Killing the Buddha of well-temperament

Hello one and all,

In the ensuing dialog about various well-temperaments, Lehman's vs.
Werckmeister vs. Neidhardt vs. Secor's vs. Wendell vs. 1/7 comma or 1/6-comma
modified meantones vs. Vallotti or Young or Vallotti/Young, I did an
experiment: I loaded these tunings into my synth one after the other and
played various chords and bits of music and decided that arguing the virtues
of one over the other is really just an enormous waste of time. I really
*could* hear differences, but they are more noticable to the tuner, and so
subtle I think that they would mostly go unnoticed in a perfomance, except
that the ones with more Pythagorean thirds would sound a bit more jangle-y
and aggressive.

I say this knowing full well that I have really, really fine ears, and many of
you do to.

I'm willing to put this to test with anyone who would challenge me....!!!

Best,
Aaron.

P.S. I'm well aware that I'm implicating myself here, i.e. to say, I 'waste my
time' arguing the virtues of my pet tunings over others (eg. my
pro-NeidhardtI position vs. Johnny Reinhard's pro-WerckIII position.)

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...>
wrote:
> (...) my pro-NeidhardtI position (...)

For my curiosity: in your frequent references to "Neidhardt 1", is
that the "Circulating Temperament #1" of Murray Barbour's table 151
(p167, and explained on p179)? If that's your source of it...there's
a typo in Barbour's calculation for the note Eb. He gave it a 0
superscript but it should be +1/12, i.e. a slight nudge higher in
pitch. His cent value for that Eb is correct, though.

That's also the temperament that Neidhardt published in 1724
recommended for a village, and upgraded to a small city in 1732,
renamed as third-circle #2.

The confusion grows; Mark Lindley has given two different readings of
it in various articles of his over the past 20+ years, with the
discrepancy being in the handling of the note G#. (1/12 comma must
be absorbed somewhere in C#-G#-D#; sometimes he has the C#-G# pure
and the G#-D# tempered, while elsewhere it's vice versa.) And both
of these are *not* the same as Barbour's, due to the Eb problem noted
above.

Even more confusingly, since I took them by counting serially from
Lindley's presentation in "J S Bach's Tuning" (_Musical Times_, 1985)-
-it's the one I have labelled "Neidhardt #3" in my web materials!
I'm working on a page of errata that will explain this better.

Whatever these various temps were called in the various publications,
and whatever sizes of establishment they were for: it's more
important to get the pattern right than to quibble about names of it.

In practice, of course, the nudge of G# by 1/12 lower or higher
doesn't make a large amount of audible difference, and likewise on
the Eb. But just as a matter of academic thoroughness....

Anyway, I think I agree with your broader point that many of these
"well temperaments" (what an awful term) sound scarcely
distinguishable from one another, in practice. They all at least
avoid foot faults, put the ball into play, and have a decent ground
stroke. But there are little telltale areas in them here and there,
melodically or harmonically or both, where it matters. To my ears
and theory, the most important harmonic distinctions happen in the
way a temperament balances the major triads of A, E, B, F#, Db, and
Ab. And the most important melodic distinctions come up when playing
music of zero to five flats, and especially in the minor scales.
Good old C major and A and D minor: if the naturals themselves aren't
regular or nearly so, and if the sharps/flats that occasionally come
into the texture are way too high or low for their melodic contexts,
within the flowing sound as a whole, that's where I perk up and
notice melodic problems most readily. Notes not being where they're
expected when approached by various steps or leaps.

Brad Lehman

On Wednesday 31 August 2005 12:51 pm, Brad Lehman wrote:
> To my ears
> and theory, the most important harmonic distinctions happen in the
> way a temperament balances the major triads of A, E, B, F#, Db, and
> Ab. And the most important melodic distinctions come up when playing
> music of zero to five flats, and especially in the minor scales.
> Good old C major and A and D minor: if the naturals themselves aren't
> regular or nearly so, and if the sharps/flats that occasionally come
> into the texture are way too high or low for their melodic contexts,
> within the flowing sound as a whole, that's where I perk up and
> notice melodic problems most readily. Notes not being where they're
> expected when approached by various steps or leaps.

...and being conditioned for years by 12-equal, is 'where we expect them to
be' related to 12-equal ? ;)

best,
Aaron.

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...>
wrote:
> On Wednesday 31 August 2005 12:51 pm, Brad Lehman wrote:
> > To my ears
> > and theory, the most important harmonic distinctions happen in the
> > way a temperament balances the major triads of A, E, B, F#, Db,
and
> > Ab. And the most important melodic distinctions come up when
playing
> > music of zero to five flats, and especially in the minor scales.
> > Good old C major and A and D minor: if the naturals themselves
aren't
> > regular or nearly so, and if the sharps/flats that occasionally
come
> > into the texture are way too high or low for their melodic
contexts,
> > within the flowing sound as a whole, that's where I perk up and
> > notice melodic problems most readily. Notes not being where
they're
> > expected when approached by various steps or leaps.
>
> ...and being conditioned for years by 12-equal, is 'where we expect
them to
> be' related to 12-equal ? ;)

Not really, at least for me. (Others' mileage may of course vary.)
My conditioning is set up by the regularity that constitutes the
basis of whatever temperament it is: 1/3, 1/4, 2/9, 1/5, 1/6, 1/12,
whatever. The *regularity* of the 5ths (at least in most of them)
generates a series of tones and semitones, from whatever size the
basic 5th happens to be. And then as a listener I expect the melodic
notes to hit on or near those points, spelled correctly
enharmonically. The more they diverge from some semblance of
regularity, or are played misspelled, the more chaotic the whole
thing sounds.

I hardly ever play in 12-equal anywhere anymore, unless engaged to
guest somewhere on piano or organ where it happens to be set up that
way, and beyond control.

If we're playing in, say, regular 1/4 comma and some interval from 12-
equal shows up, that's just as much an anomaly (and against
expectations) as vice versa.

Some of the fun features of regular systems:
http://www-personal.umich.edu/~bpl/larips/meantone.html

Playing again in "Kirnberger 3" for several hours last week, after
some years mostly away from it, I was delighted again by its melodic
smoothness. Eight 5ths one size (less a schisma in one that's really
a diminished 6th), and the other four 5ths the other size, grouped
together nicely.

Brad Lehman

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@a...>
wrote:
>
> Hello one and all,
>
> In the ensuing dialog about various well-temperaments, Lehman's vs.
> Werckmeister vs. Neidhardt vs. Secor's vs. Wendell vs. 1/7 comma or
1/6-comma
> modified meantones vs. Vallotti or Young or Vallotti/Young, I did
an
> experiment: I loaded these tunings into my synth one after the
other and
> played various chords and bits of music and decided that arguing
the virtues
> of one over the other is really just an enormous waste of time. I
really
> *could* hear differences, but they are more noticable to the tuner,
and so
> subtle I think that they would mostly go unnoticed in a perfomance,
except
> that the ones with more Pythagorean thirds would sound a bit more
jangle-y
> and aggressive.
>
> I say this knowing full well that I have really, really fine ears,
and many of
> you do to.
>
> I'm willing to put this to test with anyone who would challenge
me....!!!
>
> Best,
> Aaron.

Hi Aaron,

I have to admit that I had a somewhat similar reaction to some of the
WT's I tried way back in 1964, several months after I first started
investigating alternate tunings. When I tried the 1/6-pythagorean-
comma Valotti WT (identified by Barbour as "Young's No. 2"), e.g., I
observed that its 4 best triads sounded considerably less consonant
than 1/4-comma meantone, its 4 worst were basically pythagorean, and
the 4 remaining were not significantly different from 12-ET. Others
may disagree, but I drew the conclusion that if I couldn't have
meantone-like intonation in the best keys, then unequal tempering
probably wasn't worth the effort.

I've since evaluated circulating temperaments by assigning a letter
grade to each major triad, as follows:

A - not significantly less consonant than 1/4-comma MT
B - noticeably more consonant than 12-ET, but significantly less
consonant than 1/4-comma MT
C - not significantly different from 12-ET
D - noticeably more dissonant than 12-ET; comparable to pythagorean
E - noticeably more dissonant than pythagorean, but still usable
F - unacceptable (e.g., a triad with a wolf fifth)

So in my book a temperament gets graded on how many A's and B's it
has, vs. how many D's and E's, and where they occur:

Major triad: Db Ab Eb Bb F. C. G. D. A. E. B. F#
Valotti:.... D. D. C. C+ B. B. B. B. C+ C. D. D.
Lehman-Bach: D+ C. C. B. B. B. C+ C. D. D+ C. C.
Werckm. III: D. D. C. B. A+ B. C. C. C. C. D. D.
Secor #2:... D. D. C- B- A. A. A. B- C- D. D. D.
Secor #1:... E+ D. C. B+ A. A. A. A- B- C. D. E+
Secor #3:... E- E. C- A. A. A. A. A. B. C- E. E-

If I'm able to come up with a temperament extraordinary enough to
have noticeably better intonation in 6 triads and am able to pay for
it with noticeably worse intonation in only 4, then I would say that
it's definitely not a waste of *my* time.

Best,

--George