Septimal Intervals

The perfect fifth 3:2 is comprised of the minor third 6:5 and major
third 5:4. This in turn means that the consonant chords of the 3-limit
and those of the 5-limit are congruent, that is to say, they can exist
together without producing dissonant intervals.

But when we reach the septimals, we find that the perfect fifth 3:2 is
comprised of 7:6 and the undoubtedly dissonant 9:7. The other possible
septimal bisection of the fifth, 8:7 and 21:16, also includes an
undoubted dissonance (21:16) although the closeness of 8:7 makes it too,
undoubtedly dissonant.

Now a chord with one dissonant interval, is dissonant. Someone may try
to deny this, but I am afraid he will fail.

There do exist a few septimal triads that seem to escape this argument,
e.g. 5:6:7, 4:5:7, 4:6:7. But a few triads do not begin to compare with
the richness and variety of the harmonies of the senario.

If follows that the septimals, even if one admits them to be weakly
consonant - which I do _not_ - certainly give rise, for the most part,
to undoubtedly dissonant chords. They have only the most tenuous
relation with the harmony of the senario, which on the contrary, forms a
closed, well-ordered system.

All this was observed centuries ago. Mersenne is full of highly
ingenious arguments regarding the septimals - nihil sub sole novum. The
Renaissance and Baroque were much occupied with debating whether the
septimals might ever be used as consonances, and were much more
acquainted with the septimals than the average modern. They concluded, I
would say quite reasonably, that the septimals make charming, effective
dissonances of a peculiar and valuable kind - but very poor consonances.

In former centuries musical theory was an honored and well-rewarded
study, and so we should not be surprised if most of what we now think
terribly modern questions, are actually very ancient questions. Nor does
the accident of being dead make a man necessarily wrong.

There is a disposition to assume that because one calls an interval
dissonant, one hates it, and wishes to banish it from music. One can
trace this assumption to the early Renaissance, during which a certain
school of composition did actually try to rid music of all dissonant
chords, which were felt to make impossible any attempt to join different
melodies harmonically. So today, some people still take it as a personal
insult if an interval they fancy is called dissonant, and - very
absurdly - try to make consonance and dissonance purely relative ideas
with no basis in physics. It is as if everyone were convinced red were
the only beautiful color, and were mortally offended if anyone dared to
call a green shirt anything but red. But the shirt would still be
_green_.

But I - just as about 99% of all the Western musical theorists who have
ever lived - do really hate and wish to banish a certain narrow class of
dissonances - those which are so close to consonances that they beat
badly, but yet are melodically confounded with the consonances. These
are called mistuned consonances, and anyone who really loves these
intervals does really deserve to be insulted, for if these intervals are
accepted they will drain instrumental music of most of its expressive
power.

We find a perfect analogy in modern poetry, where not merely rhyme, but
even metre - nay, even clear sense and ordinary grammar - is felt by a
certain kind of poet to be too constricting on his power to express his
emotions and ideas. And what has been the result? In the mouths of such
personnages, language itself becomes more irrelevant to culture than the
worst babblings of the Christian or Muslim Fundamentalists. Poetry is
now perfectly irrelevant to modern literature, which is dominated by the
most miserable, low, fourth-grader prose. But that prose can at least be
understood, and is _genuine_ language, and so the people take it to
their hearts. Were a true poet to appear today, using metre and even
rhyme in the service of easily noble or pathetic thoughts and emotions,
he would seem a veritable monster, and would probably be regarded as a
madman.

But to return to music ? singers will never be corrupted by the lunacy
of deliberately using badly mistuned consonances, for they will never be
able to sing them, unless perhaps one could induce some hopelessly
tone-deaf people to become singers. In an age where a composer -
personally he was a charming fellow, I believe - can write a piece
consisting entirely of _silence_, why not a new music exclusively for
the tone-deaf?


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: Melodic Limen or Threshold
PostedDate: 17-12-97 05:20:45
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