Temperament / Key Character / Tuning
Discussions - Part 2

Continue from Part 1

Getting short of temperaments

Alex Riedlmayer wrote (May 7, 2003):
Bradley Lehman wrote:
< No, he wrote the Well-Tempered Clavier for a _well_ temperament. In the well temperaments, every key is different. Equal temperament is not well temperament. >
I have often seen equal temperament excluded from well temperament, but it doesn't seem to be anything but unprovable snobbery. Ditto for the supposed lack of key characteristics in equal temperament.

[from another message]
< G# and Ab ARE different notes, and always have been, functionally (until atonal music came around). >
What makes them functionally different, as opposed to other enharmonics? What has atonal music to do with any of this? (You're surely not referring to Schoenberg's and Webern's arrangements of Bach's music.)

< [BOR-ing.] >
This seems to sum up your views of equal temperament.

< This may sound like an advert for bleach detergent (or High Definition TV, or Monosodium Glutamate), but the brights really are brighter and the whites are whiter and the darks are more colorful, and the sweet parts are sweeter and the vinegary parts are more pungent. >
It still sounds like advertising, particularly desperate advertising.

Robert Sherman wrote (May 7, 2003):
Somebody (I've lost track of who) wrote
< G# and Ab ARE different notes, and always have been, functionally (until atonal music came around). >
This is absolutely true, but it leads to a puzzle I've never been able to understand. Maybe Brad or another of the theory boffins can explain it.

String players consciously play G# different (higher) from Ab, D# different from Eb, etc. But for natural notes (C, F, whatever) they only play them at one given pitch.

Now consider a transposing instrument, say a horn in Bb.

Should the horn player play his F# higher than his Gb? Presumably he should. But whoops, that note is in reality (concert pitch) an E natural, which the string players consider to be always the same. So the hornist is playing at two pitches what the strings are playing at one.

Conversely, when the hornist plays what he regards as C, it sounds Bb. Or is it A#? Should he play C a bit high some times and a bit low some other times, depending on whether the string parts (which he can't see) show Bb or A#?

In fact, at a given center pitch (A=440 or whatever) of course there are many pitches for each written note, depending on the key. And in reality the strings and horns just tune to each other and do what sounds best to their instincts. But I have heard string players insist emphatically (and very wrongly) that while Bb is different from A#, all Cs are the same. So if we were to establish a universal system of true (non-tempered) intonation for all (non-keyboard) instruments that can tune on the fly, what would it be?

And to really compound the issue, consider the trombone, which is physically pitched in Bb but played as if it were in C.

Sorry, I know this is way OT.

Bradley Lehman wrote (May 7, 2003):
Bradley Lehman wrote:
<< No, he wrote the Well-Tempered Clavier for a _well_ temperament. In the well temperaments, every key is different. Equal temperament is not well temperament. >>
Alex Riedlmayer wrote:
< I have often seen equal temperament excluded from well temperament, but it doesn't seem to be anything but unprovable snobbery. Ditto for the supposed lack of key characteristics in equal temperament. >
File your complaint with the gentlemen who invented the terms "wohltemperiert" and "well temperament."

As for characteristics in equal temperament, there IS a theory going around (within the last ten years, mainly promulgated by a pair of people in Michigan) that the 12 equally-tempered notes each have a distinctive vowel color. They haven't proved it empirically. I do give it some credence, as it aligns fairly well with my own perceptions (I can often hear if music is in sharps or flats, even when it's in equal temperament, due to the 'colors' I sense from it...not visual colors as such, but tonal brightness...it's hard to explain). But is that learned from listening to tonal music for many years and making associations? Or is it innate? That's what they haven't shown yet.

[from another message]
<< G# and Ab ARE different notes, and always have been, functionally (until atonal music came around). >>
< What makes them functionally different, as opposed to other enharmonics? >
Is this a rhetorical question or a serious question? Judging from your generally erudite postings, you DO understand functional harmony (dominant chords, subdominants, mediants, secondary dominants, diminished sevenths, etc.), do you not?

And were you paying attention when I patiently explained the functional difference between chromatic semitones and diatonic semitones?

< What has atonal music to do with any of this? (You're surely not referring to Schoenberg's and Webern's arrangements of Bach's music.) >
Enharmonic equivalents are functionally interchangeable only in atonal music. That's what it has to do with all of this. You're good at logic; take the contrapositive of this and apply it to tonal music.

<< [BOR-ing.] >>
< This seems to sum up your views of equal temperament. >
Yeah, pretty much. :) If most of the music we listen to is tonal music, why not use tonal temperaments to let it be even more vivid?

Somebody in Nashville told me that some of the studio pianos are kept in well temperaments rather than equal temperaments, because the people who come through and work with them stick to only a few harmonies anyway, and they like the way it makes those particular keys sound especially good. That's a very good practical reason.

<< This may sound like an advert for bleach detergent (or High Definition TV, or Monosodium Glutamate), but the brights really are brighter and the whites are whiter and the darks are more colorful, and the sweet parts are sweeter and the vinegary parts are more pungent. >>
< It still sounds like advertising, particularly desperate advertising. >
Only to someone who prefers not to take a taste test.

Thomas Braatz wrote (May 7, 2003):
Brad Lehman stated:
>>File your complaint with the gentlemen who invented the terms "wohltemperiert" and "well temperament."<<
DWB lists 1^st instance of this technical term in German in a book by Harsdörffer "Teutscher Secretarius" (1656) "als musikalischer Fachausdruck zur Bezeichnung gleichmäßiger Intervallabstufung auf Tasteninstrumenten." ["a technical term in music to designate equal division of the intervals on keyboard instruments."]

OED lists 1^st instance of this technical term in English (with the meaning: 'tuned in equal temperament') as occurring in 1820 in a translation of Forkel's "Life of John [sic] Sebastian Bach" Grove's Dictionary recognizes the term for the 1^st time in 1889: "The well-tempered Clavichord".

Of course there are the articles in the New Grove on 'well-tempered' and 'temperaments.' Of interest are the early attempts at equal temperament referred to under the section "Equal Temperament to 1735."

I like the Neidhardt (1732) quote in the article on 'temperaments': "Thus equal temperament brings with it comfort and discomfort, like blessed matrimony."

Bradley Lehman wrote (May 7, 2003):
Thomas Braatz wrote:
< Of course there are the articles in the New Grove on 'well-tempered' and 'temperaments.' Of interest are the early attempts at equal temperament referred to under the section "Equal Temperament to 1735."

I like the Neidhardt (1732) quote in the article on 'temperaments': "Thus equal temperament brings with it comfort and discomfort, like blessed matrimony." >
Ah, Neidhardt, the guy famous for developing a series of fake equal temperaments. Instead of bunching the tempered fifths together, as normal in the well temperaments, he sprayed them symmetrically around the circle separated by the pure fifths. This causes all the resultant major thirds to be the same size, eliminating modulatory differences; plus these temperaments are easier to set up than real equal temperament is. (I've used some of these, and listnever noticed it was fake.) What kind of marriage did Neidhardt have? :)

Bradley Lehman wrote (May 7, 2003):
And even this supposedly clear terminology "gleichmäßiger Intervallabstufung" does not necessarily refer to 12-note equal temperament (that is, it probably does NOT). In ALL the meantone temperaments, the (correctly spelled) whole steps are equally spaced.

It should be remembered that music from the 14th, 15th, 16th, and into some of the 17th century was still built on principles of hexachords (the "Guidonian Hand," solfege, all that stuff)...the six-note scale "Ut re mi fa sol la"...and the church modes. (A late example: Pachelbel's collections of Magnificat fugues on the various tones.) "Major" and "minor" scales came in during the 17th century and eventually took over from those older systems.

The 12-key layout on keyboards came up in the 14th century to supply the most commonly needed notes, starting from C. (Alex, that's another answer to your question from yesterday: the specific notes Eb-Bb-F-C-G-D-A-E-B-F#-C#-G# are the ones most closely related to the primary hexachord C-D-E-F-G-A.) Normal temperament was the "equal" temperament of the regular meantone systems: interlocked and overlapping hexachords.

E-F#-G#-A-B-C#
A-B-C#-D-E-F#
D-E-F#-G-A-B
G-A-B-C-D-E
C-D-E-F-G-A
F-G-A-Bb-C-D
Bb-C-D-Eb-F-G

In all of these hexachords, "Ut re mi fa sol la", in meantone temperaments, the pattern is the same: there are two equal whole steps, followed by a diatonic semitone, followed by two more equally spaced whole steps. And those hexachords supply all the commonly used notes!

In each of those hexachords, notice that we simply add another group of three notes before or after the previous hexachord, to make a new one:E-F#-G# A-B-C# D-E-F# G-A-B C-D-E-F-G-A Bb-C-D Eb-F-G

Also notice that all eight of the standard German note names are generated by the three main hexachords, giving the natural notes:
G-A-"H"-C-D-E
C-D-E-F-G-A
F-G-A-"B"-C-D

In case I haven't said it strongly enough yet, I'll point out again: in all these hexachords, the whole steps are equally tempered. In that sense, all the meantone temperaments are "equal" temperaments! (Tom, that's necessary background for your 1656 quote below....) And there's that diatonic semitone (the melodic type of semitone) in the middle.

When accidentals pop up in pre-17th century music, it means we've shifted to a different hexachord. :)

The chromatic semitones (such as G-G#: a note of the same name) only crop up when all these hexachords are jammed together into a collection and musicians start crossing willy-nilly among them, instead of staying within a hexachord.

The term "meantone" MEANS that the note Re is exactly the "mean" (the geometric average, the middle) equally spaced between Ut and Mi; and Sol is equally spaced between Fa and La. Instead of being a just intonation tone of 9:8 or 10:9, Re is some compromised "mean" tone between its neighbors.

All the meantone temperaments (including Pythagorean, with pure fifths) are generated by choosing a consistent size of fifth and then stacking them up. They all result in Ut-Re-Mi equally tempered; Fa-Sol-La equally tempered...in all the hexachords.

Fun, eh?

-----

See also this historical summary of the terms "well tempered", "meantone", "equal temperament", etc.: one of the introductory chapters in Owen Jorgensen's book Tuning (1991): http://www.vaix.net/~bpl/jorgensen.htm

Thomas Braatz wrote (May 7, 2003):
Brad Lehman commented:
>>Ah, Neidhardt, the guy famous for developing a series of fake equal temperaments. Instead of bunching the tempered fifths together, as normal in the well temperaments, he sprayed them symmetrically around the circle separated by the pure fifths. This causes all the resultant major thirds to be the same size, eliminating modulatory differences; plus these temperaments are easier to set up than real equal temperament is. (I've used some of these, and listeners never noticed it was fake.) What kind of marriage did Neidhardt have? :)<<
Then looking at the Neidhardt (1732) quote in the article on 'temperaments' from the New Grove: "Thus equal temperament brings with it comfort and discomfort, like blessed matrimony," means that the comfort he derived (from same-sized major thirds) meant more discomfort elsewhere. Not a very equitable marriage arrangement!

Brad, are you getting ready to tell us that Harsdörffer in his "Teutscher Secretarius" (1656) in defining 'wohltemperiert' ('well-tempered') "als musikalischer Fachausdruck zur Bezeichnung gleichmäßiger Intervallabstufung auf Tasteninstrumenten." ["a technical term in music to designate equal division of the intervals on keyboard instruments"] [Harsdörffer's own words!] really did not mean what he said or that he did not truly understand what 'equal' meant (that 'equal' = 'something less than equal)? Notice that Harsdörffer does not say a 'good' temperament (one without a wolf 5th)!

The New Grove article on 'well-tempered' admits that despite the fact that while there were other temperaments 'employed at that time' [Bach's time], "Bach's choice of title ("Das wohltemperierte Klavier") disallows any form of regular mean-tone temperament." And "Bach had evidently instructed Kirnberger as a student to temper all major 3rds larger than pure" (which still allows for many variations of temperament, as you have pointed out.) But then the article goes on to equate equal temperament (as presumably understood by Bach - there is no firm evidence to either prove or disprove this) with other less-than-equal temperaments: Valloti, Werckmeister, Neidhardt. The fact that J.S.Bach would not allow others to tune his keyboard instruments (I am assuming here mainly harpsichords and clavichords) and the fact that around him the proponents of other temperaments were pushing their views on these matters even long after Bach had died, could possibly have indicated that Bach had discovered for himself (equal temperament had existed before his time) the advantages of equal temperament and became its proponent wherever it was possible. Bach's organ music may be in a category by itself since it would have been much more difficult to change the properties of the existing pipes that had been constructed with another temperament in mind. Judging from Bach's usual method of instruction (he seems to have been more interested in modeling and demonstrating true musicianship rather than also documenting it as Heinichen, Mattheson, et al had done,) he would have calmly persisted in achieving his 'goal' of 'wohltemperiert' by providing and playing the most excellent music possible (the '48') as 'proof' that these other temperaments are lacking in one respect or another. In a few cases, he may have been successful his endeavor to persuade others: C.P.E. Bach is known to have possibly sided with his father: From the New Grove on 'Temperaments': "Since C.P.E. Bach was sufficiently concerned to give not only a warning about the limitations of mean-tone but also emphatic advice about the tuning of the clavichord and piano, the fact that he did not recommend exploiting the inflections of a circulating unequal temperament in a genre which, by his own definition, ‘modulates into more keys than is customary in other pieces’ suggests an indifference to those inflections. When C.P.E. Bach spoke of ‘remote’ keys, he meant keys remote from the tonic key, not keys remote from C major or D minor....his favorite instrument, the clavichord, was the least likely of all normal keyboard instruments to display to much advantage the niceties of an irregular temperament. If the music of any leading 18th-century German composer ought to be performed in equal temperament, C.P.E. Bach is the best candidate."

Perhaps C.P.E. Bach really did absorb what J. S. Bach had been 'modeling' for almost 30 years (the last, most mature years): equal temperament was the ideal way to go.

Thomas Braatz wrote (May 7, 2003):
Brad:
>>Fun, eh?<<
You had better rewrite Mark Lindley's article on temperaments in the New Grove! It seems that you have just defined 'equal=unequ.'

From his article:

"The ratio 18:17, familiar to theorists from well before the Renaissance and recommended by Vincenzo Galilei in 1581 for equal temperament on the lute, corresponds mathematically to a semitone of 99 cents, virtually indistinguishable from the 100-cent semitone of equal temperament."

"In 1603 G.M. Artusi attributed to the unnamed opponent whom he criticized for certain modern tendencies (Monteverdi) a mathematical theory of intervals approximating to equal temperament and justifying the use of diminished 4ths and 7ths in vocal music (Lindley, 1982). The practical history of equal temperament, then, is largely a matter of its refinement in various respects and its gradual acceptance by keyboard musicians from the late 1630s, when Frescobaldi endorsed it, to the 1870s, by which time even the conservative English cathedrals were won over."

So that battle was still being fought in Bach's time, but his major 'argument' in favor of equal temperament remains the WTK.

Perhaps he wrote the '48' in such a way that keyboard player would be tempted to try some of them out on an organ (in an unequal temperament as most organs were in Bach's day) and determine that equal temperament was 'the wave of the future.'

Dick Wursten wrote (May 7, 2003):
Is it allowed to ask to take the topic about "meantone and other temperaments" etc. to another Mailing List (the relevance to the cantatas is relative and extensively shown). People who are interested in this -very interesting - matter can find many websites on the net, including schemes and sound-examples, yes complete tuning programs are freely available... with all info necessary. Just type 'meantone' and your resultlist will flow over... as does this Mailinglist

with all respect,

Bradley Lehman wrote (May 7, 2003):
Thomas Braatz wrote:
< "In 1603 G.M. Artusi attributed to the unnamed opponent whom he criticized for certain modern tendencies (Monteverdi) a mathematical theory of intervals approximating to equal temperament and justifying the use of diminished 4ths and 7ths in vocal music (Lindley, 1982). The practical history of equal temperament, then, is largely a matter of its refinement in various respects and its gradual acceptance by keyboard musicians from the late 1630s, when Frescobaldi endorsed it, to the 1870s, by which time even the conservative English cathedrals were won over."

So that battle was still being fought in Bach's time, but his major 'argument' in favor of equal temperament remains the WTK.

Perhaps he wrote the '48' in such a way that keyboard player would be tempted to try some of them out on an organ (in an unequal temperament as most organs were in Bach's day) and determine that equal temperament was 'the wave of the future.' >
Tom, perhaps you should read chapter 42 of Jorgensen's book. He cites Rousseau's Dictionnaire de musique (1779), reproducing Rousseau's comments on temperament. Jorgensen then comments:

"The above writing by Rousseau stated that equal temperament was known since the sixteenth century but that it was not used on keyboard instruments. It was not used at all in 1768. Further, he believed that well temperament descended from equal temperament (not the other way around as is commonly believed). Evidence of this was his statement that only 'the first fifths' and not all the fifths were weakened (narrowed) in order to create the common temperament. Thus, the philosophy of Rousseau was that well temperament was a great improvement over the much older equal temperament when it became necessary to perform in all keys. As such, well temperament was not a primitive substitute for equal temperament. Instead, it was a sophisticated development out of equal temperament. Although Rousseau was against the philosophy of equal temperament because of the destruction of key-character and the overly harsh major thirds in the diatonic natural keys, he cannot be classed as an anachronism because his temperament was as advanced as any other practiced at that time in history. Rousseau was against Rameau's proposal (a proposal was all that it was) for introducing equal temperament into practice on keyboard instruments. To Rousseau, the equal temperament proposal was an academic exercise for reintroducing an ancient impracticable temperament that had long since been attempted and which had finally failed for the last time in the days of Francois Couperin (1668-1733)." [Jorgensen, p152]

That is, discerning musicians have listened to equal temperament and decided that it sounds bad. (And other discerning musicians have come to the opposite conclusion too, of course.) I'm with the former set.

What makes you think that J S Bach really meant "equal temperament" but was clueless and/or sloppy when he titled his work "Das Wohltemperierte Klavier"? If he had really meant equal temperament, he could have titled the work "Das Gleichschwebende Klavier". He didn't.
http://www.google.com/search?q=gleichschwebende

Isn't it possible that Bach REALLY DID want to illustrate the DIFFERENT characters of the keys (in well temperaments) through these two books of preludes and fugues?

Have you seen the (rather famous) article by Barnes in which he has analyzed the WTC harmonically and melodically, and come up with the most likely well temperament for this work? He examined the textures in the music to see what Bach emphasized or avoided, as evidence of a temperament choice. Barnes came up with a 1/5 comma well temperament. (And yes, in that temperament all the major thirds are somewhat sharp, like in that even more famous set of instructions to Kirnberger.)

Bradley Lehman wrote (May 8, 2003):
Robert Sherman wrote:
< This is absolutely true, but it leads to a puzzle I've never been able to >understand. Maybe Brad or another of the theory boffins can explain it.

String players consciously play G# different (higher) from Ab, D# different from Eb, etc. But for natural notes (C, F, whatever) they only play them at one given pitch. >
In their choice to play sharps high rather than low, they are being influenced by the Pythagorean tuning of their instruments. Four pure fifths generate a major third that is even sharper (farther out of tune) than the major third of equal temperament. And if we go all the way around to get twelve different notes from pure fifths, the sharps are indeed higher than the enharmonic flats. (And in 12 fifths we overshoot 7 octaves by a "Ditonic Comma" of about 24 cents. In four fifths, such as C-G-D-A-E, we end up with two octaves plus a major third, but it is sharp by a "Syntonic Comma" of about 22 cents. Two different commas here, but of similar size, and they're interchangeable in practice.) Pythagorean tuning results in diatonic semitones that are smaller than chromatic semitones...that is, high or close "leading tones".

This Pythagorean scheme of pure fifths is the opposite of keyboards, where we use narrowed tempered fifths to generate all the notes. A top goal in meantone-based keyboard tempering is to end up with pure or nearly pure major thirds. A secondary goal is to deal with the "Diesis" formed by stacking up three pure major thirds and ending up considerably short of an octave (C-E-G#-B#...there are about 41 cents leftover there between that B# and the C that would be next to it!). That guy has to be distributed somewhere. So, to deal with him and the Syntonic Comma, we chop up the Syntonic Comma (22 cents) into 3 or 4 or 5 or 6 pieces and take it out of all of the fifths. It results in diatonic semitones that are larger than chromatic semitones. And the Diesis ends up in the intervals we don't care so much about using anyway: the diminished fourths such as G#-C and B-Eb.

It's an age-old battle: the Pythagorean style with high "leading tones" and extremely wide major thirds; vs the regular meantone styles where we shoot for good major thirds and end up with low "leading tones". It's the battle of melody vs harmony. Welcome to the 17th century.

Orchestral string playerwho care about the overall harmony should not be playing sharps high anyway, if it's harmonic music! As you brass-ensemble players know, major thirds in chords need to be played low in pitch so they lock in where they belong, pure against the fundamental. And the same goes for 7th scale degrees ("leading tones")...when they're really part of a dominant harmony, as the major third of that harmony, they should be played low. That takes care of the main situations with sharps in the music: when they're the major third or the major 7th they should be played low. (When they're supplying a minor third of a triad, or part of a diminished chord, it doesn't matter so much: the ear will tolerate almost anything as a minor third.)

String players who insist on high sharps are (dare I say it?) soloists, not team players. :)

=====

Many present-day "Baroque" violinists, violists, and cellists (i.e. period instrument string players) tune all four of their open strings to the keyboard, instead of merely taking an A and going with pure fifths from there. They recognize the need to listen to the keyboard's temperament and play accordingly.

Some modern-instrument players also do this with piano (especially for the G string), but it's more crucial when working with an organ or harpsichord that are not in equal temperament. I've played in many orchestras of modern instruments where they simply take an A from me at the organ or harpsichord and then ignore everything else, tuning in their usual manner by pure fifths, and then try to fudge their intonation to match the keyboard later (if they're listening to it at all).... In such situations I usually just pick my battles, especially when there's very little rehearsal time: I put on a very mild well temperament or one of the Neidhardt fake equal temperaments, and nobody notices that it's not equal.

< Now consider a transposing instrument, say a horn in Bb.

Should the horn player play his F# higher than his Gb? Presumably he should. But whoops, that note is in reality (concert pitch) an E natural, which the string players consider to be always the same. So the hornist is playing at two pitches what the strings are playing at one.

Conversely, when the hornist plays what he regards as C, it sounds Bb. Or is it A#? Should he play C a bit high some times and a bit low some other times, depending on whether the string parts (which he can't see) show Bb or A#? >
When a hornist in Bb plays a C, the note should be a Bb, not an A#....

And as I've pointed out, in all the temperaments except equal and Pythagorean, the sharps are lower than the flats. A# is a lower note than Bb.

< In fact, at a given center pitch (A=440 or whatever) of course there are many pitches for each written note, depending on the key. And in reality the strings and horns just tune to each other and do what sounds best to their instincts. But I have heard string players insist emphatically (and very wrongly) that while Bb is different from A#, all Cs are the same. So if we were to establish a universal system of true (non-tempered) intonation for all (non-keyboard) instruments that can tune on the fly, what would it be? >
As you've said: tune to each other and do what sounds best.

< And to really compound the issue, consider the trombone, which is physically pitched in Bb but played as if it were in C. >
...and which can play any microtone....

Bradley Lehman wrote (May 8, 2003):
Thomas Braatz wrote:
< Brad, are you getting ready to tell us that Harsdörffer in his "Teutscher Secretarius" (1656) in defining 'wohltemperiert' ('well-tempered') "als musikalischer Fachausdruck zur Bezeichnung gleichmäßiger Intervallabstufung auf Tasteninstrumenten." ["a technical term in music to designate equal division of the intervals on keyboard instruments"] [Harsdörffer's own words!] really did not mean what he said or that he did not truly understand what 'equal' meant (that 'equal' = 'something less than equal)? Notice that Harsdörffer does not say a 'good' temperament (one without a wolf 5th)! >
Did you read my posting from this morning about that (hexachords etc), and check out the Jorgensen chapter that I scanned and mentioned?
http://www.vaix.net/~bpl/jorgensen.htm

Alex Riedlmayer wrote (May 8, 2003):
Bradley Lehman wrote:
< discerning musicians have listened to equal temperament and decided that it sounds bad. (And other discerning musicians have come to the opposite conclusion too, of course.) I'm with the former set. >
If every discerning musician besides you were to have proclaimed the virtues of equal temperament, would you have decided otherwise?

< What makes you think that J S Bach really meant "equal temperament" but was clueless and/or sloppy when he titled his work "Das Wohltemperierte Klavier"? >
What sort of faith makes you believe the opposite?

< If he had really meant equal temperament, he could have titled the work "Das Gleichschwebende Klavier". He didn't. http://www.google.com/search?q=gleichschwebende >
Is anything proven about Bach by a counterfactual assertion? Does a citation of evidence make that assertion a scholarly inquiry into fact?

< Isn't it possible that Bach REALLY DID want >
No - in the present, Bach's intentions retain no authenticity.

< Have you seen the (rather famous) article by Barnes in which he has analyzed the WTC harmonically and melodically, and come up with the most likely well temperament for this work? He examined the textures in the music to see what Bach emphasized or avoided, as evidence of a temperament choice. Barnes came up with a 1/5 comma well temperament. >
It was Barnes's choice to make, and should be credited as his own, made by conscious deliberation, and not Bach's, by mystical devotion.

Thomas Braatz wrote (May 8, 2003):
[To Bradley Lehman] Brad, it seems our ‘getting short on temperaments’ is really getting longer, while readers such as Dick Wursten may be ‘getting a short temper[ament]’ about the length of our discussion. To any reader of the BCML: If I, for any minute, thought this was OT, I would drop this discussion immediately. A very positive aspect of this list is that there is a great variety to the list discussions, and while some aspects of the cantata recordings may seem rather detailed and scholarly(?) for listeners who are at various stages of becoming acquainted with the Bach cantatas, there may come a time later on when these or future listeners may wish to inform themselves regarding aspects of Bach’s music and performance practices. Hopefully they will be able to find pertinent information on Aryeh’s wonderful site which he has made available on the internet.

All the factors that impinge upon or issue from the recordings should be open to discussion, whether they concern original or non-original texts for the cantatas or whether they concern the use of different temperaments in the recordings of the cantatas. Although many contentious topics will not be easily or quickly resolved, at least an individual listener will be able to look at various aspects that might help to understand in greater depth and truly enjoy the best recordings that are available.

We all come from different directions with varying amounts of experience in listening or even performing Bach’s music. When we express our opinions here on this list (these lists, if you include the BRML), it is with the idea that we offer our assessments/critiques honestly without any ulterior motives, if such a thing is possible. In her recent post, Zbiczek has stated many notions with which I can identify. At the risk of being accused of adding to the long thread on Kozena, I would like to reiterate, because I can identify with her well-considered statement, a particular portion of it:

>>Having heard a huge dose of vocal music in my life, I learned how to rely on my own judgment and I probably won't exaggerate if I say that I developed a certain objectivity in judging vocal performances, independent of my taste. IT may sound absurd to some of you, but yes, it is true. That's what I believe hato professional critics who spent most of their lives listening to some particular genres of music. Yet a difference between me and them is that I am not being paid for my opinions and hence - I don't have any extra-musical agendas when I write about or discuss a performance or recording. And these extra-musical agendas are what really matters here.<<
Now back to Brad, who sometimes seems to delight in leading me and others who are reading his posts in circles without fully concentrating on one item: what did Bach mean when he wrote the title, “Das wohltemperierte Klavier” and just what does ‘wohl temperiert’ mean in the German language? Brad has now led us far afield (using Google) to obtain information which he hopes will answer his question:

>> What makes you think that J S Bach really meant "equal temperament" but was clueless and/or sloppy when he titled his work "Das Wohltemperierte Klavier"? If he had really meant equal temperament, he could have titled the work "Das Gleichschwebende Klavier". He didn't.<<
Here Brad reveals his lack of understanding of the German language because he does not bother to check out the meanings of key words. If he wanted to know the history of a term in English, he would consult the OED, but when it comes to German, he simply ‘wings’ it by relying on secondary sources offered by a Google search or by Owen Jorgensen.

One of the more significant hits in a Google search which he suggested is one from a description of lute temperaments. It goes as follows:

>> Um das Problem des offenen Kreises zu lösen, wurden über die Jahrhunderte verschiedene Temperaturen (Temperatur = «Mässigung» der reinen Intervalle) entwickelt. Eine Temperatur hat sich in unserer Zeit durchgesetzt, nämlich die gleichstufige (gleichschwebende) Temperatur: << [„In order to solve the problem of the open circle, various temperaments were developed over the centuries (Temperament = the ‚evening-out’ of pure intervals) One temperament has prevailed/asserted itself in our time, specifically the ‚equal-stepped’ (equal) temperament.“]
Notice that ‚gleichschwebend’ = equal.
There is an interesting footnote pertaining to ‚gleichschwebend’:
>>Auf Empfehlung von Dr. phil. Bernhard Billeter, Zürich, verwenden wir in dieser «Fermate» den Begriff «gleichstufig» anstelle von «gleichschwebend». «Gleichstufig» ist die bessere Bezeichnung, weil die Intervalle nicht in allen Oktaven gleich schweben. Der englische Begriff «equal temperament» entspricht dieser Stimmung viel besser.<< [„Upon the recommendation of Dr. of Philosophy Bernhard Billeter of Zürich (here is someone who ought to know about the use and meanings of German words!) we are using the word ‘equal-stepped’ rather than ‘equal.’ ‘Equal-stepped’ is a more apt term, because the intervals do not modulate (move up and down {beating?}) the same way (the same amount.) The English term “equal temperament” gives a much better representation of this temperament.”]

Why has Dr. Billeter given up on ‘gleichschwebend’ = ‘equal’ temperament? Perhaps he knows what the DWB can tell us about the history of this word as a technical musical term. This word is documented for the 1st time in the complete works of Johann Jakob Wilhelm Heinse (1746-1803.) His earliest publications (not necessarily having to do with music) are 1773, 1787, 1794. The actual quotation is taken from the complete works published in Leipzig from 1902-1925: “die Quinten sollen forthin…auf den Klavieren gleichschweben.” [“the 5th should, from this point forward…have the same ‘schweben’” Here is a dictionary definition in order to understand ‘schweben’ = ein Ton der nicht ganz rein ist; Abweichung nach oben oder nach unten = a tone which is not quite pure; a deviation either higher or lower}

The next significant entry on “gleichschwebende Temperatur” occurs in Riemann’s “Geschichte der Musiktheorie” (1921): als musikalischer Fachausdruck, besonders in der Verbindung “gleichschwebende Temperatur” mit der jene Stimmung der Instrumente bezeichnet wird, in der alle gleichartigen Intervalle in gleichem Maße und Verhältnis von ihrer Naturreinheit einbüßen, um die ‚gleiche Schwebung’ höher bzw. niedriger gestimmt werden. Gegen Ende des 17. Jahrhunderts von Andreas Werckmeister als Forderung aufgestellt und von ihm als ‚wohl temperierten Zustand’ bezeichnet, welcher Ausdruck hinter der kurz nach 1700 aufkommenden Bezeichnung‚ gleichschwebende Temperatur’ im 18. Jahrhundert. sehr bald zurücktritt. [„as a technical musical term, particularly in connection with the phrase „equally-beating temperament” which was used to designate the tuning scheme of instruments in which all similar intervals lose some of their natural purity to an equal degree and in relationship to each other and are tuned accordingly higher or lower. Toward the end of the 17^th century Andreas Werckmeister called for a “wohl temperierten Zustand” {a well tempered condition} which was the expression that was soon replaced by a term, ‘gleichschwebende Temperatur’ {equal temperament} that arose in the early 1700s and quickly supplanted ‘wohl temperiert.’]

According to Rieman, Werckmeister wanted a ‘well tempered’ [wohl temperiert] condition, but this was quickly replaced by ‘well tempered’ [gleichschwebende] temperament.

In any case, ‘gleichschwebend’ is a rather poor choice to designate ‘equal’ temperament (as Dr. Billeter has pointed out.) Technically each interval, as you proceed up or down by semitones, will not be equal (equal number of beats,) but according to Riemann (1921), Werckmeister demanded a ‘wohl temperiert’ tuning {Riemann assumes that this refers to an ‘equal’ temperament}, the term used by Bach. This was, however, replaced (according to Riemann) in the early 18th century during Bach’s lifetime by the term, “gleichschwebend” {Riemann, once again, assumes that this means the same thing as ‘equal’ but he gives no documentation on the history of this word, which according to the DWB can only be documented in the last quarter of the 18^th century at the earliest (Heinse)} Unless someone else, (Brad, how about it?) can come up with an earlier documentation of the term ‘gleichschwebend’ = ‘equal’ temperament, it is impossible for Bach to have used this term for the WTK as Brad suggested that he could have.

When Owen Jorgensen in his book “Tuning” (1991) (Nomenclature page shared by Brad – it did not fully load for me on my computer - no footnotes were given, which in this case would be very important) states the following opinion as he makes up his own definitions, there is no reference given to the contexts and dates as to just when, where, and under which circumstances the term ‘wol temperirt’ is used in German. Allowing for Brad to share the all-important footnotes which might shed light on this matter, I do not want to prejudge Jorgensen’s assertions, but currently I am rather concerned that he (Jorgensen) may not have investigated the word history of this term thoroughly.

“Still later in the 17th century in Germany…the term ‘wol temperirt’ (well tempered) came to mean temperament that was in favor or good standing in which one was unrestricted while modulating freely through all the keys (modi ficti) without encountering encountering inharmonious wolf invervals. ‘Well tempered’ at this time still did not mean ‘equal tempered’ even though one could perform in all tonalities. 5 In recent years, the term ‘well tempered’ developed to include also the meaning of ‘equal tempered.’ Thus a term such as ‘well tempered’ has changed its meaning through the centuries to accommodate whatever was considered the most proper or appropriate temperaments of the time. 6”

By mixing ‘wol temperirt’ with ‘well tempered’ in English, Jorgensen has completely confounded whatever meaning ‘wohl temperiert’ actually had in German. The problem with ‘gleichschwebend’ in German only served to make matters worse than they already were.

Quoting from Jorgensen who quotes from Rousseau’s Dictionnaire de musique (1779), really does not add much of anything to this discussion. It begins to resemble some of the evidence seriously put fortby proponents of the ‘shortened accompaniment in secco recitatives’: references that are not specifically related in time and place to Bach’s tenure in Leipzig, Germany.

Hugo Saldias wrote (May 8, 2003):
[To Thomas Braatz] My understanding of the German language is not asbroad as yours and I consider you an authority in this matter I also thank you for looking into Hugo Rieman (for me his writings in theory etc is like the bible...).Now remember what I asked you yesterday? Please look into the Die Kantaten written by the amazon critic Michael Wersin and tell meplesae if you agree on the basis and may be it could be included in this web site to guide us all in how to eveluate any Bach Cantata Recordings.

Bart Stolzel wrote (May 8, 2003):
Thomas Braatz wrote:
< A very positive aspect of this list is that there is a great variety to the list discussions, and while some aspects of the cantata recordings may seem rather detailed and scholarly(?) for listeners who are at various stages of becoming acquainted with the Bach cantatas, there may come a time later on when these or future listeners may wish to inform themselves regarding aspects of Bach’s music and performance practices. >
Well yes, but it would be nice to know which cantata recordings are affected by all this discussion. All I've got so far is Brad's statement in 4856 in Cantata BWV 116 Harnoncourt used a temperament that sounds like regular 1/6 comma meantone, or perhaps slightly modified (lowered E-flat); and Leusink in that same cantata uses a well temperament (i.e. something more moderate than that meantone, but also not equal temperament).

Continue on Part 3

The Keyboard Temperament of J. S. Bach: Article | Music Examples | Feedback: Part 1 | Part 2 | Part 3
Discussions of Temperament / Key Character / Tuning: Part 1 | Part 2 | Part 3 | Part 4 | Part 5 | Part 6 | Meantone