22-tone equal, reply to Ehrlich

My manner of saying that the 22-tone equal does not close the cycle of
fifths was too abbreviated and has given rise to misunderstanding. Of
course all temperaments are cyclic by definition, in the sense that
their fifths return to the same point, with the exception indeed of a
few such as 24- & 34-tone equal which consist of two non-communicating,
parallel series of fifths. When I say the fifths are non-cyclic, I mean
that, although the thirds and sixths are consonant so long as one does
not modulate or use certain melodic intervals, nevertheless they give
rise to such dissonant thirds and sixths that the cycle of modulation is
broken. And not only the cycle of modulation, but of many melodic
progressions as well.

Your phrase "vanishing of the syntonic comma" is unfortunate. This comma
does vanish in the 22-tone equal, but at a value (218 cents) that leads
to excruciatingly dissonant 'major thirds' (436 cents), minor thirds
(273 cents), major sixths (927 cents) and minor sixths (764 cents) as
soon as one modulates more than a few keys. But even if one remains
within the same key, many intervals within the tonal fabric become
dissonant so long as fifths of 709 cents are preserved. To those who
treasure each new whining, commatic dissonance like the goose's golden
egg, and hate consonance with a passion, this temperament is indeed a
gift from the gods.

The major semitone (164 cents) and minor semitone (55 cents) are
utterly divergent from western habits, though the former is melodically
usable.

Another and simpler way of expressing the non-cyclic character of the
22-tone equal is to observe that the three consonant cycles (those of
the fifth, major third and minor third with their inversions) are
incommensurable. What this really entails is often overlooked. Some
theorists simply look at the 327- 382- & 709-cent intervals of 22-tone
equal, and conclude that this temperament has good representations of
the consonances. In doing this, they forget that as soon as one
modulates (or proceeds by any number of melodic phrases that involve the
simultaneous use of the 5- and 3- limits) one obtains highly dissonant
thirds, so long as the fifths are held consonant. This is doubtless
obvious to many theorists, but not to all. Mandelbaum, for example, a
person of no inconsiderable theoretical attainments, fell into this
trap.

It is meaningless to call a temperament non-cyclic in the sense that one
calls the just or pythagorean intonations non-cyclic. When I say that a
temperament is non-cyclic I mean that the three consonant cycles do not
agree with each other, and that the cycle of fifths does not close in
such a way to permit cyclic modulation, or indeed any but the most
constrained melodic progressions. 17- 22- 29- 41- & 53-tone equal all
fall into this category.

Our age is accustomed to very cavalierly dismiss every shred of musical
theory left to us by our ancestors - or else to blindly worship the
past. An academic minority is eager to deny every principle that the
past held dear - while the popular majority tends rather to preserve
certain musical elements in simplified form, while accepting many
non-Western melodic elements. The same people who detest the very idea
of consonance, without quite knowing why, are very often the same people
who blindly worship Beethoven or Mozart. Those who are truly "freemen in
thought" are respectful of the past at the same time that they
searchingly question it.

Indian singers - see Levy: Intonation in North Indian Music - do not
seem to use the 22-tone equal at all. They certainly do not sing
436-cent major thirds, which occur repeatedly in the melodic texture of
22-tone equal, unless very flat fifths of 655 cents are employed. Of
course the centre of 22-tone equal in India is nowadays supposed to be
the South.

Tuning now to a different issue, you appear to assume that because the
historic Arab theorists - most of them more concerned to interpret
ancient Greek theory than the practice of their own musicians -
prescribe or record a tuning, all are Neanderthals who do not fall down
before this tuning in awe. I certainly do not hold Arabic music in
contempt. I have devoted much attention to the subject. Gamelan scales
by the way can be very satisfactorily reproduced in 19-tone equal.

I am aware of the cents in a (12-tone equal) tone. Difference of opinion
need not give rise to random unpleasantness. Certainly I mean no offence
to anyone in stating what I am convinced are facts.

I had much rather be called a 'popularist' than an elitist.

Your attempt to equate pitch variation in the articulation of spoken
words with musical melody deserves careful consideration. Why, however,
would anyone wish to replace (or confuse) melody, which is reproducible,
and which is ideally meant to _heighten _ the effect of language or
poetry, with the articulation of spoken language, which is
nonreproducible, and a wholly different art besides. There have been
attempts in this direction, not all of them flat failures. Popular
singers occasionally lapse into spoken language for effect. But if this
becomes usual it is in very bad taste.

I do not deny that non-Western traditions use intervals different from
those commonly used in the West. Thank God that they do!
I do however categorically deny that any singers whatever (allowance
made for the occasional alien with 31-tone equal ears)
can reliably reproduce intervals narrower than 55-60 cents in melody.
Those who imagine I am insulting non-Western musical traditions in
making an observation of fact, misinterpret my motives. I am a great
admirer of Indian music and culture, for example. In the actual world
these musical traditions are under assault by the overwhelmingly
dominant 12-tone equal temperament (instrumentally considered.)
Meanwhile, paradoxically enough, our own popular music - vocal rock
music - is busily assimilating as much non-Western melos as it can. But
it is _not_ assimilating vocal melodic intervals less than about 60
cents in width, for the excellent and quite matter-of-fact reason that
singers cannot deliberately reproduce or remember such intervals. It is
easy to say: "oh yes they can," and I have no objection if someone
wishes to attempt to prove the contrary. The evidence is very much
against this, however. There are not a few advocates of 12-tone equal
who have managed to convince themselves that the melodic limen is in the
region of an equal semitone, which I also deny.

There does seem to be an elitest attitude abroad that one demonstrates
one's own musical superiority by hearing - or asserting that one hears -
extraordinarily minute intervals as essential melodic changes. One is
reminded of the bright young student who 'proved' that Helmholtz had
preferred just intervals to 12-tone equal ones only because he suffered
from a disease of the inner ear, that made his aural faculty
preternaturally sensitive!
Or again, I am reminded of the Greek theorists made fun of by
Aristoxenos - very estimable persons, no doubt - who cared nothing for
living or practical music, but who occupied themselves with ceaseless
attempts to distinguish ever narrower intervals. Meanwhile, around them
even the enharmonic was abandoned, perhaps for want of any such firm
theoretical basis as the 19-tone equal might have provided them.

Music is primarily a creative, not an exhibitionist art.


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: More on 22-tone equal
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