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#2061897 - 04/09/13 12:47 PM Re: Best UT for Voice Teacher [Re: Mwm]
Ed Foote Offline
1000 Post Club Member

Registered: 05/03/03
Posts: 1184
Loc: Tennessee
Originally Posted By: Mwm

If, in the math of 12ET, which forms the baseline in most modern visualizations for comparing the various historical temperaments, all octaves are truly beatless, and all other intervals beat to a greater or lessor extent, then, as soon as we apply stretch to "harmonize" the whole compass of the piano, we have moved away from 12ET, since every interval has some beat to it. My ear, as a musician, doesn't really hear the errors, as it were. Now Kirnberger III, which has a number of beatless fifths and major thirds, if stretched to suit the iH of a piano (an inappropriate use of Kirnberger III I might add, but good for illustration), all intervals will have some beat and the sense of the pure, relaxed sound that would have been there without the stretch is lost.


Greetings,
The IH has little to do with the effects of tempering. It is the comma that is demanding compromise. The presence or lack of beating is not a defining characteristic of ET, since the "E" of ET is referring to a quality of equality, and this equality remains, regardless of stretch. The unequal temperaments maintain their balance, regardless of stretch.

In the Kirnberger, the quality of purity that the C-E offers extends farther from the middle of the keyboard than the human ear can discern, and the more highly tempered thirds actually begin to sound harmonious as one takes them below C3. (This is due to the critical band beginning to limit partials).
Though there are no beatless intervals on a piano, we usually accept a 4 cent M3 as pure, and a fifth that is only tempered by half doesn't sound that much different from an normal ET fifth. Thirds don't have to be totally pure to create the effect and the contrast of WT. Few people would tell the difference in the tempering of the C-E between the Young and Kirnberger. There are certain bell-like intervals on a piano in a Kirnberger, and these are the fifths of the most remote keys. I don't think this tuning on a Steinway is inappropriate, at least, not to my customers that use it, and I don't think it is nearly as inappropriate as Bach in ET (which to my WT polluted ears, sounds like a bee hive buzzing, all the time, everywhere, in the music).
Regards,

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#2061979 - 04/09/13 02:41 PM Re: Best UT for Voice Teacher [Re: Ed Foote]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Thanks Ed for your observations. I think I begin to understand the concept of stretch as not affecting the temperament. Interesting.

Do you do concert tunings in UTs on pianos that normally have a different temperament, and then return them to the original temperament after the concert? I am thinking of the limitation on repertoire - does Prokofiev or Poulenc sound good in Valotti?

Cheers.

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#2062091 - 04/09/13 06:32 PM Re: Best UT for Voice Teacher [Re: daniokeeper]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 678
Loc: Canberra, ACT, Australia
Mwm, I like to think of a rubber band analogy:

If a 12ET is drawn as intervals on a horizontal rubber, and the rubber is stretched, the intervals are stretched but the ET remains.

If the horizontal rubber is 8 octaves long and stretched from each end it will slightly stretch the center octave but stretch more at the extremities.

If there are more lengths of rubber attached perpendicular to the rubber for every note, like a comb, then we have an analogy for the iH for each note. If each harmonic is drawn as an interval on each perpendicular rubber then stretching those rubbers will represent the increase in frequency due to iH.

The amount of stretching for the perpendicular rubbers is fixed depending on the dimensions of the real piano strings, and varies for each string. The perpendicular rubbers at extremities stretch further.

The amount of stretching for the horizontal rubber will depend on the frequency coincidence of selected harmonics from several arbitrary perpendicular rubbers with selected harmonics from other perpendicular rubbers. There will never be perfect matching but only a best fit which depends which, and how many, perpendicular stretched rubbers are chosen.


Edited by Chris Leslie (04/09/13 06:34 PM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2062096 - 04/09/13 06:50 PM Re: Best UT for Voice Teacher [Re: daniokeeper]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Thanks Chris for the analogy.

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#2062160 - 04/09/13 10:09 PM Re: Best UT for Voice Teacher [Re: Mwm]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 678
Loc: Canberra, ACT, Australia
Thinking further about the analogy: a UT would be represented by uneven intervals drawn on the horizontal rubber band. Stretching the rubber should widen the intervals but keep the relationship. However, since the stretch is actually variable depending on the perpendicular rubber bands, and more so at the extremities, then the UT relationship will break down towards the extremities.

I think that if a tuner balances several intervals in tuning single notes, then the extremities will converge towards equal temperament.


Edited by Chris Leslie (04/09/13 10:10 PM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2062162 - 04/09/13 10:22 PM Re: Best UT for Voice Teacher [Re: Chris Leslie]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Originally Posted By: Chris Leslie
Thinking further about the analogy: a UT would be represented by uneven intervals drawn on the horizontal rubber band. Stretching the rubber should widen the intervals but keep the relationship.However, since the stretch is actually variable depending on the perpendicular rubber bands, and more so at the extremities, then the UT relationship will break down towards the extremities.
I think that if a tuner balances several intervals in tuning single notes, then the extremities will converge towards equal temperament.
Emphasis added by mwm


Don't let anyone else here at PW know what you said above. It might start a revolution!

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#2062170 - 04/09/13 10:29 PM Re: Best UT for Voice Teacher [Re: Chris Leslie]
Ed Foote Offline
1000 Post Club Member

Registered: 05/03/03
Posts: 1184
Loc: Tennessee
Originally Posted By: Chris Leslie
Thinking further about the analogy: a UT would be represented by uneven intervals drawn on the horizontal rubber band. Stretching the rubber should widen the intervals but keep the relationship. However, since the stretch is actually variable depending on the perpendicular rubber bands, and more so at the extremities, then the UT relationship will break down towards the extremities.
I think that if a tuner balances several intervals in tuning single notes, then the extremities will converge towards equal temperament.


Actually, the effects of temperament are only really discernable in the middle four octaves of a piano. above or below, and the beating of ET is too fast or slow to register as beating. The color of say, a m3 in the 6th octave, is about the same, regardless of temperament. Same goes for the first two octaves, as far as 3rds are concerned.


>>Do you do concert tunings in UTs on pianos that normally have a different temperament, and then return them to the original temperament after the concert? I am thinking of the limitation on repertoire - does Prokofiev or Poulenc sound good in Valotti?<<

I keep the concert pianos in a mild Victorian era WT, which hasn't yet caused anyone to notice it wasn't strictly equal. I don't want to change them since everyone likes the way the pianos sound, right now.
People seem to respond favorably to the slightest departure from ET, as long as that departure follows the traditional order. Unlike tuners, who suffer the occupational hazard of comparative listening, Temperament has to get fairly strong to draw musicians' attention. A 21 cent third, such as found in the Valotti or Young, might be disruptive in performing music written by composers imbued with ET from the beginning of their musical exposure. However, Debussy, for all his sweeping harmony, sounds fine and textured in a tuning that allows a range from 8 to 18 cents around the circle of fifths. Could his early imprinting have been burnished by a sense of key character? I don't know, but there are plenty of plausible routes to that conclusion.

How much tempering is optimum is like asking how much salt is needed in the soup. There is a taste component, hence, no fixed answer. Those composers who likely matured in a harmonic environment of WT could be expected to use the keys to create familiar harmonies. Those that came later possibly gave it no thought, and in their music, additional consonance and dissonance, rather than assisting in the creation of an emotional response, might cause unintended results in chord voicing, phrasing, and general overall tonal feel.
Regards,





Edited by Ed Foote (04/09/13 10:40 PM)

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#2062171 - 04/09/13 10:40 PM Re: Best UT for Voice Teacher [Re: Ed Foote]
Mwm Offline
500 Post Club Member

Registered: 02/20/13
Posts: 752
Well stated. Thank you.

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#2062182 - 04/09/13 11:07 PM Re: Best UT for Voice Teacher [Re: Mwm]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
Originally Posted By: Mwm
Originally Posted By: Chris Leslie
Thinking further about the analogy: a UT would be represented by uneven intervals drawn on the horizontal rubber band. Stretching the rubber should widen the intervals but keep the relationship.However, since the stretch is actually variable depending on the perpendicular rubber bands, and more so at the extremities, then the UT relationship will break down towards the extremities.
I think that if a tuner balances several intervals in tuning single notes, then the extremities will converge towards equal temperament.
Emphasis added by mwm


Don't let anyone else here at PW know what you said above. It might start a revolution!

This has been discussed extensively here in the past.

What I remember is that there is no point in keeping the UT structure outside the midrange, and the temperament morphs outside there. (No music uses M3's in the bass.) This is possible because there is no unique P8 on the piano because of IH and opens the possibility of an UT on 88 notes, rather than 12.

Interesting stuff!

Kees

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#2065400 - 04/16/13 08:26 AM Re: Best UT for Voice Teacher [Re: DoelKees]
alfredo capurso Online   content
1000 Post Club Member

Registered: 07/10/07
Posts: 1077
Loc: Sicily - Italy
Originally Posted By: DoelKees
Originally Posted By: Mwm
Originally Posted By: Chris Leslie
Thinking further about the analogy: a UT would be represented by uneven intervals drawn on the horizontal rubber band. Stretching the rubber should widen the intervals but keep the relationship.However, since the stretch is actually variable depending on the perpendicular rubber bands, and more so at the extremities, then the UT relationship will break down towards the extremities.
I think that if a tuner balances several intervals in tuning single notes, then the extremities will converge towards equal temperament.
Emphasis added by mwm


Don't let anyone else here at PW know what you said above. It might start a revolution!

This has been discussed extensively here in the past.

What I remember is that there is no point in keeping the UT structure outside the midrange, and the temperament morphs outside there. (No music uses M3's in the bass.) This is possible because there is no unique P8 on the piano because of IH and opens the possibility of an UT on 88 notes, rather than 12.

Interesting stuff!

Kees


Hi All,

Yes, interesting stuff, at least for me (as an aural piano tuner); beyond general discussions, I would really like to come to some logical conclusions, to some steady and shareable points that may better explain "voice intonation" as well as "taste", UTs and modern ETs properties.

Would you please let me know if one of you is (really) interested in this kind of analysis?

Regards, a.c.
.
_________________________
alfredo

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