Equal Temperament Revised
Alfredo...@libero.it
Ozan Yarman
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Alfredo...@libero.it
----Messaggio originale----
Da: "Ozan Yarman" <ozany...@ozanyarman.com>
Data: 28/08/2016 21.12
A: <micro...@googlegroups.com>
Ogg: Re: Equal Temperament Revised
Ozan Yarman
Alfredo...@libero.it
----Messaggio originale----
Da: "Ozan Yarman" <ozany...@ozanyarman.com>
Data: 29/08/2016 14.42
Claudio Di Veroli
> Alfredo wrote : ... paper by Hinrichsen
> Ozan wrote: ... the whole paper aimsa t fairy dust magic ...
Grazie Alfredo for the link and Ozan for the comments!
I just gave a look at the article. It is written by somebody who LOOKS well informed, and acknowledges that different modern proposals have been made: all of them are slightly different, and here we have yet another one.
The paper raises interesting points in the field of mathematical acoustics. Unfortunately, I find that some statements are at odds with what we know about the history and acoustics of the Western musical scale and temperament:
1) Abstract: says that "ET has been in use since the 19th century."
Actually, this has been known to be untrue for decades, and more recently the matter has been fully investigated by different specialists. It is well documented (and researched) that ET was in use during the 16th century as a system for fretted string instruments. It was then abandoned as first meantone variants and then circular temperaments became widespread, until eventually ET came into use again after the middle of the 18th century, NOT the 19th century.
2) P.2. "temperaments [2], i.e. tuning systems seeking for a reasonable compromise between harmonicity and invariance under transposition, attempting to reconcile the exponential structure of the scale with the linear organization of the partials. This development culminated in the so-called equal temperament (ET)".
The belief that ET developed out of unequal temperaments, claimed by Barbour in his 1951 book, is a myth, as agreed upon by all present-day leading scholars, and as shown by extant evidence. Most of the unequal temperaments in use in Western music, with the only exception of meantone, developed AFTER the 16th century, i.e. after ET had already been mathematically described in treatises and used in practice for decades in fretted instruments. Later in the late 18th century musicians went back to already-known ET.
3) P.3. "To this end we apply the concept of entropy as a measure for the harmonicity of a temperament."
Which is a problem because historically, ever since the Renaissance up to modern times, the harmonicity of a temperament has been based on how in tune it plays the consonant intervals: this relates to how musicians and audiences aurally perceive dissonances. I am not aware that we can aurally perceive the entropy as described by Hinrichsen. He seems mainly concerned by the description using advanced mathematical calculus on pp.8-15. Actually this is what most of the paper is about. The point is: can we hear the difference? The few lines about this matter in section 8., at the end of p.15, hardly clarify the matter.
4) P.4. "equal temperament ... rediscovered in Europe in the 18th century".
This contradicts a previous statement where Hinrichsen wrote that it has been in use since the the 19th century, and anyway we have already seen that ET was already described and in use in the 16th century.
5) P.16. "Conclusions: Using entropy as a measure of harmonicity we have provided numerical evidence that the standard equal temperament with semitone frequency ratio 21/12 does not represent the harmonic optimum, the optimum is rather obtained for a slightly larger frequency ratio."
Unfortunately, Hinrichsen has just shown that his development agrees with a mathematical measurement of entropy that he has arbitrarily defined. This circular reasoning therefore fails very short from proving that intervals sound better in his "c.ha.s" system that in ET. Actually the difference is so small (as rightly pointed out by Ozan) that I believe that not even professional keyboard tuners can tell the difference.
6) P. 17. "An important open question would be the appropriate choice of the parameter "e" such a new standard. Would it be sufficient to choose a fixed value as a reasonable
compromise for all purposes? Or do we have to keep "e" as a free parameter varying in the range (33), chosen as a matter of taste?
Ideas like this one, i.e. frequently retuning by changing significant details of the temperament, have already been advocated for other temperaments by other modern writers. They all seem to forget that Western music is not restricted to solo instruments. In an ensemble, if the piano or organ or harpsichord is retuned changing the "e" paramenter, you have also to expensively rebore the modern oboes, clarinets and flutes that will play in an ensemble with such a keyboard!
7) "References": one looks in vain for well-known modern temperament scholars, such as Lindley, Barbieri, Rasch, Schulter, Sturm ...
Best regards
CDV
Ozan Yarman
Alfredo...@libero.it
----Messaggio originale----
Da: "Claudio Di Veroli" <d...@braybaroque.ie>
Data: 29/08/2016 18.40
A: "microtonal"<micro...@googlegroups.com>
Cc: <Alfredo...@libero.it>
Ogg: Re: Equal Temperament Revised
Alfredo...@libero.it
----Messaggio originale----
Da: "Ozan Yarman" <ozany...@ozanyarman.com>
Data: 29/08/2016 20.02
A: <micro...@googlegroups.com>
Ogg: Re: Equal Temperament Revised
Mr. Capurso,Obviously you did not respond to the critical issue. Those cumulative effects are "for the worse" in the case of two octaves, and utterly negligible in the case of "perfect fifths", and next to null in effect in the case of "major thirds" and "minor thirds" with or without the addition of the octave. The only improvement to speak of is for the octave+fifth, and to the detriment of practically all else.The standard you mention is utterly defunct and non-applied in the case of continuous-pitched instruments, piano-less orchestras, as well as historical performances relying on many other non-equal temperaments of Early European music - to say nothing of the rest of the world. Furthermore, I couldn't appreciate anything out of the ordinary tuning-wise in the video link you shared. If anything, I found the piano sound very bland and dull if this is due to the espoused 6/1-EDO instead of owing to the recording quality or the intonation problems of the orchestra. We seem to be beating around the bush needlessly.Dr. Ozan Yarman
On Aug 29, 2016, at 6:09 PM, 'Alfredo...@libero.it' via microtonal wrote:
Hi Dr. Oz,Normally, I make a distinction between common practice and theory, and I never forget what models are meant for.I am glad you are aware of "cumulative" effects: as mentioned, a "little" difference will not only affect the octave(s) but all intervals.In my experience, considering live performances, a little difference can make a very big difference in terms of resonance and harmoniousness.A live sample:Tedious as it may seem, 12th root of two is still the Western standard model. Any effort aimed at perfecting our first ET model is, in my opinion, commendable.
Kind regards,Alfredo Capurso
----Messaggio originale----
Da: "Ozan Yarman" <ozany...@ozanyarman.com>
Data: 29/08/2016 14.42
A: <micro...@googlegroups.com>
Ogg: Re: Equal Temperament Revised
Mr. Capurso, you must be kidding us. No human being can, in live performance, notice the proposed 0.063 cent difference (let alone acoustically tune it), or the cumulative difference of 0.42 cents for a perfect fifth - but maybe, just maybe, succeed to feel that the octaves are deformed (for the worse) by 0.72 cents for the middle to high registers. Yes, the cumulative effect goes up as you travel to 6/1 (resulting in even worse double octaves deformed by 1.45 cents for instance), but the idea of recuperating the tedious 12 equal pitches to the octave practice does not, in my opinion, require such long papers to be written on the subject - especially when musics around the world, including Western common-practice, feature pitches and intervals that significantly deviate from the 100 cents grid or their proposed substitutes.Cordially,
Dr. Ozan Yarman
On Aug 29, 2016, at 2:25 PM, 'Alfredo...@libero.it' via microtonal wrote:
Hello Dr. Oz,I do not understand what makes you think of a joke, perhaps you can explain?As for "little" differences that "..no one can noticeably hear..", in my experience that may depend on the ear of the individual listener/musician.Furthermore, any "little" difference will affect not only one particular interval, but (obviously) all intervals, and please note that once you expand the temperament, the original difference becomes inevitably larger and larger.As far as I am concerned, the real difference is between a "compromise", like 12th root of two, and the ideal solution. Is that little?
Kind regards,Alfredo Capurso
----Messaggio originale----
Da: "Ozan Yarman" <ozany...@ozanyarman.com>
Data: 28/08/2016 21.12
A: <micro...@googlegroups.com>
Ogg: Re: Equal Temperament Revised
Division of 6/1 into 31 parts? This gives:100.063064544044748which diverges from 100 cents semitone by an absolute 0.06 cents. 7 of them makes a perfect fifth that is 700.4 cents. Unless this is a joke, the whole paper aims at fairy dust magic, since no one can noticeably hear that little a difference compared to 12-equal pitches.Dr. Oz.
✩ ✩ ✩
On Aug 28, 2016, at 9:22 PM, 'Alfredo...@libero.it' via microtonal wrote:
Hi All,About one year ago Professor Haye Hinrichsen, from the University of Wuerzburg, published the results of a research where the 12th root of two Equal Temperament is compared with three more recent ET models.The assumption is that the lowest degree of disorder can achieve maximum harmoniousness.You can download his paper from the link below. Hope you enjoy reading about that:Best regards,Alfredo Capurso
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Jake Freivald
Jake
Claudio Di Veroli
Ozan Yarman
Alfredo...@libero.it
----Messaggio originale----
Da: "Claudio Di Veroli" <d...@braybaroque.ie>
Data: 30/08/2016 10.23
A: "microtonal"<micro...@googlegroups.com>
Cc: <Alfredo...@libero.it>
Ogg: Re: Re: Equal Temperament Revised
Salve Alfredo!> Anyway, on your points 1 and 2, I would be sincerely grateful if you could mention your source, i.e. the indisputable proof that "..ET was in use during the 16th century".Well, actually there is plenty of evidence in ancient sources, both in texts and in paintings of lute necks showing a geometrical progression of fret spacings.If you are really interested in this subject you should read the well-known treatise by Mark Lindley: "Lutes, Viols and Temperaments", Cambridge University Press (UK) , 1984.Its "Chapter 3. Equal temperament" begins thus: "Most theorists between 1550 and 1650 regarded lutes and viols as equal temperament instruments". You should really read the whole 24 pages long chapter. The first mathematical-geometrical exact description of ET is in Zarlino's Istitutioni Armoniche, Venice 1558.> On point 4, the feeling I get is that we all look for some sort of certainty, though it remains difficult to project one single picture for the whole Western musical scenary in the 16th century.I did not say this (neither does Lindley): just that it was strongly prevalent in lutes and viols in the 2nd part of the 16th century and beginning of the 17th. And for this reason Italian treatises of the time advises of the impossibility of playing lutes together with keyboards, which were tuned in meantone. But some lute and viol players did, and so probably they were already fretting in meantone: this would become commonplace around mid 17th century.> On point 5, I have good news: so far I have been able to instruct a good number of pro tuners, about 90 students and have worked for an endless number of musicians, their feedbacks are univocal.Good. I would like to read in the future about scientifically/statistically valid experiments about this, thanks!> On point 7, I hope you did not miss to much of what you already know.No, my point is that the Reference shows that, unfortunately, Hinrichsen has not read the main modern scholars on temperament. Even worse, he has read the bad ones: he quotes Barbour's book of 1951, which already in the 1970's was shown to contain more wrongs than thruths.Tante cose,Claudio da Lucca_____________________________________
On Tuesday, 30 August 2016 01:13:43 UTC+2, Alfredo Capurso wrote:
Hello Claudio,Thanks for your reply. I am not here to defend Professor Haye Hinrichsen's paper, but simply to share his work with you.Anyway, on your points 1 and 2, I would be sincerely grateful if you could mention your source, i.e. the indisputable proof that "..ET was in use during the 16th century".On point 3, it is hard to say if we all would hear a difference, in general I would not expect that.On point 4, the feeling I get is that we all look for some sort of certainty, though it remains difficult to project one single picture for the whole Western musical scenary in the 16th century.On point 5, I have good news: so far I have been able to instruct a good number of pro tuners, about 90 students and have worked for an endless number of musicians, their feedbacks are univocal.On point 6, I agree with you.On point 7, I hope you did not miss to much of what you already know.
Kind regards,Alfredo Capurso
----Messaggio originale----
Da: "Claudio Di Veroli" <d...@braybaroque.ie>
Data: 29/08/2016 18.40
A: "microtonal"<micro...@googlegroups.com>
Cc: <Alfredo...@libero.it>
Ogg: Re: Equal Temperament Revised
> Alfredo wrote : ... paper by Hinrichsen
> Ozan wrote: ... the whole paper aimsa t fairy dust magic ...
Grazie Alfredo for the link and Ozan for the comments!
I just gave a look at the article. It is written by somebody who LOOKS well informed, and acknowledges that different modern proposals have been made: all of them are slightly different, and here we have yet another one.
The paper raises interesting points in the field of mathematical acoustics. Unfortunately, I find that some statements are at odds with what we know about the history and acoustics of the Western musical scale and temperament:
1) Abstract: says that "ET has been in use since the 19th century."
Actually, this has been known to be untrue for decades, and more recently the matter has been fully investigated by different specialists. It is well documented (and researched) that ET was in use during the 16th century as a system for fretted string instruments. It was then abandoned as first meantone variants and then circular temperaments became widespread, until eventually ET came into use again after the middle of the 18th century, NOT the 19th century.
2) P.2. "temperaments [2], i.e. tuning systems seeking for a reasonable compromise between harmonicity and invariance under transposition, attempting to reconcile the exponential structure of the scale with the linear organization of the partials. This development culminated in the so-called equal temperament (ET)".
The belief that ET developed out of unequal temperaments, claimed by Barbour in his 1951 book, is a myth, as agreed upon by all present-day leading scholars, and as shown by extant evidence. Most of the unequal temperaments in use in Western music, with the only exception of meantone, developed AFTER the 16th century, i.e. after ET had already been mathematically described in treatises and used in practice for decades in fretted instruments. Later in the late 18th century musicians went back to already-known ET.
3) P.3. "To this end we apply the concept of entropy as a measure for the harmonicity of a temperament."
Which is a problem because historically, ever since the Renaissance up to modern times, the harmonicity of a temperament has been based on how in tune it plays the consonant intervals: this relates to how musicians and audiences aurally perceive dissonances. I am not aware that we can aurally perceive the entropy as described by Hinrichsen. He seems mainly concerned by the description using advanced mathematical calculus on pp.8-15. Actually this is what most of the paper is about. The point is: can we hear the difference? The few lines about this matter in section 8., at the end of p.15, hardly clarify the matter.
4) P.4. "equal temperament ... rediscovered in Europe in the 18th century".
This contradicts a previous statement where Hinrichsen wrote that it has been in use since the the 19th century, and anyway we have already seen that ET was already described and in use in the 16th century.
5) P.16. "Conclusions: Using entropy as a measure of harmonicity we have provided numerical evidence that the standard equal temperament with semitone frequency ratio 21/12 does not represent the harmonic optimum, the optimum is rather obtained for a slightly larger frequency ratio."
Unfortunately, Hinrichsen has just shown that his development agrees with a mathematical measurement of entropy that he has arbitrarily defined. This circular reasoning therefore fails very short from proving that intervals sound better in his "c.ha.s" system that in ET. Actually the difference is so small (as rightly pointed out by Ozan) that I believe that not even professional keyboard tuners can tell the difference.
6) P. 17. "An important open question would be the appropriate choice of the parameter "e" such a new standard. Would it be sufficient to choose a fixed value as a reasonable
compromise for all purposes? Or do we have to keep "e" as a free parameter varying in the range (33), chosen as a matter of taste?
Ideas like this one, i.e. frequently retuning by changing significant details of the temperament, have already been advocated for other temperaments by other modern writers. They all seem to forget that Western music is not restricted to solo instruments. In an ensemble, if the piano or organ or harpsichord is retuned changing the "e" paramenter, you have also to expensively rebore the modern oboes, clarinets and flutes that will play in an ensemble with such a keyboard!
7) "References": one looks in vain for well-known modern temperament scholars, such as Lindley, Barbieri, Rasch, Schulter, Sturm ...
Best regards
CDV
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Claudio Di Veroli
Thanks Alfredo for your kind reply.
Alfredo...@libero.it
----Messaggio originale----
Da: "Jake Freivald" <jdfre...@gmail.com>
Data: 30/08/2016 3.54
A: <micro...@googlegroups.com>
Ogg: Re: Equal Temperament Revised
Claudio Di Veroli
Alfredo...@libero.it
As mentioned, my purpose was sharing his findings with you, which is what I have accomplished.
----Messaggio originale----
Da: "Claudio Di Veroli" <d...@braybaroque.ie>
Data: 04/09/2016 16.02
A: "microtonal"<micro...@googlegroups.com>
Cc: <Alfredo...@libero.it>
Ogg: Re: Re: Equal Temperament Revised