Liminatory Fulminations

In response to my statement that the melodic limen of music is 55-60
cents, and that universally for the human species in general (not for
aliens of course) several persons have, with varying degrees of impotent
outrage, asserted that people - or at least the musical elite - can be
trained to make essential melodic distinctions as fine as 10-20 cents.

I do not believe this for a moment. Were this so, then even the simplest
of our melodies would disintegrate into unrecognizable, essentially
different melodies every time a different singer rendered them. This
does happen if the singers are extremely unskilful, or simply bored with
the old melody, but never as a matter of course. For even skilled
singers occasionally stray from whatever tuning be taken as standard, by
at least a comma. Note in passing that this means the melodic limen -
the zone within which intervals retain a unique melodic character -
would be more than double a comma, for if a singer strays by so much as
half the melodic limen, he enters the melodic orbit, as it were, of the
adjacent degree of the temperament being used.

But let us grant, for the sake of argument, that we _could_ train
singers to reliably and continually make such hyperfine distinctions as
10-20-30-40 cents ? far beyond anything known to the Arabs or Indians
(known in practice not in theory) ? what would be the result?

Well, singers that actually do make such distinctions - though quite at
random - are not uncommon. In Western musical cultures they are said to
be 'tone-deaf', 'incapable of carrying a tune' etc. A rock or opera
singer so afflicted would be booed and hissed off stage within about 30
seconds.

It occurs to me that there might seem to be a logical inconsistency
between saying that listeners do not perceive a melody to be changed
until at least one of its notes has been changed by at least 55-60
cents, and then observing that listeners notice even smaller variations
and dislike them. But in fact there is no inconsistency; the human mind
seems to desire that melody consist of definite pitch classes, about
which there should be no doubt. If more than a very few notes of a
melody betray these expectations by threatening to careen into the
adjacent pitch class, the effect is heard as a mistuned interval. There
is an immense difference between hearing a variation in pitch, and
hearing a variation in pitch class and therefore in melody.

I do not wish to refer here to what non-Western musical cultures label
as 'non-music' or 'without tune' for despite my acquaintance with
certain of these cultures I certainly do not consider myself qualified
to pass judgement thereon, and I doubt if any Westerner is. But within
the Western musical culture, which no less in popular than in academic
music, is the dominant musical force of our time, the performer trained
to deliberately and continually make such 10-20-30-40 cent distinctions
- if this is possible, which I do not believe - would be hilariously
laughed at by the people. I doubt if even the cowed audiences of our
concert halls would refrain from giggling.

Perhaps some would be delighted to have another reason to consider the
populace morons, and themselves, great artists (unappreciated of
course.) But a musical culture which deliberately courts popular disdain
in so very aggressive a manner as deliberately singing like the
tone-deaf is... how to put it politely? gravely aberrant.

A more philosophical person might inquire: _why_ does the West, at
least, classify some people as 'unable to carry a tune'? Because in the
West at least - and this includes rock music no less than older music -
listeners expect most notes at any rate to possess a definite, memorable
pitch. Music in all the major musical cultures definitely consists of
more-or-less fixed pitches, not of pitches free to wander with the same
kind of freedom and endless pitch variety we associate with the spoken
voice - though even there there is no absolute freedom.

I do not wish to be dogmatic here; there seem to be elements of this
free variation of pitch in some of the 'ornaments' of Indian music, for
example. But even the most ornamented Indian melody stands worlds apart
from the free pitch variation of the spoken voice. But this free pitch
variation in music is what is implied by the assertion that 10-20-30-40
cent intervals can be melodically significant.

Without falling into such absurdities, it is possible to argue that the
melodic limen of 55-60 cents is incorrect, and the true limen is
(slightly) narrower (or wider.) In the literature one can find values
from the mid forties all the way up to nearly an equal semitone (the
latter group rather untrustworthy) depending partly on the pitch at
which the measurements are taken. It is possible that a people trained
from childhood to focus most of their musical attention on enharmonic
melody alone might score a few cents lower than a people accustomed to
pentatonic melody, say. It would be very impractical for music to set
the melodic limen so low that any very large part of a typical audience
could not readily identify melodic changes. In this respect the true
debate is not between the advocates of 19-tone equal and those of some
system with a larger number of degrees, but between the advocates of 19-
versus those of 12-tone equal. I am convinced that the melodic limen is
narrow enough so that the ~63 cent tuning degree of 19-tone equal does
always, save perhaps in the very low register (well outside the vocal
range), effect a change in melody when a given note of a melody is
flatted or sharped by this interval.

But to argue that the melodic limen is so narrow as virtually not to
exist, involves us in the severe logical and esthetic difficulties I
have referred to.

For all these reasons we can state categorically that the melodic limen
exists, and is not more than marginally susceptible of adjustment
downwards by training or special attainment.

More than casually related to the question of the melodic limen is the
determination of how many distinct pitches (or pitch classes) human
subjects can remember in a given melody. This number is finite, and
almost certainly lies between 5 and 9, apparently influenced by the
musical culture. The weight of the evidence favors a value of 7 or 8. I
trust I need not dig out the references to this experiment from my files
- it is a locus classicus. The human mind possesses marvelous powers of
discrimination, but the musician who continually demands that listeners
stretch their discriminatory powers beyond what is pleasurable (or
possible) for them will pay for his folly.

The best possible thing for a creative artist, you know, is to be hissed
at a few times. This concentrates the mind wonderfully, and purges the
understanding of many silly notions. Our poor rock musicians,
disrespected and for the most part ignored, have all had this privilege
of being called inventive names in public, which is one reason why they
are so very creative, and beloved by the common folk. They may suffer
personally because of this, but their art is basically sane and mature
(or as mature as it can be without the benefit of any coherent body of
theory or intonation to guide them.) Academic musicians on the other
hand live in a kind of cocoon, which they often try to break out of by
deliberately adopting the most esthetically bankrupt musical principles
they can find.

Both kinds of musician like to be thought daring and iconoclastic. But
the daring of a rock vocalist who shimmies his hips while occasionally
throwing in a 1/3 tone, all the while watching to see if the audience
likes him, and if he's going to eat that night... and the daring of the
safely tenured academic who demands that some singer screech like a cat
for a bunch of bored, vaguely offended symphony-goers, really have
nothing in common at all.

I have deliberately exaggerated to make a point. Academic musicians
possess advantages that popular musicians can never hope to have. But
the greatest advantage of all is an audience that worships your every
note. And this is denied to those who imagine themselves musical gods,
and ordinary people beneath notice.

How is all this relevant to tuning questions? The system of intonation
is one of the two or three most basic elements of music. It is not
chosen by people seeking to puzzle or shock, or even by lonely souls
experimenting with new systems in a vacuum. It is chosen by the culture
itself because creative musicians, in intimate contact with the people,
want and need that system of intonation. I am convinced our people need
the 19-tone equal temperament in order to express on instruments (and
hence more consciously and richly) what they are already expressing in
their songs. As a side-benefit, this temperament also gives us back our
own musical past, which 12-tone equal has grossly distorted and
ossified.


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: A Parlor Trick
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