Reply to Paul Ehrlich

Your point regarding the 3/4 tone of Arabic music is at least debatable;
in highly conjunct music the voice and the musical understanding are
appreciably more sensitive than in more disjunct music. Nevertheless
most researchers have found Arab singers quite unable to reliably
reproduce these very narrow intervals, much less anything so esoteric as
the neutral third, which usually amounts to nothing more than a slightly
inaccurate minor third.

You are incorrect that 31-tone equal has more usable melody than 19-tone
equal. Between C and D, for example the 31-tone equal has Dbb, C#, Db
and Cx ascending. The first of these is melodically confounded with C,
the second two are melodically confounded with each other, and the last
is confounded with D. The 31-tone equal is in fact a monstrously
complex, inefficient way of returning us to our melodic starting-point
of 12-tone equal. It is much smoother indeed, but melodically it is a
dead-end. There is one exception; as I intimated, the augmented tone in
this system does seem to be distinct from the minor third, perhaps
because the former is both conjunct and dissonant, while the latter is
consonant and at least putatively disjunct.

I appreciate that even worthless systems are worthy of extensive study -
else how would we know them to be worthless? I also have studied the 22
system. It enjoys extensive advocacy by those who associate it with
Indian music, which is certainly worth some attention!

The 22-tone equal suffers from two grave defects however, either one of
which would be sufficient to condemn it to the category of a curiosity.
Its tuning degree is at the outermost limit of what can be reliably
distinguished in melody. By this I mean if one flats or sharps a note by
55 cents that note will sometimes be interpreted as having essentially
changed the melody, but sometimes not - and more often not. Musicians do
not write for exceptionally acute listeners, but for the masses. The
second defect of the 22-tone equal involves its failure to close the
cycle of fifths. I am aware that some will say to themselves - so what?
But a musical system that does not close the cycle of fifths has at a
stroke isolated itself from 99% of the music not merely of the western
19th century, but from virtually the whole of the western tradition, and
from many other musical traditions as well. Such musical systems, like
just intonation, are mere curiosities, and are far more impoverished in
usable, aurally distinct resources even than the 12-tone equal.

The four scales I gave have consonant triads (major or minor) available
on four of their seven degrees. For example:

C D E F G Ab B

has consonant triads on C, E, F & G, but not on D, Ab or B. I hope this
clarifies the matter.

Your refer to the 7 and 11 limits. The latter is a mere fantasm of the
just intonationists, and is not audible to the ear as anything other
than dissonance. The septimal limit is more interesting. But it is
dissonant, however this may trouble those who aspire to forever extend
the boundaries of consonance, until someday I presume, we shall find
everything consonant, and music need trouble itself no longer with any
rules or constraints whatever... It will also no longer need to trouble
itself with pleasing an audience, for it will have none. Actually
however, the 19-tone equal is the _only_ temperament that gives the
septimal intervals in such a form that they can be melodically
distinguished from adjacent intervals. This is a consequence of the fact
that in this system only are the septimal intervals far enough away from
adjacent intervals to preserve their own unique melodic character.

Your reference to individuals being trained to reliably distinguish
melodic intervals as close as 10 cents is the most fantastic piece of
information I have ever been privileged to encounter. Presumably such
monsters would no longer recognize "Mary Had a Little Lamb" as a single
melody, but would distinguish several hundred million essentially
different melodies instead! You will forgive me if I remain skeptical of
this possibility.


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From: Carl Lumma
Subject: Misc 3
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