Wendy Carlos on meantone

Wendy Carlos does not appear to agree with Manuel Op de Coul, Dave Keenan,
and Carl Lumma's perceptions of the relative dissonance of errors in the
perfect fifth versus errors in the thirds. Here are some comments she makes
in her article, "Tuning at the Crossroads":

"
More frustrating than [the limited tolerance of acoustic intruments and
analog synthesizers] is the usual limit on number of tones in an octave,
which really was the wholly "economic" reason for musicians in Bach's time
to yield the much preferable sounds of the several varieties of meantone
tuning for 12th-root-of-2 equal temperament. Ellis describes the results in
his fine appendixes [sic] to Helmholtz's book (1954, p. 434):

If carried out to 27 notes . . . it would probably
have still remained in use. . . . The only objec-
tion . . . was that the organ-builders, with rare
exceptions . . . used only 12 notes to the octave
. . . and hence this temperament [Meantone]
was first styled "unequal" (whereas the organ,
not the _temperament_ was -- not unequal, but --
_defective_) and then abandoned.

Not everyone agreed with abandoning meantone. The English held out on many
instruments until the end of the last century. Even now the truce of equal
temperament is not altogether as benign as all of us born into it commonly
assume

[. . .]

Earlier I suggested about meantone that we have excellent reasons to
believe that were it not for modulation problems of "wolf tones" (when
instruments were tuned to only 12 meantone pitches), this form of
temperament would likely be in use right through to the present. . . .
What is actually occuring is that we are trying to force (3/2)^4 * (1/2)^2
to be = 5/4. The left terms total 81/64, or 81/80 higher than 5/4. In cents,
the left side is (4 * 701.9950) [should be 701.9550] - (2 * 1200.0) =
407.8200, and that is greater than 386.3137 by the _syntonic comma_ of
21.5063. But musicians for centuries have notated the major triad on C to
be: C--E--G, not: C--E-flattened-by-one-comma--G . . . Something had to
give, and the best-sounding way was meantone. There are four fifths to
absorb the excess comma, so let's give each a quarter of it: 701.9950
[should be 701.9550] - (21.5063/4) = 696.5784 for the meantone fifth. (Two
of these up (and down an octave) form a "tone" which is exactly in between
the "major tone" of 9/8 and the "minor tone" of 10/9, hence the name,
_meantone_. . . .) Since low partials are involved, the resulting flat
fifths beat much slower than if some higher ratio were mistuned by the same
5.3766 cents -- if you will, the fifth can "stand it" better. The major
third that results from four of these fifths is . . . perfect: 386.3137
cents.
To round out this capsule explanation, what occurs in the equal-tempered
version is easily shown . . . In cents we have the familiar fifth, 700.0.
Now go up four of these and down two octaves: (4 * 700.0) - (2 * 1200.0) =
400.0. And this is 400.0000 - 386.3137 = 13.6863 cents sharp for a major
third. A 5/4 involves harmonics double those for a 3/2, so the beats of this
sharp third are worse than only four times the meantone fifth's error . . .
"

Inre Wendy Carlos, Paul quotes her as saying:
>"
> More frustrating than [the limited tolerance of acoustic intruments and
>analog synthesizers] is the usual limit on number of tones in an octave,
>which really was the wholly "economic" reason for musicians in Bach's time
>to yield the much preferable sounds of the several varieties of meantone
>tuning for 12th-root-of-2 equal temperament.

I am amazed that Wendy Carlos would ascribe 12-ET to musicians of Bach's
time. There is scant evidence that anyone at that time wanted it, and no
evidence that anyone knew the techniques that would make it was possible. You
cannot just "feel" your way to an acceptable ET on a strung keyboard, it has
to result from a system of cross measurements.
If she is of the opinion that the only historically used tunings on a 12
note keyboard were either a restrictive meantone or ET, then I submit there
is a huge hole in her intonational picture.
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

To Ed Foote and the List:

Wendy Carlos now understands and accepts that there were other irregular 12
note constelations. I had asked her to retract earlier views, but she
preferred to just move on. She no longer speaks of Bach as 12ET exclusive.

Johnny Reinhard
AFMM

On Wed, 5 May 1999 Afmmjr@aol.com wrote:
> Wendy Carlos now understands and accepts that there were other irregular 12
> note constelations. I had asked her to retract earlier views, but she
> preferred to just move on. She no longer speaks of Bach as 12ET exclusive.

I should hope so, considering _Switched-On Bach 2000_.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Hey--do you think I need to lose some weight?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

I quoted Wendy Carlos:

>> More frustrating than [the limited tolerance of acoustic intruments and
>>analog synthesizers] is the usual limit on number of tones in an octave,
>>which really was the wholly "economic" reason for musicians in Bach's time
>>to yield the much preferable sounds of the several varieties of meantone
>>tuning for 12th-root-of-2 equal temperament.

Ed Foote wrote,

>I am amazed that Wendy Carlos would ascribe 12-ET to musicians of Bach's
>time. There is scant evidence that anyone at that time wanted it,

That's true, except for many lute and guitar players, and a handful of
theorists.

>and no
>evidence that anyone knew the techniques that would make it was possible.
You
>cannot just "feel" your way to an acceptable ET on a strung keyboard, it
has
>to result from a system of cross measurements.

The monochord measurements were available, so one could tune a keyboard to
the monochord, if one could get enough precision on the monochord.

>If she is of the opinion that the only historically used tunings on a 12
>note keyboard were either a restrictive meantone or ET, then I submit there

>is a huge hole in her intonational picture.

Perhaps, but the point she is making is still valid. One could substitute
"12-tone-circulating-temperament" for "12th-root-of-2 temperament" in the
quote above and then Wendy would be making a very true and important point
(which I'm prepared to defend)! There is no evidence that anyone at the time
wanted sharp major thirds, but they had to have them in order to get the
circle to close at 12. Today, most musicians want sharp major thirds in most
contexts, probably as a result of acculturation of the compromises made in
Bach's time.

One could also substitute "musicians in Bach's time" for "musicians from
1700-1850", which period saw meantone gradually give way to progressively
more and more equal circulating temperaments until finally total equality
won out.

The point is that multiple division would have won out (Handel had 16 notes
of meantone on his organ) had economic considerations not dictated that most
instruments would be limited to 12 pitches. Today the economic circumstances
are quite different, at least when it comes to electronic instruments, and
the restriction to 12 tones has outlived its usefulness.

Greetings,
I wrote:
>You
>>cannot just "feel" your way to an acceptable ET on a strung keyboard,
>it has to result from a system of cross measurements.

And Paul replies:
>The monochord measurements were available, so one could tune a keyboard
>to the monochord, if one could get enough precision on the monochord.

I must ask if there is anybody on the list that has tried this, with
acoustic instruments? I have, and the resulting ET was not E.
Getting a temperament note to within two cents by unisons between a
monochord and a struck string is pretty close, but that still leave you a
random error of 4 cents in any given interval. This is enough to make a
noticible difference in tonality and render a temperament audibly unequal.
Perhaps on paper, the idea of ET seems easy enough, but the reality of
strings is a different story. I would suggest to anybody that wants to
accept that there was ET on strung keyboards before 1850 attempt to tune one
with the documented procedures of the era. Lutes and viols are a different
matter, of course.
REgards,
Ed Foote

>The point is that multiple division would have won out (Handel had 16 notes
>of meantone on his organ) had economic considerations not dictated that most
>instruments would be limited to 12 pitches. Today the economic circumstances
>are quite different, at least when it comes to electronic instruments, and
>the restriction to 12 tones has outlived its usefulness.

I'm not sure the limiting factor was entirely the added expense (or,
alternatively, the diminished range) of the instrument. Increasing the
number of keys greatly increases the complexity that performers have to
master. A very few split-key instruments were available to players (such as
Handel) dedicated enough to adapt their technique. Otherwise, I think that
12-tone-per-octave standardization of keyboards was driven not by
19th-century mass production (as some have claimed), but by 14th-century
player convenience as much as economic compromises.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

On Thu, 6 May 1999 A440A@aol.com wrote:
> Perhaps on paper, the idea of ET seems easy enough, but the reality of
> strings is a different story. I would suggest to anybody that wants to
> accept that there was ET on strung keyboards before 1850 attempt to tune one
> with the documented procedures of the era. Lutes and viols are a different
> matter, of course.

So what about tuning a keyboard to a lute or viol?

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Hey--do you think I need to lose some weight?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

Paul Hahn wrote:

> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
>
> On Thu, 6 May 1999 A440A@aol.com wrote:
> > Perhaps on paper, the idea of ET seems easy enough, but the reality of
> > strings is a different story. I would suggest to anybody that wants to
> > accept that there was ET on strung keyboards before 1850 attempt to tune one
> > with the documented procedures of the era. Lutes and viols are a different
> > matter, of course.
>
> So what about tuning a keyboard to a lute or viol?

How were these instruments tune and what makes you think they would be closer
than a monochord. I suggest you try fretting a string instrument and see how far
off it is most of the time. That ET was acceptable when it could only be
approximated. No ET can be tuned by ear which shows its own absurdity. This
becomes really apparent once one has worked with the just intervals it
approximates.

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Unless someone has new information, G.F. Handel had 14 keys per octave (not
16). R.H.M. Bosanquet wrote in his 19th century monograph on Temperament
that he could still see the shadows of the split keys where the split keys
used to be. I recall his deduction to be a mere 14.

Johnny Reinhard
AFMM

When I said:
> I would suggest to anybody that wants to
>> accept that there was ET on strung keyboards before 1850 attempt to tune
>one with the documented procedures of the era. Lutes and viols are a
different
matter, of course.

The question comes up:
>So what about tuning a keyboard to a lute or viol?

Very difficult, since the sustain is so short. Try it, you will see.
Also the strings of the 18th century were usually quite inconsistant, so
trying to arrive at an ET with the cumulative error of strings and frets
would be very chancy effort at best.
Regards,
Ed Foote

Kraig
>No ET can be tuned by ear which shows its own absurdity. This
>becomes really apparent once one has worked with the just intervals it
>approximates.

Hmm. I tune an ET by ear, but only with 20th century techniques.
Regards,
ED Foote

Have to disagree that one can't hear 12TET by ear, at least today. La Monte
Young often included in his lengthy concert programs that one could only hope
to hear JI intervals accurately. Irrational equal temperaments he had
thought impossible.

Truth is that with a Masters Degree education in Music Performance one learns
to hear EVEN 12TET with the same accuracy as any other tuning so learned,
including JI. After 12 comes 24 then 48: even 31TET can be learned by diesis
and by non-just intervals. Admittedly, few music students take these further
divisions as seriously. ;)

Johnny Reinhard
AFMM

I wrote,

>>The point is that multiple division would have won out (Handel had 16 notes
>>of meantone on his organ) had economic considerations not dictated that most
>>instruments would be limited to 12 pitches. Today the economic circumstances
>>are quite different, at least when it comes to electronic instruments, and
>>the restriction to 12 tones has outlived its usefulness.

Bill Alves wrote,

>I'm not sure the limiting factor was entirely the >added expense (or,
>alternatively, the diminished range) of the >instrument. Increasing the
>number of keys greatly increases the complexity >that performers have to
>master. A very few split-key instruments were >available to players (such as
>Handel) dedicated enough to adapt their >technique. Otherwise, I think that
>12-tone-per-octave standardization of keyboards >was driven not by
>19th-century mass production (as some have >claimed), but by 14th-century
>player convenience as much as economic >compromises.

Yes. By economic I meant the physical and mental economy for the player as well as the monetary cost. I could say, "it is not economical to have that many notes on an acoustic instrument" without any reference to affordability or mass production.

Johnny Reinhard wrote,

>Unless someone has new information, G.F. Handel >had 14 keys per octave (not
>16).� R.H.M. Bosanquet wrote in his 19th century >monograph on Temperament
>that he could still see the shadows of the split >keys where the split keys
>used to be.� I recall his deduction to be a mere >14.

The 16 were produced by organ stops, not split keys.

In the pitch table that you yourself co-authored for Ear Magazine East, did you and your colleagues not ascribe 16 pitches to Handel's organ?

On Thu, 6 May 1999, Kraig Grady wrote:
> Paul Hahn wrote:
>> So what about tuning a keyboard to a lute or viol?
>
> How were these instruments tune and what makes you think they would be closer
> than a monochord. I suggest you try fretting a string instrument and see how far
> off it is most of the time.

I probably should have included a smiley in my previous post--naturally,
a fretted stringed instrument isn't going to be any more accurate than a
monochord, which was already mentioned (probably worse, actually).
Sorry for the lame joke.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Hey--do you think I need to lose some weight?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

Afmmjr@aol.com wrote:

> From: Afmmjr@aol.com
>
> Have to disagree that one can't hear 12TET by ear, at least today. La Monte
> Young often included in his lengthy concert programs that one could only hope
> to hear JI intervals accurately. Irrational equal temperaments he had
> thought impossible.
>
> Truth is that with a Masters Degree education in Music Performance one learns
> to hear EVEN 12TET with the same accuracy as any other tuning so learned,
> including JI. After 12 comes 24 then 48: even 31TET can be learned by diesis
> and by non-just intervals. Admittedly, few music students take these further
> divisions as seriously. ;)
>
> Johnny Reinhard
> AFMM

You are right that people can hear 12ET. It is tuning ET directly that is least
accurate than JI. But let me not be misunderstood in implying that only certain
JI intervals can be tuned in response all phemnomenon. The properties of
difference tones in chords of many notes can lead to pitches outside of the
standard matrix. But with 12 ET boomsliter and Creel points out that what
players are hearing when playing ET is not ET (and not standard JI either). No
orchestra plays in 12ET. The biggest example of the intonational problems of
12ET are those pieces that combine string instruments with the keyboard. Some of
the ugliest out of tune music comes out of these ensembles. String players play
closer to Pythagorean. Those with Masters degrees represent for the most part a
group that produces no better music that any other and as a standard represents
one of the greatest injustices in our socalled civilization. We are talking
about individuals spending many times over 100,000 dollars on information and
attitudes that are there only to justify there own existence. This is the same
group that promoted pure ugliest as a standard. It is music for an upper class
to snub down to the lower classes. If not how could you afford it. The same is
true of our art schools. If they all shut down I doubt if little would be lost
as they blood suck the youth and destroy any real creativity they had.
Look what it did to Jazz.Killed it!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Johnny Reinhard wrote,

>Unless someone has new information, G.F. Handel had 14 keys per octave (not

>16). R.H.M. Bosanquet wrote in his 19th century monograph on Temperament
>that he could still see the shadows of the split keys where the split keys
>used to be. I recall his deduction to be a mere 14.

I had seen many references to 16 pitches, produced by stop mechanisms, on
Handel's organ. Unfortunately I didn't remember where I had seen these
references. Fortunately, I just stumbled upon another one: Mandelbaum's
dissertation. On page 251, footnote 7, he writes:

"Handel, in England, had been using an organ with 16 keys to realize a broad
range in what may well have been a temperament of more than 1/6 of a comma."