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PIPORG-L  October 2006, Week 4

PIPORG-L October 2006, Week 4

Subject:

"Out of tune thirds", and etc

From:

Brad Lehman <[log in to unmask]>

Reply-To:

Brad Lehman <[log in to unmask]>

Date:

Wed, 25 Oct 2006 10:25:18 -0400

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (185 lines)

Responding to a bunch of different ideas from yesterday's digest, excerpted:

=====

 >>Let's face it--to the average person in the pew, indeed, to the
 >>average musician, all the various tunings are esoteric enough that 
 >>most people are not interested.

Perhaps true; but why spoil it for those who *can* hear those subtleties 
and are interested to do so?  Look at it this way: if our eyes were 
built with only rods, no cones, we wouldn't care much about color 
because we couldn't perceive it directly...but different colors of light 
would exist anyway.  (And continuing this perhaps crass analogy: equal 
temperament reduces everything to aural black-and-white since all keys 
sound "the same" as one another, effectively removing color from the 
music.  But, tonal music is constructed on principles of tension and 
relaxation that *aren't* black-and-white; why wash out the music to 
colorlessness, then?)  Perhaps this is mostly a matter of training, 
familiarity, experience: if we hear *only* the black-and-white of ET for 
most or all of our music, we become desensitized to the possible 
delights of anything more colorful.

=====

 >>I'd like to take one step further and risk what might be an
 >>impossible question or two to add to the discussion.  Please know
 >>that I truly ask in an honest and sincere manner, and bear with me
 >>if, in fact, there is actually "no way to answer this".
 >>What is the part of music played in any of the various non-equal
 >>temperaments that is the beautiful part?

I suspect there's no *definitive* way to answer that.  But the answer, 
for me anyway, is that beauty is found in the organized creation and 
relaxation of tension in the music, providing variety and 
capturing/holding attention as the music naturally flows forward in 
time.  When there's not enough tension/relaxation, the whole thing 
becomes static and boring.  Or if there's too much tension, or too many 
*sudden* anomalies, that too can get dull or distracting.  The beauty 
lies in the careful and subtle balances, in between.

=====

 >>But when I hear yet another example of this or that temperament, I
 >>just hear "out of tune organ".  If there's lots of aggressive
 >>upperwork or a flock of squawky fractional-length reeds blaring away
 >>as well, it doesn't seem any more pleasant.  The occasional odd note
 >>here or there sometimes which simply howls in pain (I presume this is
 >>the infamous "wolf" oft mentioned making its appearance?) or a wind
 >>supply wiggling like a bowlful of jello doesn't help.  All of these
 >>things, when they occur, distract me from being able to hear the flow
 >>of the music being played and interrupt my ability to enjoy it.

I tend to agree with most of that.  But as I pointed out yesterday or 
the day before, most of these "out of tune" moments in keyboard music 
come from poor handling of enharmonic spelling: for example, playing an 
E# with a pitch that is too well tuned as an F, or similarly playing a 
Db as a pitch that too much favors C#.  As I said, I have large sections 
about this in my 2005 papers:
http://www-personal.umich.edu/~bpl/larips/outline.html
There's also a more focused excerpt about enharmonic handling at this 
spin-off page:
http://www-personal.umich.edu/~bpl/larips/enharmonic.html

=====

 >>To complete the picture, I must mention the Leipzigean comma, defined 
 >>by Sigfrid Karg-Elert. It is the difference between (I think) three 
 >>perfect thirds and an octave, and amounts to ca 1/8 tone.

Maybe some would call that a "Leipzigean comma" or whatever, but the 
more usual term is _diesis_.  Three stacked major thirds fall short of a 
pure octave by this amount, which is approximately 42 cents.  (~~1/8 of 
an ET whole tone....)  Technically that's three syntonic commas, minus 
one Pythagorean comma in the opposite direction.

Doing the math with multiplication rather than logarithms (such as the 
cent scale): the three pure major thirds are each 5/4, and we multiply 
them together....
5/4 x 5/4 x 5/4  ... which 125/64 is much less than a pure octave, 2/1, 
as that would be 128/64.  The leftover factor there, 128/125, is this 
_diesis_.   5/4 x 5/4 x 5/4 x 128/125 = 2.

If we're doing it with cents: those 42 cents of excess must be burned 
off within *each* of the four stacks of major thirds.
C-E-G#-C;   F-A-C#-F;   Eb-G-B-Eb;   Bb-D-F#-Bb.

"1/4 comma meantone" temperament takes the easy solution of keeping two 
of those major thirds in each stack pure, and giving all the error to 
one of them.  Typically that's C-E-G# pure and G#-C wolf; F-A-C# pure 
and C#-F wolf; Eb-G-B pure and B-Eb wolf; Bb-D-F# pure and F#-Bb wolf. 
Notice that all four of those wolf intervals are misspelled; they're not 
really major thirds at all, but diminished fourths.  They sound so 
raucous in practice because they're so far away from the pure interval 
of 5/4: 42 cents too wide, each.  Again this is that thing about the 
handling of enharmonic spelling, that I mentioned above.

Equal temperament simply whacks the 42 cents of excess into three equal 
pieces and gives 14 cents of error to each of the three major thirds, in 
each stack.  Every major third gets that same average amount.

Other temperaments distribute the excess differently, among and within 
these four stacks, usually with attempts to favor the tension/relaxation 
of the major thirds that get used most often in the music to be played. 
  The major thirds that are entirely built of naturals (C-E, F-A, G-B) 
usually tend to get the smallest portions of the error.  The really 
artful finesse here is: dealing around what's left over, is it better to 
put it into the major thirds that have a flat on the bottom, or the ones 
that have a sharp on the top?

As yet another example, here's the set of major thirds in the 
temperament style that I infer was Bach's (with full explanation in my 
papers).  Each row must always add up to that 42-cent total:

    - C-E 6 cents, Ab-C 16 cents, E-G# 20 cents.
    - F-A 6 cents, A-C# 18 cents, Db-F 18 cents.
    - Bb-D 12 cents, D-F# 14 cents, F#-A# 16 cents.
    - G-B 10 cents, Eb-G 14 cents, B-D# 18 cents.

All of this is gradual, moving around the circle of fifths in either 
direction.  But also, intervals containing sharps tend to be 
sharper/harder than their counterparts with flats: leading to a 
brilliant sound when sharp music is played, and a more mellow or relaxed 
sound when flat music is played, both in contrast to a more plain and 
resonant sound when the music is mostly in naturals.

There is much too much to explain here, but anyway that's an introduction.

=====

 >>All these silly tuning discussion sometimes make me want to scream. 
 >>It's the same as the discussion on early fingering.  Our hands are 
 >>almost a half inch larger now then 300 years ago.  The keyboard has 
 >>changed little.  The size of our fingers is larger also.  It appears 
 >>to me that some adjustments in fingerings to play more fluid and with 
 >>less hand stress are a good idea.  The whole purpose being making 
 >>music NOT AN ACADEMIC exercise.

I hate to change streams too much here, but: part of the point of "early 
fingering" is not merely to make things easier or harder, or accommodate 
fluidity or lack of stress.  The earlier styles of fingerings affect the 
*sound* of the music, in the articulations that come up: akin to 
tongueings on wind instruments, or bowings on strings, or sung syllables 
with a variety of consonants and vowels.  Complete facility is not 
necessarily a musical virtue, as to helping the music communicate 
directly/immediately with listeners....  I agree with your statement 
that this is "NOT AN ACADEMIC exercise"; it's rather about musical 
delivery.  The variety helps listeners to sustain attention to the 
music, and to grasp its syntax immediately.

I find that when I play on equal-tempered organs, or (ugh) 
equal-tempered harpsichords (my specialty is harpsichord...), I have to 
do *more* conscious stuff with special fingerings, exaggerated 
phrasings, sharper staccatos, etc etc to offset the fact that the 
temperament isn't giving me anything expressive to work with, as in the 
tensions/relaxations that can be available in intonation.  Equal 
temperament requires me to insert more artifice into my playing to 
deliver comparably engaging effects...making the music harder work to 
play.  In better unequal temperaments I can simply relax, listen to what 
the music is already doing in its tensions/relaxations, and sculpt my 
performance style accordingly...which feels like a much more natural 
process to me as a musician.  And if I'm using earlier styles of 
fingerings there as well, it's to get the right articulations and 
accents in the musical texture, the hands doing it automatically rather 
than having to add in such things artificially (on top of modern "piano 
fingering" with thumb under, etc etc).  I use period fingerings because 
I feel that they help the music to *sound better* and more natural.  It 
also depends on factors such as the room acoustics, instrument 
responsiveness, and more: always coming back around to listening, and 
trying to be clearly communicative with enough variety, balanced with 
enough consistency...in search of beautiful expression....

Other people's experiences may of course vary.


Bradley Lehman
http://www.larips.com
http://www-personal.umich.edu/~bpl/larips/recordings.html

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Note:  opinions  expressed on PIPORG-L are those of the  individual con-
tributors and not necessarily  those of the list owners  nor of the Uni-
versity at Albany.  For a brief  summary of list  commands, send mail to
[log in to unmask]  saying  GET LSVCMMDS.TXT  or see  the  web
page at http://www.albany.edu/piporg-l/lsvcmmds.html .
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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