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Bernhard, this is exactly why I thought it would be a good thing to drop this theory. I do not know of one single acclaimed music scholar/researcher/theorist today that would claim that Bach used ET. This unfortunate theory somehow gained ground during the advocating of ET, but it is gone by now. Really.



No, no… The music remains different, but the advantage of the key colors are gone. I really can't find a way to be more clear about this than I have in my earlier postings, and if you can't see/hear/feel this major (sic!) difference, I am truly sorry.


My memory might fail me, but I don't think that I've said that I find ET unmusical? What I'm talking about here is the musical strength of color in the keys.
And to be very clear, I do NOT make any claims that EBVT automatically produce a better sounding recording. I find the AB tests fascinating in that sense, because they give feedback without predjudice

I see all of this as a great research, where you, me and others are most needed.

What have been been completely demolished through the AB tests, though, are the claims that remote keys in EBVT are offensive to the ear. If so, there should have been no hesitation on deciding which Clair de Lune (Db flat) was ET and which was EBVT.

So, honestly all - you can't have it both ways. Some argue that EBVT is simultaneously a) offensive in remote keys, b) a quasi-ET that is too close to a truly super-duper perfect ET (which we all of course tune ) to be of any worth. Make up your mind, or keep silent, guys!

(disclaimer: this was not in any way directed towards you personally, Bernhard, I just tried to economize my posts a bit )



Thank you for the concern, but there is no need to apologize - we are in no hurry!

Patrick, you write:

...“No, I haven't heard Bach on CHAS (except for Isaac's Bach/Siloti, which I think sounded really good). But as far as the Well-tempered Clavier, It is really evident that close keys in a WT/UT results in music that are different from the remote keys. You don't really have to listen to any other thing than the springiness of the prelude in C# major and compare it to the calm C major prelude to see what I mean. These characteristics of the keys get lost in ET, no matter which version of ET.”...

You say...WT/UT results in music that are different from the remote keys? I would not say “music” but ambient atmospheres, and in modern ET's atmospheres (and emotions) do change within the highest degree of euphonicity. Then, leaving Bach's intentions aside, we could learn from Beethoven and understand, once for all, that the same key-signature can open to any “calmness” and any “springiness”. Is this what you mean when you say “colour”? Really, I do not get your point.

http://www.youtube.com/watch?v=yR5AVUiNI-0&feature=related

http://www.youtube.com/watch?v=9nBSGi86r-c&feature=related

...“A fixed modern ET might be the most euphonious solution to you and others, but not to many non-piano musicians. At least in my experience of working with strings, choirs, wind/brass etc. by themselves, the intonation is not ET. Why would it be?”...

Any theoretical ET, once put into practice, will soon result in a modern quasi-ET (due to ordinary decay). And let's put our discussion into context, you are looking for conceptual contents for featuring UT's but, do you really think that “...others...strings, choirs, wind/brass etc.” have EBVT in their mind? Out of an ideological effort, you seem to refuse modern ET's validity in terms of tuning reference. Anyone would still be able to play with ETD few cents deviations, they would simply be what they are, singular deviations from modern ET. 

You ask why should others go for modern ET intonation. That is simply because modern ET sounds absolutely euphonious in all keys. If you ask how can it be so, for what I can explain, it is because our physiology is in line with nature's logarithmic geometry and proportions. And I still do not see how we could agree on a "subjective" template, more than on a "natural" template. 

...“I'd love to have the luxury of setting a new tonal center on the fly and deal with the intervals the way they sound best, but this is an impossibility with the piano. So yes, these nuances - the power of intonation - gives a sound that reminds me of a good UT… a temperament where interval sizes (most prominently = the major 3rds) vary from one key to another.”...

Intervals sizes could, should and would variate on the bases of your taste, like intervals sizes could, should and would variate for anyone, on the bases of their "in tune" taste. Can you imagine? That would not even be brown, as Stopper mentioned, it would be black like heck. 

Originally Posted By: alfredo capurso
As a musician, I should hope that you retain the meaning of "a chord that could sound better in tune".

You reply: “Yes this I do, and it happens almost every time i strike chords in an ET tuning.”...

I was not really looking for this kind of answer, since you (admittedly) can not talk about Chas. I was trying to understand: what is the pleasure in going from a dullish to a wolfish key? On this, can you sing? If you can sing, would you say you are “in tune”?

Originally Posted By: alfredo capurso
Thanks, I shall reword my question: How is it possible to refer to "colour" as to the feeling we get from a sequence of chords that could sound better in tune?

You reply: “Same problem here. You ask me somehing giving facts that I disagree with - how could I answer anything such? Ask a decent question that, at least slightly, leaves the door open for your ideals not being universial, then we could talk about that.”...

Actually, I'm saying that some chords may sound well tuned, others may not, and you seem to agree. Anyway, the issue is “color”. My points are: 1. it will not be alternating dullish and wolfish chords the way we can add “color”, nor enhance cadences, unless we admit cacophony. 2. Anyone may prefer its own (color) template, but that would be like heck (referred to ensamble / orchestra). 3. You seem to talk about "color", meaning either your own “in tune” preference or your own “practical tuning” preference. 4. My ideal (Chas) is not universal in that it is just mine, but in that it can be explained as “proportions (read harmony) in nature”. 

Originally Posted By: alfredo capurso
And the other question: Can a musician ever be vexed when he/she finds that all key-signatures sound absolutelly beautyfull? When all key-signatures, like in my experience, can readly and generously give back all their harmonic potential?

...“But of course! I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC).”...

Your conclusions about WTC and colored keys have the value of an arbitrary inference and I would really drop this kind of proof. Anyway, you may tell those musicians that now they could enjoy modern ET, not the age-old compromise but a tangible ideal. And I say this out of my pro experiences and only after having made sure that Chas model is shareable, both in scientific and practical terms.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Originally Posted By: Bernhard Stopper
"I see no contradiction at all. ET´s of that time were probably performed with an intuitive amount of stretch to satisfy musicality. I assume that this was done very close to what i am doing and what Bach (and every other musical individual including you) preferred/is preferring with his inner ear on melodical (musical) perception."

Kees, you reply:..."ET was not used in Bach's time."...

J.S.Bach died in 1750. The first, historical ET (12th root of two) had been formalised about 50 years earlyer. If I were you, Kees, I would explain that statement of yours, possibly in another thread. In any case, Stopper said: "ET´s of that time were probably performed with an intuitive amount of stretch to satisfy musicality." Indeed, even in those times, they had to stretch octaves so, what is relevant here, 12th root of two was simply inadeguate. The other two wrong axioms, pure octaves and a 12 semitones module will have been misleading for any temperament.

..."Harpsichords and baroque organs do not tolerate it. Very low inharmonicity of the hpschd translates in almost no room to stretch the octave."...

I haven't tuned baroque organs yet, but I have tuned Chas ET on harpsychords a good number of times (for concerts), never have I had troubles. You say "...almost no room to stretch octaves", yet it is possible.

..."Of course he (Bach) didn't use ET. No self-respecting early music performer uses ET anymore these days."...

Any reliable poster would not confuse his/her own ideas with real facts. For what I can say, many early music (concert) performers enjoy the use of modern ET.

..."As the purpose of playing Bach on the piano is to make it sound good it may be more important to let the piano sound good than to be historical."...

Playing Bach on the piano may be explainable with more than one purpose, but if the purpose was to make Bach and the piano sound good (professionally) there is no doubt, you have to be able to tune.

..."Of course "good" is a matter of taste."...

Nonsense. You can sing on your own, no matter how "out of tune" you are. But if you sing (and/or play) with others, you have to "sound good". If you are not in tune, many musicians could/would tell you.

a.c.

You forgot to mention Chas.

Kees

Everyone likes a little ***, but nobody likes a smart ***.

Well, Alfredo, maybe where you live. I haven't heard an ET-tuned harpsichord in any high-level early music concert for many, many years.

And, oh, I really think you should stop dissecting paragraphs, (and even sentences!) to make your case. Soon you will be down to single words, and then you can debate almost anything. It won't be in context, though, and that makes your counter-arguments pretty much worthless.

Respect us other posters when you quote, please.

I do not speak of proof, I just made an observation.

I have a big problem with you referring to ET as 12th root of 2 as the old way, and CHAS as the revelation. I do not know of any decent tuner that has ever tuned a theoretical ET. On the other hand, I know of many who have tuned a temperament octave between 4:2 and 6:3, and expanded this temperament along the principles of equal-beating 12ths and 15ths. This I think would be quite the same as your CHAS, and I think it is implemented every day, all around the world. Without the need for exclusiveness.

Patrick, you write:

...“And, oh, I really think you should stop dissecting paragraphs, (and even sentences!) to make your case. Soon you will be down to single words, and then you can debate almost anything. It won't be in context, though, and that makes your counter-arguments pretty much worthless.
Respect us other posters when you quote, please.”...

Patrick, you could have replied my previous post, you could have explained more in depth what you really mean when you talk about color, enhancement, emotions, ET's etc., but you prefer to post about an issue that I cannot take seriously.

You had written: “I know quite a few musicians that wouldn't touch ET with a ten foot pole, when it comes to interpret music written for "colored keys" (like, for example, the WTC).”.

My reply: “Your conclusions about WTC and colored keys have the value of an arbitrary inference and I would really drop this kind of proof.”

Now you write:... “I do not speak of proof, I just made an observation.”...

Let's see your “observation”. For what I understand, you offer a fact ( “I know quite a few musicians that wouldn't touch ET...”), and you give for granted that some music was written for "colored keys", which is debatable, and you give for sure that WTC was written for "colored keys", which again is debatable.

For what I understand, by mentioning the musicians you know, you intended to prove what you could not prove nor support with arguments, namely 1. some music was written for "colored keys", 2. WTC was written for "colored keys", 3. we need “colored keys” for expressing “calm” or “springiness” or what ever emotion. So Patrick, you may start respecting yourself, yours was not an observation.

You also write:..."I have a big problem with you referring to ET as 12th root of 2 as the old way, and CHAS as the revelation. I do not know of any decent tuner that has ever tuned a theoretical ET. On the other hand, I know of many who have tuned a temperament octave between 4:2 and 6:3, and expanded this temperament along the principles of equal-beating 12ths and 15ths. This I think would be quite the same as your CHAS, and I think it is implemented every day, all around the world. Without the need for exclusiveness."

Your post may prove your ignorance about practical tuning and theory, which might not be bad “in se”, but you could read Chas threads and deduce what is “implemented every day”. In fact, theoretical and practical aspects have long been discussed, so today it is difficult (for me) to justify your ignorance.

What may really represent a revelation, what would be offensive here is your attempt to banalize Chas temperamental theory and tuning issues. This would be bad in that you'd try to impoverish my solid sharing. And it would be worse in that it would show (to me) how your own education is not favoring your intellectual attitude. This tendency of yours, together with your (usual) arrogance and (unusual) impudence, would leave no room for more words.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf

Here is a list of organs and carillons in the Netherlands that are tuned unequally.

Not to argue any specific point, but I thought it's interesting.

Kees

Hello. Thank you, Kees, for the link above.

About colour, cadence enhancement, moods, emotions, ET's etc.

Géza Anda plays LUDWIG VAN BEETHOVEN (1770–1827): 33 Variations in C major on a Waltz by Anton Diabelli, op.120
33 Variationen C-Dur über einen Walzer von Anton Diabelli
33 Variations en ut majeur sur un thème de valse d’Anton Diabelli.

Thema and Variations 1/10:

http://www.youtube.com/watch?v=C_RMhv10y3o&feature=related

11/19:

http://www.youtube.com/watch?v=VOuWBwMD8uA&feature=related

20/29:

http://www.youtube.com/watch?v=PhB2sIZ-QKA&feature=related

30/33:

http://www.youtube.com/watch?v=-aTFkqHWjlo&feature=related

Joseph Kerman's comment:..."It is above all a work of the most violent jolts and contrasts, starting with Variation 1, an imposing, somewhat menacing march placed right after Diabelli’s speedy waltz. Later moments are sublime, tender, noble, uncanny, boisterous, raucous – clusters of variations of every kind, it seems, of every mood, character, tempo, velocity and texture."...

Who is Joseph Kerman?

http://music.berkeley.edu/people/profile.php?person=27

I found Kerman's comment (and the variations list) here:

http://www.onyxclassics.com/pressroom/ONYX4035.pdf

Out of my own interest for "colored keys" I found some "in favour" literature (Willis G. Miller):

http://www.millersrus.com/dissertation/#

My actual question:

Do you think Beethoven could ever be in need for "colored keys" (for the time being, read "non-equal temperaments")?

Regards, a.c.

a.c. writes:
>>Do you think Beethoven could ever be in need for "colored keys" (for the time being, read "non-equal temperaments")?

Greetings,
Yes, I do. There are several reasons, but the overriding one is that even today, an A-B comparison of Beethoven's keyboard works in ET and WT causes an overwhelming response in favor of the WT.(I have done this numerous times in front of audiences of piano technicians as well as musicians).
If one were to analyze LVB's choices of keys in which to compose his sonatas, it is found that the progression of use follows the same progression of dissonance in the thirds of any of the various forms of WT, i.e., C is the most common, F# the least, with all other keys used in direct proportion to their distance from C, (except for the favoritism LVB shows for Eb, which has its own possible explanation of utility).
Beethoven was adamant that his keyboard works be played in the key he composed them. The necessity to keep the harmonic balances as intended would be a more than plausible explanation for this. It is a simple matter, once one understands the organization of tempering in a WT, to 'parse' Beethoven's works and observe that only in the original key does one find coherent progressions of dissonance leading to resolutions in more consonant triads. If one were to change the key by a half-step, these coherent increases in dissonance disappear.

The following is from the technicians list, where I and another debated Lvb's choice of keys. Enid Katahn, a pianist, gives the musical reasons why a WT is important for Beethoven's sonatas, using op. 90. as an example.


inre the choice of keys in a conventional WT, a previous tech writes:
>There are some pieces where you could argue that a reverse of that system would be better; for example, Beethoven's op. 90. The opening in
Em(relative of G major) which is filled with tension might benefit from a
reverse WT.

To which Enid repsonds;
"Not true. Just because a key is more dissonant than Cmaj. doesn't
neccessarily mean it isn't peaceful. There is a difference between dissonance
as harshness and dissonance as emotionality, or expressiveness". In this
piece, Beethoven was looking for keys with more expression. As he goes
through, there are places where he creates a lot more contrast than he would
have in a more consonant key, such as C major."

Several examples:

bar 9: Beginning in a Gmaj, this passage moves downward, finally passing
through Cmaj before ending on a B triad. So, LVB places the most consonant
chord on the keyboard immediately before one of the most highly tempered. On
a WT , this juxtaposition creates a great harmonic contrast. The
pianist/historian's perspective on this is " This extreme contrast may be
read as LvB's way of letting us know that there is something going on under
the surface and it is not all as peaceful as you might think". (If LVB did
write this piece for his sponsor Baron Lichnowsky and his wife , it could be
making a musical referrence to the stormy marriage that they hid below the
verneer of civility in public. Beethoven is known for this sort of
stuff..Call the musicologists!!.)

However, what if Beethoven had written Op. 90 in C?
"If op. 90 had been composed in the "more consonant" key of C, Bar 9 would
have moved from from G to C, causing a change in how the passage works,
especially the last two chords. In the original key, the final modulation
from C to B creates a particularly strong musical resolution of this passage,
a resolution suggesting something mysterious. Had the sonata been in C, the
move from F to E would not be as dramatic. Instead, the passage would end
with two chords more similar to one another instead of its original very
"expressive" chord played against a background of maximum consonance."

In view of the above, when David writes "to argue that WT has more color
and therefore is more interesting, musical, dynamic,
multi-dimensional,<snip>is a waste of time". , I must disagree for the
following reason, among others:
In WT this modulation changes not only the pitch of the interval, but
also the beating, or "color', whereas in ET, only the pitch changes. Since
more happens when you drop 100 cents while changing from a 7 cent to a 19
cent third than when you simply drop everything 100 cents and the ratios stay
the same, I consider the WT to be more "multi-dimensional" and dynamic than
ET. The WT modulation is certainly more complex, even in the simplest
physical terms.
I would suggest that harmonic contrast, used in the above example, works
to enhance the expressive intentions of this music. (this is in the opening
bars, where we normally expect to find the musical expectations and hints of
things to come to be laid out). The choice of key determines the degrees of
contrast in the passages and I don't think Beethoven left those to anything
arbitrary.


Example 2: second mvt. going into bar 32,
The original choice for this passage in C#minor, a very colorful,
expressive key in WT. Enid writes:
" had Beethoven written op 90 in C, this would place this passage in Am,
which defeats the whole purpose. Am is a pleasant, peaceful sound, all the
way through, but this passage is supposed to be full of emotion". Played in
the key of Am on a Young temperament, the passage sounded lifeless to the
several listeners present.

Example 3: The passage beginning at 115.
Here, Beethoven goes from one extreme of consonance to the other, and does
it in a very refined fashion. Starting in C, he moves through Cm, C#min,
C#, Emaj, E7, then crashing B's resolving to E. In a WT, these modulations
create a steady rise in the amount of tension leading up to the climatic B,
from which, in the final move to E, creates a strong resolution. A
masterful example of using progressively increasing tempering as the passage
develops, arriving at a point of maximum "expression" (B) just before the
final resolution (to E). The emotionality or expression of the piece is
heightened by this coherent, organized increase.
However,if the sonata were in C, this progression would have begun in Ab! Hardly a consonant pleasant beginning, and a place from which it will be difficult to increase tension. That is a very intense key to begin a passage such as this! Where is there to go??
Had Op.90 been composed in the "more consonant" Key of C, the movement
would travel through: Ab, Abm , Am, A, C C7 G then ending on C. So, the passage
would have had the softening of the tempering going against the rise of
musical tension plus that odd return to consonance in the middle A to C move.
Also, the climatic, expressive chord would not be the original's heavily
tempered B, but rather, a usually dulcet G. This would be an odd use of
temperament and wouldn't be supportive of the musical direction the passage
exhibits.
All in all, Mrs. Katahn feels like Beethoven knew exactly what he was
doing. The "color" effects created in a WT consistantly work with the
musical direction of his music. This is to be expected, since,as she points
out, composers didn't just start with the first note and go through to the
end, but rather, they had distinct musical moments that they would go about
linking together, figuring out how to get from here to there,etc. In
anything but ET, the choice of key is a fundamental component of how the
harmony functionswith the musical direction.
Hope that helps
Regards,

I'm impressed!

I guess musicians, and specially composers of piano music, are better placed than we piano technicians to talk about temperaments.

Thank you, ED Foote, for your feedback.

I was asking: Do you think Beethoven could ever be in need for "colored keys" (for the time being, read "non-equal temperaments")?

You write:..."Yes, I do. There are several reasons, but the overriding one is that even today, an A-B comparison of Beethoven's keyboard works in ET and WT causes an overwhelming response in favor of the WT.(I have done this numerous times in front of audiences of piano technicians as well as musicians)."...

I'm sure what you report can happen indeed but, in my experience, it may depend on the ET and WT that were/are compared.

We needed to stretch 12th root of two octaves but we had no indications about how octaves should be stretched, nor about how/why 4ths, 5ths, 12ths and 15ths could effect the tuning of modern ET's.

This is why I would not be surprised to hear a stretched (attempt) version of our historical ET that sounds worse than a (stretched) non-ET. Today, though, you could compare any WT with an advanced, modern ET model and perhaps update your preferences. BTW, did you get to know that our historical ET (12th root of two) has evolved into advanced ET models?

By mentioning Beethoven (and links above) I meant to ask:

For what concerns music, may not Beethoven Variations prove that it is up to the composer to manage emotions, moods, tensions Vs release, dark Vs bright atmospheres etc., on the basis of their own creativity, their imagination and intentions, even playing in the same one key? Even if they were deaf?

Today I would also ask: which (stretched) WT would Beethoven have had in its ears? Would Beethoven have based his musical energy and modulations on close to C and remote “colored” keys issue?

I would also ask: What makes up for a “mild WT” today? Just any temperament that, by design, deviates a few cents from ETD's variants of the first ET? Few cents, otherwise it gets too wolfish, few cents, otherwise it would be called ET?

I ask all this because my urge for singing “in tune” and for composing (small c) came much earlier than any temperamental issue. My "in tune" urge was already there when I was five. So I would never rely on a particular temperament for my inspiration, I could not care less. At the opposite, if I had had precise sounds in my ears, different from what a semitonal scale can sound like, I would have created my own temperament. And this is actually happening today with microtonal scales. But perhaps I'm wrong, perhaps Composers would check their piano and semitonal temperament first, and only then would they compose and play.

Regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf
.

Greetings,
I wrote:
"even today, an A-B comparison of Beethoven's keyboard works in ET and WT causes an overwhelming response in favor of the WT.(I have done this numerous times in front of audiences of piano technicians as well as musicians)."...

Al responds:
>>I'm sure what you report can happen indeed but, in my experience, it may depend on the ET and WT that were/are compared.

I don't know that it matters too much, any of the plausible tunings of 1800, (Young, Kirnberger/Prinz, Prelleur,) have blown the finest ET's available out of the water! For modern ears, the Coleman 11 is still enough to make the profound difference.

A.C.
"We needed to stretch 12th root of two octaves but we had no indications about how octaves should be stretched, nor about how/why 4ths, 5ths, 12ths and 15ths could effect the tuning of modern ET's."

I have found that the amount of stretch is a moot point when an ET runs into a WT. ET sounds like a constant buzzing after the ear has been introduced to a WT that varies the tempering from say, a 6 cent C-E to a 21 cent F#-A#. I have stretched and compressed octaves on tunings, Stretching for concerto work, compressing in the Nashville recording studios, (for the bass players and producers listening to the congruence between the bass and piano). The high stretch is also favored by jazz players trying to cut through an overly energetic combo. I hate the sound, hearing it as unrelenting tension, and coupled with the lack of variety between the consonance and dissonance of a WT, it gets to be exhausting.

>> Today, though, you could compare any WT with an advanced, modern ET model and perhaps update your preferences.

Been there, done that. ET, regardless of stretch, is still a hyper-active intonation, and lacks the ability to affect our autonomic systems, (sympathetic and parasympathetic). The psycho-emotive effects of consonance/dissonance have been scientifically shown to be real, subliminal, and consistent. Stripping them out of music that was composed to utilize them compromises the emotional impact.

A.C.
I meant to ask:
For what concerns music, may not Beethoven Variations prove that it is up to the composer to manage emotions, moods, tensions Vs release, dark Vs bright atmospheres etc., on the basis of their own creativity, their imagination and intentions, even playing in the same one key? Even if they were deaf?"

I'm not sure they prove anything, but if you plot the key usage in the Variations, you will find a pattern. This same pattern shows up in the micro as well as macro view of music, i.e. Mozart's use of the keys, as well as Schubert and Brahms, display the same pattern. Chopin, interestingly enough, shows the exact same pattern but in reverse!

A.C.
"Today I would also ask: which (stretched) WT would Beethoven have had in its ears? Would Beethoven have based his musical energy and modulations on close to C and remote “colored” keys issue?"

I believe that his modulations were to create the coherent rise and fall of tension in his compositions, and the use of the resources of a WT, regardless of stretch, was a consistent and ever present factor. I would suggest you look at his sonata in F#, (can't remember the number). It is a singular piece in his work, and only makes real sense if you play it on a keyboard with a WT in place. You can't get pure fifths any other way.

A.C.
"I would also ask: What makes up for a “mild WT” today? Just any temperament that, by design, deviates a few cents from ETD's variants of the first ET? Few cents, otherwise it gets too wolfish, few cents, otherwise it would be called ET?

I would consider any tuning that deviates, in the historical pattern, from ET by less than two cents to be mild. However, even three cents can create a C-E that is only tempered 7 cents by raising the C and lowering the E. Also, if you lower the F# and raise the A# by three cents, you are very near the full syntonic comma, so it takes little to create huge differences from ET.

A.C.
"I ask all this because my urge for singing “in tune” and for composing (small c) came much earlier than any temperamental issue. My "in tune" urge was already there when I was five."

Did you naturally sing a 14 cent wide third? If so, you are unique in my experience. I have only heard that amount of stretch in unaccompanied voice when the singer is strongly leading to something else, otherwise, most voices I have heard naturally gravitate towards Just. As one singer told me, "Everything changes as soon as the piano begins to play".
I see nothing natural about out of tune singing, and a tempered third is, technically, "out of tune". (assuming by 'in tune' we mean no dissonance).

A.C.
" perhaps Composers would check their piano and semitonal temperament first, and only then would they compose and play."

I think it more plausible that composers of the time were aware of the resources available in the various keys, and selected them for particular musical purposes. We don't hear funeral dirges in the simple keys, nor lullabies in the remote ones. When the musical tension builds, we find a common reliance on modulation from consonance to dissonance,and we never hear a resolution occurring by moving to a more highly tempered key that what leads up to it. This is not coincidence, since the practice was nearly universal between 1700 and 1850, with echos following even after that.
All in all, if one were to play all the piano literature composed between Bach and Brahms on a well-tempered piano, there would be far less total dissonance than if it were played on one that had all thirds tempered 13.7 cents. What I think is important is that we get away from the idea that consonance is good and dissonance is bad. As Plutarch said centuries ago, "Music, to create harmony, must investigate discord".

Regards,

Hello Ed,

I'm again leaving for some days, so excuse the "quantity" of my replies. I'm very glad for getting to know your outlook on this subject, actually I went to your site...and I'll be happy to read the whole content.

Me:>>I'm sure what you report can happen indeed but, in my experience, it may depend on the ET and WT that were/are compared.

ED:..."I don't know that it matters too much, any of the plausible tunings of 1800, (Young, Kirnberger/Prinz, Prelleur,) have blown the finest ET's available out of the water! For modern ears, the Coleman 11 is still enough to make the profound difference."...

Sorry for my ignorance, what does "blown the finest ET's available out of the water", I do not know this idiom. Then, which "finest" ET are you referring to? Aural or ETD? One stretched-octaves version of 12th root of two or a modern ET? I think that would matter a lot, actually it may be foundamental.

ED:..."ET sounds like a constant buzzing after the ear has been introduced to a WT that varies the tempering from say, a 6 cent C-E to a 21 cent F#-A#. I have stretched and compressed octaves on tunings, Stretching for concerto work, compressing in the Nashville recording studios, (for the bass players and producers listening to the congruence between the bass and piano). The high stretch is also favored by jazz players trying to cut through an overly energetic combo. I hate the sound, hearing it as unrelenting tension, and coupled with the lack of variety between the consonance and dissonance of a WT, it gets to be exhausting."...

My first guitar would variate 3rds very much, though I cannot say how many cents. That I could not stand, I wanted all chords to sound in tune. In the ET I tune, 3rds like F#4-A#4 are so tense that I would never ask for more tension. You say "I hate the sound, hearing it as unrelenting tension, and coupled with the lack of variety between the consonance and dissonance of a WT, it gets to be exhausting."

Yes, perhaps we go for different settings. What for me gets exhausting in non-equals is this hearing a quite nice interval but, soon after, having to reduce my openness, my acceptance when, playing another interval, the wolf shows out. It is all this ear-adjustment that tires me, that would put me off and distract me every time.

I'll be back. Regards, a.c.

Alfredo writes:
" what does "blown the finest ET's available out of the water", I do not know this idiom.

It means no comparison. At one class, in a room of 20 techs, comparing the Coleman 11 to an ET, 2 preferred ET. In numerous comparisons, even after playing in all the keys of a WT, the overwhelming preference has been for the WT piano. I have compared them to my own ET, as well as several other ET's created by very fine technicians. One time, in Texas, the ET piano was tuned by Tom Seay, and it was as fine a tuning as I have ever heard. The audience still heard the WT as more pleasing. It is not the execution of the ET that causes its shortcomings, but rather, the selection!
All the stretch in the world does not create the variety of the keys.

"Then, which "finest" ET are you referring to? Aural or ETD? One stretched-octaves version of 12th root of two or a modern ET? I think that would matter a lot, actually it may be foundamental."

I don't think so, but perhaps we should give ET a definition we can use for comparison. Let us consider that a piano tuned in ET will have an equal amount of tempering in all like intervals, i.e. all thirds are tempered the same. Which casts an inquisitive light on the following two statements:

"My first guitar would variate 3rds very much, though I cannot say how many cents. That I could not stand, I wanted all chords to sound in tune."

By the above definition, if the thirds vary, it is not ET.


"In the ET I tune, 3rds like F#4-A#4 are so tense that I would never ask for more tension."

By the definition above, why would one third be more tense than another? The F#-A# third is tempered the same as the G-B, otherwise,the tempering is not equal! As was stated earlier, we hear logarithmically, so the tempering of the F#-A# should be heard no more "tensely" that any other. Even though the G-B third will beat faster than the F#-A#, it is not heard as more highly tempered because it is occurring at a higher set of frequencies. The human perception of tempering is not pitch dependent.

If one hears a particular key as being more tense on an ET, I submit that it is conditioning,based on an individual's ability to recognize keys by pitch, which brings the whole musicological/historical precedent into consideration.
Consider that if we always were slapped every time we saw the color red. it would be normal for us to wince at ever stop light. If we always heard the key of F# used for high tension composition,(which is not far from the truth in classical music), the pitch-cognizant listener will automatically ascribe tension to the key, regardless of how it is tuned. Pavlov was right!
Looking over piano literature as a whole, we see very clear trends in how keys were used by composers. The most expressive parts of the sonatas are most often placed in the most remote keys, and rarely are those remote keys used to resolve a composition. Why? Listen to LVB's "Waldstein". The second mvt. was written to replace the original, (which became "Andante Favorite"). It begins in F, goes through a step by step journey into highly dissonant chords, and slowly returns to a place that creates an incredible resolution in C for the final mvt. I suggest that any musical listener,if deprived of hearing the final mvt.after this section, will feel like they have been left hanging. However, when that bass note C hits, there is a strongly visceral relaxation that takes place. The effect of tempering is totally syncronized with the composition. This is not by random choice of key!
I suggest that trying for resolution by going from any given key to a more highly tempered key is so extremely rare because it does not allow the listener to feel the relaxation, on the subliminal level, that the composer is attempting to create.
We are calmed by consonance, and stimulated by dissonance. Thus, the use of UT's allow the ebb and flow of tension is a critically important factor in getting the most impact from the music.

Sonatas are harmonic journeys, they build tension and then resolve it. This creates the emotional response. When the tempering is employed to heighten this effect, (by resolving to less tempered sounds,which is a near constant in classical music), the emotional impact is stronger because our bodies are being manipulated in the same direction that our conscious minds are. This sounds like hocus-pocus, but is easily demonstrated.
If we truly want the most out of the music we love, we have to try all plausible alternatives, and the use of WT's in the 1800's is more than plausible.
Best regards,

Very excellent post, Ed.

Thanks

Glen

Hi all, have been away for a few days, just catching up on the forum now.

Alfredo:



WHAT? You asked:



... and I replied:



... and you start talking about proof? I don't get it. Still don't.



Well, there are quite a lot of very good tuners and math persons on this forum who can't understand what you're trying to say in your paper, nor in the elaborations in the CHAS threads, so I don't feel left out in the cold here.

You can call me, or others ignorant (which you have done quite some times now), but if you see all the cars on the highway driving in the wrong direction you'd really be wise to start asking yourself if you drive on the wrong side of the road...

If mostly everybody else that discuss with you sooner or later are considered arrogant and ignorant, that should be a sign that something is not quite right - either with your CHAS, your polemic skills, or both.

Ed,

I really like your extensive postings of Mrs. Katahn's comments. I haven't found a really suitable punch line for what a WT does to harmony yet, but I've been speaking quite a bit of its affect on the harmonic progression of a musical piece. It is good to see these analytical quotes underlining the same phenomenon.



I like that description, hyper-active intonation ET as a temperament doesn't really stimulate the listener or the musician in more than one single way, a little bit like driving a car in 2nd gear all the time.

Hello.

ED, those days are really busy for me but I shall reply properly on what you have said, thank you. Amongst your own arguments there is one that sounds nicely and unusually "dissonant", it is this one:..."What I think is important is that we get away from the idea that consonance is good and dissonance is bad. As Plutarch said centuries ago, "Music, to create harmony, must investigate discord"...

This is where we may agree on, as you mentioned (by chance?) one of Chas theory's pillars. This is why you do not find any "pure" interval in Chas ET model. That is how you could stop this maso-romantic game, this going through alternate pain and pleasure, wolfish and justish chords, remote and close keys-signature. Today we can explain (and go for) a consistent and solid "in tune" choir. Which non-equal/WT can you detect?

Mozart - The Magic Flute - end of opera (duet and chorus)
http://www.youtube.com/watch?v=bFdB8Zz8VOo

The Swingle Singers - Badinerie (Johann Sebastian Bach)
http://www.youtube.com/watch?v=jHcNHL8AyfU&feature=related

Bach aria 4° corda Swingle Singers
http://www.youtube.com/watch?v=4xQdboqVOzA&NR=1

Patrick, you write:

..."Well, there are quite a lot of very good tuners and math persons on this forum who can't understand what you're trying to say in your paper, nor in the elaborations in the CHAS threads, so I don't feel left out in the cold here."...

Despite what you can read in Chas threads, I'll never leave you out in the cold.

..."You can call me, or others ignorant (which you have done quite some times now), but if you see all the cars on the highway driving in the wrong direction you'd really be wise to start asking yourself if you drive on the wrong side of the road..."...

This is what I wrote: "Your post may prove your ignorance about practical tuning and theory, which might not be bad “in se”, but you could read Chas threads and deduce what is “implemented every day”. In fact, theoretical and practical aspects have long been discussed, so today it is difficult (for me) to justify your ignorance.

What may really represent a revelation, what would be offensive here is your attempt to banalize Chas temperamental theory and tuning issues. This would be bad in that you'd try to impoverish my solid sharing. And it would be worse in that it would show (to me) how your own education is not favoring your intellectual attitude."

That means that I'd find difficult to justify your ignorance, and that I'm puzzled about the effects of your education on your intellectual attitudes, since I wonder whether you intented to be offensive or what.

..."If mostly everybody else that discuss with you sooner or later are considered arrogant and ignorant, that should be a sign that something is not quite right - either with your CHAS, your polemic skills, or both."...

Patrick, I think it is the first time ever that I admit ignorance, wanting to go for the "easyest" option. This could prove you how polemics do not interest me. Yet I'd like you to check yourself (you'd want to be reliable) and list (for me too) all these "mostly everybody else...".

Thanks and regards, a.c.

CHAS Tuning MP3 - Amatorial recording on a Steinway S (5’ 1”, 155 cm)
http://www.box.net/shared/od0d7506cv

CHAS THEORY - RESEARCH REPORT BY G.R.I.M. (Department of Mathematics, University of Palermo, Italy):
http://math.unipa.it/~grim/Quaderno19_Capurso_09_engl.pdf