More on Just Intonation 2

A singer who gets all the notes perfect, and who is proceeding along
swimmingly, but then gets to a note that he just can't seem to sing, and
who then totally loses his way, and starts to use notes that sound
vaguely wrong, and then hits another really bad note, and starts to use
notes that sound definitely wrong and off-key, so that the audience
starts whispering and fidgetting ? this is the effect of the just
intervals when untempered.

Theorists who have never actually tried to play much music in just
intonation take one look at the 'movable second' of this system (both
above and below the tonic) and say to themselves: "No matter, what is
all the silly fuss about? let us remain just, pure and holy - let us
simply add the requisite additional tone." In so doing they fail to
understand that in music one crack in the dike is enough to flood the
village fifty feet deep beneath our old enemy, the sea.

For as soon as our unfortunate too-perfectly-skilled singer (or
instrumentalist) reaches that movable tone (and this quite apart from
any question of modulation or musical style), all hell breaks loose.
Entirely new notes are needed, and then still more, which do not fit
into the old tonal fabric. This is not the momentary tension of
modulation, but the creaking sound of the ocean liner before it splits
in two. That a handful of presumptuous people aggressively declare that
they love this sound, and are able to make great masterpieces with it,
is as may be ? but so far they have made no masterpieces, but only
curiosities wholly irrelevant to music as an art.

All these difficulties were completely and intimately known to the
musicians and theorists of 400 years ago. It was also known long before
to musicians, but the theorists, in the grip of their worship of one
particular Greek school of theory, the Pythagorean, preferred to pretend
no difficulty existed. Quite strained arguments have been made to the
effect that the ancients universally defined even the thirds as
dissonant - hence the hopeful attempts of a long series of Western
theorists to gradually extend the number of consonances to include the
septimals. But this is definitely true only for the Pythagorean
tradition, not for Greek musical theory as a whole, whose conclusions
are largely lost to us. Pythagorean intonation is simply a variety of
just intonation in which the fifth/fourth cycle is alone used, resulting
in difficulties just as excruciating as those of the true just
intonation, although of a different kind. To pretend that a singer can
accurately produce an interval four or five perfect fifths above the
tonic is nonsense; this is a commatic disjunct dissonance, and not
accurately singable.

These matters are widely known ? they are also widely ignored or denied
or imperfectly known. The ignorant very typically imagine that We Clever
Moderns have invented a new music in which all the Stupid Old Ideas of
the dead past don't matter. Every generation thinks like this ? and
every generation is wrong. The poor, itinerant singers ? many of them
great geniuses of a kind that are largely absent from our academies ? to
whom our people deliberately go listen, know little of temperament. But
their profession prevents them from falling into the excesses of the
just intonationists, who imagine that some clever new mathematics will
somehow find a way to eliminate the necessity of tempering, or permit us
to use with success some temperament even more self-inconsistent than
just intonation itself. But the best mathematical minds in Europe once
busied themselves very largely ? I almost said 'primarily' ? with
escaping from temperament, and never found a way. Popular singers are
also preserved from the extravagances of the academics who cultivate
such monstrosities as 22- 29- or 41-tone equal, which merely reproduce
the worst deformities of just intonation, with very few of its benefits.

The irony is that just intonation itself is considerably poorer in
usable melodic resources than the 19-tone equal, of which matter I omit
to treat again here.

Now an important consequence of the observation that a singer who uses
absolutely pure intervals involves himself in fearsome practical
difficulties, is that singers do indeed temper intervals. But how?

I have presented evidence to suggest that the seven consonances and
twelve tonal dissonances form a tonal fabric to which 19-tone equal
temperament corresponds far more closely than any other intonational
system. The 19-tone equal intervals are with _no_ exceptions very close
to the 19 melodic pitch classes into which just intonation tends to
resolve. I am not alone in this opinion.

This by the way, is _not_ a circular argument, which I anticipate
someone will suspect it to be ? and should so suspect as a matter of
normal skepticism. The 19 just intervals were not invented or chosen
arbitrarily in order to favor the 19-tone equal; they follow ineluctably
from the consonances, and from the nature of singers' ability to sing
dissonances vis-?-vis the tonic. I was dumbfounded when I first noticed
this correspondance; I expected that 31-tone equal would offer a better
correspondance; but this is not the case. 31-tone equal corresponds
better to the atonal dissonances, but much less well to the tonal ones.

Another possible source of circularity in my arguments might be supposed
to be the choice of melodic limen of circa 60 cents, which is quite near
the 19-tone equal tuning degree. But in fact a melodic limen as narrow
as circa 50 cents or as wide as circa 70 cents, still results in much
the same melodic pitch classes when applied to the 19 just intervals.

Finally, it is to be noted that even if onesuppose the atonal
dissonances to be perceptibly part of the tonal fabric, which I doubt,
they are melodically confused with the tonal dissonances, and more
objectionably yet, with the consonances.

I have also remarked that all microtonal systems other than 19-tone
equal tend to reduce to about 12 melodic pitch classes in the octave.
This may well help to explain why the 12-tone equal, which was known for
centuries by our ancestors, but nearly always rejected by them with the
most sovereign contempt, has achieved such a peculiar destiny. It is
that intonational system toward which ignorance and error converge; it
is that system which a random choice of tuning, in violation of the
canons of just intonation and the human voice, and therefore in
violation of the musical understanding, must finally produce.

Error is manifold, truth one. This is not a statement that arises from
religio-dogmatical habits of thought, but from science, which usually
supplies many incorrect conclusions, but only one correct answer, or
group of answers.

The 19-tone equal temperament is the only closed, fully cyclic system
toward which just intonation, in its practically audible aspect, tends;
it is therefore the only correct system.

Having now given sufficient information to, at the least, propel the
open-minded to a close examination of the 19-tone equal temperament,
having also perhaps discouraged a few frivolous triflers from disgracing
the 19-tone equal temperament by any use of it, and finally, having
communicated my discovery of the octave stretch (which noticeably
improves the harmony of this temperament,) I shall abate very
considerably the frequency of my postings, not wishing to interfere with
the learned debates of others, and unwilling to devote too much of my
time, which is to me very precious, to correcting vulgar errors or
trivial disapprobations.


SMTPOriginator: tuning@eartha.mills.edu
From: Robert C Valentine
Subject: Re: 19, 22, 29, etc...
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