.

A piano can't be tuned from one single interval. You must hear to all of them and tune accordingly.
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#1485819 - 08/01/10 11:23 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
All intervals progress in their beat rates when going up the scale, as predicted by the "12th root of 2" + "beats are produced by nearly coincident partials" theories. But, 5ths (and 8ves) are the most affected by iH.

Why 5ths and not M3s? Because in ET fifths are very close to pure and stretching them, even a little, put them a the limit of purity, changing their character.

For the other intervals this is not an issue. A little more tempering does not change their characteristic sound.

In the same way, iH creates several types of octaves. There is no pure octave, there are several types of stretched octaves.



Edited by Gadzar (08/01/10 11:26 AM)
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#1485909 - 08/01/10 02:10 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
DoelKees Offline
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Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Suppose you have laid a master tuning on a nicely scaled piano using whatever scheme you want.

As a thought experiment let's now raise the 3'd partial of A3 by a bit, leaving everything else as-is.
How would you fix the tuning?

An ETD like tunelab draws a smooth curve through all the partials, so the A3 would be considered just an anomaly, and the original tuning curve would stay in place. The result would be unusually busy E3A3 and A3E4.

As an aural tuner if you try to normalize the beat rates of the fifth A3E4 you would probably raise A3 a bit.
Since you drag along the other partials this would result in a revere well temperament with FA wider than equal temperament and AC# narrower than ET.

Would you not say that tunelab's solution is actually better? I.e., just average and smooth all the inharmonicity measurements, ignoring the details of each string, and use a tuning curve based on that. Irregularities in the partials will result in some unusual beat rates, but no musician ever hears beat rates anyways.

Your thoughts would be appreciated.

Kees

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#1485923 - 08/01/10 02:22 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 211
Loc: Germany
Originally Posted By: Gadzar
I don't know what Onlypure does in the low bass, but If I tune pure 12ths I get busy 6:3 octaves, too narrow to be acceptable.

A piano can't be tuned from one single interval. You must hear to all of them and tune accordingly.



Duodecimes (twelfths) tuned with OnlyPure (by the aural method or with the ETD software) in StopperStimmung (the tuning) should be aurally pure. That means they rather have a 9:3 or 6:2 size than a 3:1 in the bass depending on the instrument. Whole tone aural purity (doesn´t matter if the intervals are octaves, duodecimes or fifths etc) is defined as a point where the sum of the beats of the involved partials are minimal.
If whole tone duodecimes are pure, resulting whole tone octaves are generally wide and not narrow. The 6:3 level of such a wide whole tone octave is generally not on the narrow side either in the bass.

Bernhard Stopper




Edited by Bernhard Stopper (08/01/10 03:34 PM)
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#1485997 - 08/01/10 04:18 PM Re: How to tune Tempered Octaves ? [Re: Bernhard Stopper]
DoelKees Offline
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Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Thanks Bernard. Below interval plots for pure 6:2 in the bass going smoothly to pure 3:1 at C5 and then 3:1 all the way to the top. It is as you say.


Heintzmann upright


Steinway D

Kees

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#1486008 - 08/01/10 04:33 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Originally Posted By: DoelKees
Suppose you have laid a master tuning on a nicely scaled piano using whatever scheme you want.

As a thought experiment let's now raise the 3'd partial of A3 by a bit, leaving everything else as-is.
How would you fix the tuning?

An ETD like tunelab draws a smooth curve through all the partials, so the A3 would be considered just an anomaly, and the original tuning curve would stay in place. The result would be unusually busy E3A3 and A3E4.

As an aural tuner if you try to normalize the beat rates of the fifth A3E4 you would probably raise A3 a bit.
Since you drag along the other partials this would result in a revere well temperament with FA wider than equal temperament and AC# narrower than ET.

Would you not say that tunelab's solution is actually better? I.e., just average and smooth all the inharmonicity measurements, ignoring the details of each string, and use a tuning curve based on that. Irregularities in the partials will result in some unusual beat rates, but no musician ever hears beat rates anyways.

Your thoughts would be appreciated.

Kees



This is a good question, Kees, and I reasoned exactly this way when I strolled the exhibit hall at the convention.

I spoke to Robert about Tunelab, and told him that I look at the Iphone/Tunelab combination as a possible buy in the feature. Still Nokia for me, though, patriotic and all... :-D No, but I use Symbian for so much that a platform switch would be a major change for me.

Then I checked Verituner, and read up on it a bit on the web. Same procedure with the RCT.

I decided on the RCT because of its interface, and the fact that it DOESN'T measure iH on-the-fly. Still haven't used it, but I will soon.
_________________________
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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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#1486258 - 08/01/10 11:14 PM Re: How to tune Tempered Octaves ? [Re: Bernhard Stopper]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
Thanks Bernhard,

It is very interesting. I always think of 12th as being 3:1, I'd never thought about 6:2 and 9:3 wich are most audible in the low bass, and that will prevent narrow 6:3 octaves.
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Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1486271 - 08/01/10 11:32 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
Originally Posted By: DoelKees
Suppose you have laid a master tuning on a nicely scaled piano using whatever scheme you want.

As a thought experiment let's now raise the 3'd partial of A3 by a bit, leaving everything else as-is.
How would you fix the tuning?



If correcting aurally, I'll leave A3 as is. My way of tuning A3 gives priority to a 6:3/4:2 balance in A3:A4 octave, so I would not hear to 3rd partial of A3.

But even if it was A#3 I will leave it as is also. In this case I will hear the A#3-F4 narrow 5th but I give priority to 8ves and progressive M3s over 5ths. A note is involved in many intervals up and down and my tuning won't prioritize 5ths over all the other intervals.

If using Verituner I don't know exactly what it will do. It is supposed to measure every partial, so it will take note of the anomaly and I suppose it will adjust its "targets". But, here again, A3 is a special case. It is the second note tuned and it is tuned from A4, so the 3rd partial of A3 is not involved and maybe the anomaly will be ignored.
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Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1486272 - 08/01/10 11:33 PM Re: How to tune Tempered Octaves ? [Re: Bernhard Stopper]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Originally Posted By: Bernhard Stopper

If whole tone duodecimes are pure, resulting whole tone octaves are generally wide and not narrow. The 6:3 level of such a wide whole tone octave is generally not on the narrow side either in the bass.

Bernhard Stopper




What is a "whole tone duodecime"? Doesn't make sense at all in music theory, but I think you might mean something else?

[EDIT]: Oops, my fault, got it…

Originally Posted By: Bernhard Stopper

Whole tone aural purity (doesn´t matter if the intervals are octaves, duodecimes or fifths etc) is defined as a point where the sum of the beats of the involved partials are minimal.


...but I seriously recommend that you change your definition. "The whole tone" is, and will remain, 1 full step = one half step = two semi-tones in all musically related discussion. It is well established, and not easily changed. Thus, there will not be such a thing as "a whole tone 5th" or "a whole tone 12th" in English. [/EDIT]
_________________________
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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#1486306 - 08/02/10 12:40 AM Re: How to tune Tempered Octaves ? [Re: pppat]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
I've often seen the term "whole tone": listen at a note/interval as a whole tone, opposed to listen at specific or near coincident partials. When we voice we speak also of the "tone" of the piano as being the sum of all partials of a given note.

We are talking as tuners and I believe the term describes fine what it means.

What do you think about: F-A# P4th, G#-C M3, for example used by most of the E.T. piano tuners, instead of the correct F-Bb P4th and Ab-C M3?


Edited by Gadzar (08/02/10 12:43 AM)
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rafaelmelo@afinacionpianos.com.mx

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http://www.afinacionpianos.com.mx

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#1486311 - 08/02/10 12:57 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Inlanding Offline
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Registered: 08/05/09
Posts: 1640
Loc: Colorado
Originally Posted By: Gadzar


What do you think about: F-A# P4th, G#-C M3, for example used by most of the E.T. piano tuners, instead of the correct F-Bb P4th and Ab-C M3?


Raphael,
What do you mean?
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#1486317 - 08/02/10 01:14 AM Re: How to tune Tempered Octaves ? [Re: Inlanding]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
Musically speaking a fourth is an interval between a note and the 4th note away.

example: C-D-E-F so C-F is a fourth.

counter example: F-G-A-A# is not a fourth it is a 3rd (augmented)
A# count as an alteration of A.

example: F-G-A-Bb so here F-Bb is a fourth.

In E.T. sharps and flats are enharmonics. So A# is the same note (same frequence) than Bb.

In just intonation for example sharps and flats are totally different from each other. So A# has not the same frequence than Bb, and there is indeed a difference between an augmented third and a perfect 4th.

So musically speaking it is incorrect to name the F-A# interval as a fourth.


Edited by Gadzar (08/02/10 01:15 AM)
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1486319 - 08/02/10 01:21 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Originally Posted By: Gadzar
I've often seen the term "whole tone": listen at a note/interval as a whole tone, opposed to listen at specific or near coincident partials. When we voice we speak also of the "tone" of the piano as being the sum of all partials of a given note.

We are talking as tuners and I believe the term describes fine what it means.

What do you think about: F-A# P4th, G#-C M3, for example used by most of the E.T. piano tuners, instead of the correct F-Bb P4th and Ab-C M3?


I have no problem with the latter, as long as we speak about the notes of the piano and do not move into harmony.

And I have no problem with "whole tone" in itself either, I just think that there could be a better expression. To say something like "a whole tone fifth" is to music theory what "a car with 4 1/2 wheels" would be to a mechanic. Impossible. Or then, if you really would go to lengths, it would be an augmented fifth, ie C-G#.

If piano tuning will have to deal with music and not become an abstract art, there shouldn't be vague terms. In fact, i think that might be the reason for the different terms harmonic, overtones and partials.

There is no full tone scale, so why not speak about "full tone" or "complete tone" or something like that? Just a thought.
_________________________
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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#1486321 - 08/02/10 01:30 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Originally Posted By: Gadzar
I've often seen the term "whole tone": listen at a note/interval as a whole tone, opposed to listen at specific or near coincident partials.


... and in this context, in a sentence, there is no ambiguity. A "whole tone 5th" is another matter.
_________________________
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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#1486394 - 08/02/10 07:28 AM Re: How to tune Tempered Octaves ? [Re: pppat]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4904
Loc: Bradford County, PA
In Kees example, I would tune the 4ths and 5ths to sound right. The difference would probably be unnoticeable in the 3rds and 6ths. Intervals that are tempered 2 cents are 7 times more sensitive than those tempered 14 cents. After setting the temperament, I usually run through the chromatic major chords. If one stands out it is always because of a fourth or fifth, never a 3rd or 6th even if they are not quite progressive.

Kees: Love the graphs! Notice that the fifths are always narrower than the 3:1 twelfths (duh!). How tall is your Heintzmann?

Pat: Or "Entire Tone" or "Whole Sound" but we know what was meant.

Mr. Stopper: Thanks! I had thought about the 6:2 twelfths in the bass lately when I noticed that my tunings had produced octaves between 6:3 and 8:4. But I am including the note an octave above the lower note in addition to the 12th, so the “Entire Tone” that I am listening to is different.
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Part-Time Tuner
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#1486401 - 08/02/10 07:37 AM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7156
Loc: France
Talking of "pure tone" Someone noticed that the beat of an octave, a third, etc, is always heard at the upper note level ?
One have to force the ear to discriminate beats at a partial match level
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#1486702 - 08/02/10 03:13 PM Re: How to tune Tempered Octaves ? [Re: Olek]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Yes, I have had a hard time because I've been listening to far too many things. Focusing on just what you're supposed to took me a lot of time.

Isaac, at least one exception would be the 4th that beats with the lower note, but then again that is pretty easily heard because it is so high in relation to the fundamental!
_________________________
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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#1486823 - 08/02/10 07:10 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Erus Offline
Full Member

Registered: 12/26/07
Posts: 386
Loc: Mexico
Originally Posted By: Gadzar

So musically speaking it is incorrect to name the F-A# interval as a fourth.


I'd say it depends on what kind of music you are talking about, and what theoretical framework you are working with. What you say is correct if you speak about the common practice period, and also correct for a lot of music from the 20th century onwards. But I'd not say *musically speaking*, because there are LOTS of different possibilities (both old, and recent).

You can have a perfectly good theoretical system saying F-A# and F-Bb are be the same interval. You can work just fine without considering "archaic" notational conventions. That difference between thirds and fourths made a lot of sense for non-fixed pitch instruments that were playing notes derived from exact ratios, and it made a lot of sense in a tonal system.

But we can write music and not have anything to do with those old ways. Most of that notational system is still used just because everybody knows it, and because it's kind of useful. But the grammar developed with that system is long gone, unless we are playing "retro" music, in which case F-A# is, indeed, a very nasty interval.

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#1486936 - 08/02/10 09:57 PM Re: How to tune Tempered Octaves ? [Re: Erus]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
Isn't just intonation used anymore? Even among singers?
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Piano Technician
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Serving Mexico City and suburbs.

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#1486946 - 08/02/10 10:09 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Erus Offline
Full Member

Registered: 12/26/07
Posts: 386
Loc: Mexico
Is it the ONLY way to build a musical scale or construct intervals? Even in electronic music?

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#1486950 - 08/02/10 10:14 PM Re: How to tune Tempered Octaves ? [Re: Erus]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
I mean, as long as just intonation will be used these are not "archaic" notations, but useful and precise ways of naming different notes.
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Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1486955 - 08/02/10 10:27 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
DoelKees Offline
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Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Originally Posted By: Gadzar
I mean, as long as just intonation will be used these are not "archaic" notations, but useful and precise ways of naming different notes.

Every time I read about tuning the "fourth" FA# I cringe.
But I know what they mean smile

Kees

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#1486956 - 08/02/10 10:30 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Originally Posted By: Gadzar
Isn't just intonation used anymore? Even among singers?

When I played in a recorder consort the way to tune (say) E6 to C6 is to listen to the difference tone and make sure it is exactly C4.

Kees

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#1486957 - 08/02/10 10:31 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Erus Offline
Full Member

Registered: 12/26/07
Posts: 386
Loc: Mexico
My point exactly: it depends on what kind of music you are talking about, and what theoretical framework you work with.

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#1486959 - 08/02/10 10:33 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1589
Loc: Mexico City
For a keyboard instrument with 12 notes to the octave it is acceptable.

For other contexts it may be wrong.
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#1486984 - 08/02/10 11:08 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Erus Offline
Full Member

Registered: 12/26/07
Posts: 386
Loc: Mexico
It CAN be acceptable, but that is not always the case, for an instrument with 12 notes per octave.

The keyboard can be the same, and it can be tuned in the same way, but the logic behind the music could be completely different for two different works to be played on that very same keyboard instrument, one after the other. In such case, it is not about tuning, but about "spelling" and "grammar."

Therefore, it can be musically correct to say "F-A# and F-Bb are both fourths" for one work, and musically incorrect for another.

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#1487019 - 08/03/10 12:05 AM Re: How to tune Tempered Octaves ? [Re: Erus]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1589
Loc: Mexico City
I guess you are right.

It is not a question of tuning, temperament, keyboard design, number of keys in an octave, instrument, voice intonation or whatever. It is a question of spelling and grammar. I mean musical rules.

Musically speaking, all of these intervals are thirds, even if they range from 2 to 6 semitones:

F-Ab, F-A, F-A#, Fb-Ab, Fb-A, Fb-A#, F#-Ab, F#-A, F#-A#

And all of these are fourths:

F-Bb, F-B, F-B#, Fb-Bb, Fb-B, Fb-B#, F#-Bb, F#-B, F#-B#

(Double flats and double sharps may be added to the above lists).


But then, in which case can it be musically correct to say "F-A# fourth"? It goes against rules.



Edited by Gadzar (08/03/10 12:30 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1487203 - 08/03/10 10:22 AM Re: How to tune Tempered Octaves ? [Re: Gadzar]
Mark R. Offline
1000 Post Club Member

Registered: 07/31/09
Posts: 1933
Loc: Pretoria, South Africa
Perhaps one could refer to Mr Stopper's "whole tone" as "complete tone envelope".

The interesting thing, for me, is that aiming for the best complete tone envelope is how I've always tried to tune intuitively - until the day I stumbled across PianoWorld and read about partials, inharmonicity, octaves types, stretch, etc. etc.

In a (rather unsettling!) way, I feel as though I've come full circle - or perhaps "full spiral".
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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