In No. 6 Prelude in D minor the last few measures have 9 chromatically descending diminished triad arpeggios. If that doesn't have Equal Temperament written all over it, I don't know what would.

And the pieces in the Well Tempered Clavier are in chromatic order with the minor pieces not in the relative minor key, having the same key signature, but in the absolute minor key (would that be the right term?) having a different key signature, and in a well temperament a different color.

And as far as the title being "Well Tempered" (meaning, as I understand it "good" rather than "thoroughly") and not "Equal Tempered", I take the meanings as synonymous. I think Bach felt that equal temperament was a "good" temperament, and I agree!

And the curious squiggle on the cover is probably just a curious squiggle that, if anything, would mean a chromatic order, as that is how the pieces are arranged. If Bach had written WTC for some new temperament, wouldn't he have said how it should be tuned? Of course he would!

Unless that curious squiggle ARE the instructions to the tuning...

;-)

Ron Koval

Or a Rorschach test.

I guess that finally settles a centuries old debate.

Kees

In my mind it does.

At some point, "Well Tempered" means "slightly different from equally tempered." That point will come at different situations for different music, instruments, and people.

Jeff,
Remember that Bach did not play a modern piano, but a harpsichord on which the tuning could be changed more easily than on a piano. In my student days here at Westminster I remember hearing that Bach was aware of ET, but did not like it. May be true, may not be true. Listen to some of these pieces in an WT tuned for the key in which the piece is being played-they take on a whole new life.

The Well Tempered Clavier was not written for harpsichord. And what I, or anyone else, happens to like has nothing to do with it. But what difference does it make how easily an instrument is tuned????

It is really unlikely that ET existed on any keyboard instruments during Bach's time. It simply wasn't the goal for any of the written standards of the time. Was it possible, given the aural tuning techniques? Perhaps. Was it practiced? I doubt it!

That doesn't discount our general preference to hear a tuning style that has been aimed at and tested for during the last generation of tuners. Teaching to the test? You betcha!

Considering the wide variance of ET practiced by today's aural tuners, it becomes more clear that ET is a goal that many think they achieve, but a smaller percentage actually perform...

Ron Koval

Dissertations and books have been written on temperaments and tunings in Bach's time. The consensus of the scholars is quite clear. What anyone chooses to believe or not is fairly inconsequential - does it really deserve a thread on this forum?

Um, are you aware that "Well Temperament" was a technical term employed that referred to a particular kind of temperament (or, at least, family of similar temperaments)? It didn't mean anything generic like "kinda good sounding" or "competently done" or anything vague like that that would allow us to apply all kinds of interpretations of our own. Well Temperaments are "well" known in circles who have given more than cursory investigation to historical temperaments.

Equal temperament emerged after the development of logarithmic tables -- which weren't around in Bach's time.

Keith, logarithms were developed in the early 1600s, and equal temperament was well known long before Bach's time. Lutenists were, and still are along with guitarists, constrained to equal temperament because of the parallel frets although pitch could be subtly varied in performance.

Regardless, that doesn't negate the fact that the WTC was written for well-tempered tuning. This is pretty well researched and indisputable.

Jeff. I think you made up your mind on this one years ago. You may have wavered just a little about 3 weeks ago but, rest assured, it didn't show much in your posts.

I normally skip the temperament posts but some of the recordings of the standards of the '30's and 40's simply don't work in their standard keys in unequal temperament. The style of hharmony loses a lot. Maybe if they were transposed they might gain something.

Which version of well temperament did you compare the diminished triads with before reaching your conclusion? I can't help thinking that, in a succession of broken minor triads in an unequal temperament, the many different sizes of minor third would lend more interest. When you add the acoustical environs of a pipe organ or the acoustic properties of a harpsichord, these notes would run into each other a bit. Then we might begin to hear what the devious old prankster was really saying to us. It's as though he was saying, yet again "Here's something else to think about before I shut this thing down"

Thank you for starting this thread. It has brought some interesting thoughts out of the woodwork.

Did some quick research on this last night. Most scholars believe that well tempered means most likely a well temperament, possibly equal occasionally, but not a meantone temperament which had been the norm before that. Bach tuned his own instruments, and used temperaments in which all keys could be used. As far as what WTC was written for, some believe they were written for Clavichord, others believe Clavier stands for keyboard instruments, clavichord and harpsichord, and now played on our modern piano. Modern practice, at least here, is harpsichords are tuned in a variety of well temperament, which temperament depends on the music being performed, conforming to what our professors believe is the way they were tuned in the 1700's. They tell me which temperament they want, and I tune the harpsichord to that.

So is there still a debate or is there a consensus?

rXd:

Actually, I have been at war with myself on this one. And of course that makes it hard to be objective. I like the idea of tonal palates, but whenever I hear a temperament that is not equal enough to notice, it sounds out of tune! It only takes one raisin in the rabbit stew...

I am not much of a piano player- an eternal, stumbling grade four. But I have Chopin's Preludes and Bach's WTC and can play a few of each after a fashion. Looking at the music itself, I find some harmonies in Chopin that I wonder if they might be improved on with UT. I do not find this to be so in WTC.

But I am not a musicologist. And despite what some believe, there does not seem to be a consensus about WTC. And why shouldn't I have an opinion? But what to base it on? How about Occam's Razor?

So what temperament would most easily fit the criteria of WTC? What temperament would satisfy the requirement of all keys being usable with the same chord progressions being used in each, with the pieces not only containing chromatic passages, but in a chromatic order? Equal Temperament, of course! And, as has been mentioned, lutes were in ET and Bach wrote for lutes. ET was not anything new for Bach.

So ET is the "quick pick" for WTC, but not the only "pick". When I read about the evidence for some kind of WT, as we now understand them, we have to go to "experts." I read about harmonic analyses (that are disputed) and deciphering a single curlicue to prove that some sort of WT, again as we now understand them, was the intent.

Many moons ago I would be in a position of trying to figure out if an engineer on a ship really knew what they were talking about when there was a problem so as to decide on a course of action. I hadn't heard of Occam's Razor then, but used the same technique. The most obvious answer is usually the right one. Another thing that I learned is that when someone fogs up an issue, there is an ulterior motive. In the case of the engineers, it was usually to hide incompetence.

Many, but not all, WT enthusiasts seem to be very willing to fog up the issue. I do not have a problem with those that simply state, "It is what I and others prefer." I do question the motives of those that try to bring to bear obscure tidbits to confuse an issue. At the top of the list is any conspiracy theories! Next on the list is the weight of self granted authority such as dismissing an issue as already being decided and not worthy of consideration.

Everyone should be able to agree to that. Better ask Bach if he always used exactly the same temperament.

The Road to Endor?

When I first saw this title, I thought to myself, I thought, here's Jeff setting out to have some fun with us.

Now I'm convinced of it.

Good on yer.

Jones let the squiggles guide his tuning hammer before playing triads.

rXd:

It is more like me saying, "You guys tried to fool me, but it didn't work."

Both, actually.

There is consensus amongst the scholars and debate amongst the rest of humanity. It just means that if you're having a debate, you're not quite scholarly enough.

Regards from another eternally stumbling grade four. (Well, I actually passed grade 7 with merit, but what's left 25 years later is pretty much the same as in your case, scratching around in Chopin Preludes and WTC.)

This brings up a very important question. How close to perfectly equal must a temperament be, to be called equal? Would what might have been considered equal in Bach's time be considered equal now?

Emperor's New Clothes?

That "sounding out of tune" bit is the key to your particular puzzle. That perception is driven by a lifetime of ET or near-ET piano sounds, is it not? It's possible that your past is a hurdle that cannot be overcome in this journey...

My experience seems to indicate that:
1. The vast majority don't care, just give them clean unisons and usable octaves
2. A small minority likes the added palette of tonal tunings.
3. A small minority can't stand anything but near ET.

Then there are some who find that after playing in a tonal tuning for a few weeks, learn to appreciate the palette and find it jarring to go back to ET. I believe this may be the key to "un-training" ones personal musical history; make the commitment to ONLY play a tonal temperament for an extended period of time, then try to compare back to ET.

Left out of this discussion is the chosen "strength" of the chosen Well temperament. There is a HUGE perceptive difference from the players perspective in a tuning with a maximum offset of a few cents vs. a tuning with a 5 cent or more offset from ET. There were/are lots of Well Temperaments...

Ron Koval

Ron:

I have mentioned that it is difficult to be objective. Thanks for bringing this up in a new way.

I am reminded of my early musical training on brass instruments - definitively not ET. And then latter vocal training, oddly enough probably ET because of a strict choir director with absolute pitch. So my prejudice could go either way. That is until I started tuning...

Anyway, putting away any predisposition I am still convinced that WTC was written for ET.

[Edit:] And fwiw, I suspect that Chopin's Preludes were written for UT.

I'd second this wholeheartedly, Ron. And I'd also maybe add that some of the folks in categories 2 and 3 may have something to say about the octaves in category 1. Clean double octave? Triple? Quadruple? Or clean octave+fifths? It's this last part that makes the piano sound in tune with itself, and on some instruments, brings out the sonority of the thing as a whole.

Chris S.

P.S. I thought I read somewhere that one must, of course, turn the curli-cue UPSIDE DOWN in order to understand how Bach tuned.