Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum I've made up my mind about Bach's WTC and ET

Sorry, Jeff. Last weekend went something like this for me:





Kidding! I'm kidding! Actually, I was trying to puzzle out whether WTC-1 No. 9 is a Giga. And in searching out that question, I learned a few things that puts me somewhere near Chris Leslie's camp. But before summing up that thought, here's this one:

I still fervently encourage you to keep going at this idea of yours. Obviously, there is something there that you need to answer for yourself. I am just happy that you're taking your own question seriously, now. You've come a long way from "I made up my mind because I played a chord in this one prelude," to, "Hmmm. How can I test my idea?" I still don't quite understand your analysis, except to say that the focus seems so very narrow, and it might be too early to try to understand it. You have to start somewhere, though, and I'm really glad PhilD sees your trajectory. I would like to see you take a step back and restate your premise, define your thesis, and list your assumptions, which might help you gain a little more clarity. It might help you structure your test(s) and help you to explain your results to yourself and others. Personally, I feel you still need to make a qualifying nod to, and demonstrate an appreciation for, the historical refraction inherent in your inquiry, because the instrument (and its sound) was so very different. But there is much to be said for crashing around. (I do it a lot, myself...)

Now, why did I land near Chris Leslie's camp? (Hi, neighbor! ) It is because I discovered something about the WTC that was new to me, in a 1996 article by Yo Tomita. (He's written a lot about Bach.) Did you know that WTC was written for keyboard instruction? Did you know that Bach purposely left out many tempo indications as a kind of quiz, so that students would examine the music to figure out the proper interpretation? Here's how Yo Tomita said it:

The Well-Tempered Clavier, Book 1, by Yo Tomita, (1996)



Which makes me think that the squiggle on the title page is an instructional illustration that would have been accompanied by a demonstration. As has been noted in this very thread, keyboard musicians had to tune their own instruments, and so tuning had to be part of the lessons, right? (Apparently, one of Bach's students, Heinrich Nicolaus Gerber, made a copy of WTC in 1725 (that would be a hand copy (which, btw, bears some of Bach's markings)), and this copy is in the Gemeente Museum in the Hague. Does anyone reading this know whether Gerber copied the squiggle?)

Also,



Clearly, Old Wig had a lot going on under there, and WTC is, indeed, a multi-faceted work.


So, Jeff, press on! Great discoveries come from burning questions.

--Andy

Phil, Chris, Andy:

My responses to you three overlap so much that I better make it a group response.

Remember this analysis is just an example. And it would be a way of looking for evidence that WTC was written for WT, not of evidence of being written for ET. I would look for that evidence in the convoluted passages. So I am not going to continue this sort of analysis. Sorry, it is not the direction I am looking.

I have been taking steps back for a better perspective and see things much as Chris mentioned. Let me explain what I learned from the type of analysis that I used as an example. If the amount of tempering is changed, the results change also. Consider what is being observed objectively: The number of half steps between the average remote key roots and the average close key roots. Then comes the temperament part: The average beatrate for the chosen temperament. Change the temperament and the analysis changes.

For instance, the remote key’s average note is lower than the closer keys. Yet, for the chosen temperament the average beatrate is still faster than for the close keys. It could be argued that the chosen temperament was too strong. The correct, milder temperament is the one where the average beatrates would be the same. But the average note is only a little more than three semitones, and two semitones is insignificant. (I mentioned this before.) This is close enough to show that ET was the intent.

Then I consider No 1. I was thinking about my reaction to hearing it on Lindley's site. It sounded too bland in WT to me. But what would it sound like to those used to MT? It might have sounded too raucous! I can’t say that No 1 was a “sound check” for the chosen temperament, but I do wonder. Like, if No 1 is acceptable, the rest will be acceptable.

And this ties into what my intuition is telling me. The use of key color is not integral to the composition. It is only a comfort factor for the listener. It is a “season to taste” thing in the recipe. Regardless of what temperament it was written in, it was written for the universal temperament: ET.

To keep things simple, I used the last time the third step was played.

I agree mostly, except in my personal opinion it was written in and for just intonation. Reasons: 1) It is known Bach always composed in his head, not at the keyboard (hence the "in"). 2) It is known he liked the clavichord and just intonation is realizable on the clavichord (hence the "for").

Kees

I can understand that easily. As a vocalist, I never thing about temperament when singing. All intervals are pure. The piano has to be tempered, of course. However, I disagree that the choice of ET is the best compromise or the only logical one. I have 23 years of experience that has proved that to me.

I sing in ET. I was taught that way. I have heard complex choral pieces fall apart tonally when Just Intonation is attempted.

Considerng the frequent use of dim7 chords and the occasional use of augmented chords I do not think WTC was written either in or for JI. It is impossible to have these chords just.

Fine with me. We have freedom of religion here.

Kees

Ah... A breath of fresh air!

Talking about religion... Tomorrow I'll attend a performance of Mozart's Requiem at a local church. Tuning: Kellner (1/5' WT).

Kees

..."Tuning: Kellner (1/5' WT)."...

Hmmm, interesting. How is it expanded all across the keyboard? Pure octaves? Or? (please answer through a different thread)

Hi All.

Linked below you''ll find a work on temperaments (pdf. available), perhaps in the spirit of this thread. During those years the "pure 12ths" ET tuning model was elaborated by Bernhard Stopper.

..."...human voices in concert have no difficulty in making pitch adjustments necessary to achieve consonance, but the keyboard with its twelve pre-set notes is inhibited."..."...at least in Werckmeister's casey temperaments were assessed not only for their faithfulness to the accepted standards of consonance, but for their ability to give to certain keys certain affective characteristics."...

Science, opinion or cliché?

"Pollard, Joseph Victor (1985) Tuning and temperament in southern Germany to the end of the seventeenth century. PhD thesis, University of Leeds":

http://etheses.whiterose.ac.uk/325/

Off Topic: Best wishes for a serene Easter.

Regards, a.c.

IMO one of the points of the cycle is to test out Well-Temperments.

If all 24 pieces sound good in your tuning, then you've got a "Well-Temperment"!

I am thinking along the same lines now, like: If all 24 pieces sound GREAT in your tuning, then you've got an "EQUAL-Temperment"!

I prefer a well-temperment with the WTC, since it gives each key it's own effect, but it certainly works in EQ too.

To each his own.

I think Bach would have been fine with either; if it was terribly important, he would have written down explicit instructions, not some cryptic squiggle

The 8ft principal in the great is tuned first in the temperament octave, then octaves are tuned pure. Then the other stops are tuned to the 8' principal.

Kees

Agreed. In 1/4' WT like Werckmeister 3, as for example Ton Koopman's recording is tuned, it sounds it bit too rough esp. in f minor for some reason. Not EQUAL enough!

1/6' temperaments sound good to me (I'm talking about hpschd of course, he didn't write for piano). EQUAL enough! Still the normal keys sound a bit better, which is fine with me as I can't play in those remote keys anyways.

If I could and someone insisted I play all 24 pieces without retuning (a very unrealistic scenario) and without favouring keys the logical choice would be ET for me.

Kees

Slightly tangential, but a better candidate for intended ET in Bach's music is,
IMHO of course, his Art of Fugue. Despite being entirely in d minor (1 flat) the pieces seem to want good P5's more than good M3's. Esp the DA fifth is so prominent that a
1/4' WT (which has DA 3X narrower than in ET) is a bit offensive.

Kees

FWIW, this is a Well Temperment I arrived at after much fiddling around in scala. I really like it, all the major/minor chords sound good in it and have their own character.

Folks:

Really! If you want a Topic on Well Temperaments, go start one!