Melodic Limen or Threshold

I wish to elaborate yet again on the question of the melodic limen or
threshold. I shall have plenty of new things to say, so no one will be
bored.

When a note of a melody is raised or lowered by as much as 30 cents or
so - not coincidentally about half the melodic limen - the typical
careful listener begins to perceive that note as somehow vaguely
changed, as 'colored' or 'shaded', but the melody itself remains
unchanged.

The exact value depends slightly on whether the particular interval in
question is consonant or dissonant with the tonic, as well as on other
factors, notably the timbre of the instrument. It is well-known that
certain instruments producing a rich array of partials produce a more
clear conception of definite pitch in the minds of listeners than other
instruments of a harsher or more noiselike character.

According to Benade's hypothesis, which common experience certainly
supports, the mind can, even in monody, apparently perceive consonances
more exactly than dissonances.

As we sharp or flat the note by more than 30 cents or so, we begin to
convince an ever larger percentage of listeners that the note has not
merely been 'shaded' or 'colored' but essentially changed, and the
melody itself essentially altered. Those who imagine that audiences can
be taught to be more perceptive to the point of changing markedly the
point at which they consider the melody to be essentially changed,
certainly delude themselves; even peoples who treasure enharmonic melody
above all, such as the Arabs and Indians, never require such superhuman
hypersensitivity of their audiences.

But even were it possible to acquire such godlike powers of
discrimination, we would only reduce music into a different art-form,
with quite a different mission, namely spoken speech.

By the time we have sharped or flatted a given note within a melody by
about 60 cents, we have - under typical musical conditions of confusion,
distraction and excitement - eliminated virtually all doubt in virtually
all listeners that the melody has been changed. To respect these limits
on human aural acuity is to produce music that may be good; to violate
these limits is to ensure that music will be in bad taste.

Not coincidentally perhaps, it so happens that singers cannot be trained
to reliably sing intervals closer than about 60 cents. That, for
example, the Greek theorists chose 56 cents and even slightly closer
intervals to tune instruments
enharmonically, suggests at most that there is sometimes a regrettable
tendency to tune instruments so as to produce slightly narrower
intervals than what singers can comfortably sing. Snobbery is a
universal human trait, and rarely produces anything very admirable.

Note also that there are real limits on a singer's ability to reliably
sing a long sequence even of 1/3 tones. A melody with four or five 1/3
tones in a row, even if it could be sung, which is doubtful, would
probably be apt only for some strange special effect. One of the
delightful paradoxes of the 19-tone equal is that, even though it has a
wider, slightly more readily-sung diatonic semitone than the 12-tone
equal (126.6 cents versus 100 cents) nevertheless the 19 system has a
far wider variety of chromatic modes, because its tuning degree is
narrower (63.3 cents versus 100 cents).

Returning however to my immediate subject: it is easy to confuse our
ears' ability to perceive a minute change in pitch of a given note
sounded successively, with our far less accurate ability to perceive a
note's having been changed in pitch _in a given melody_, where we have
nothing to compare that note to, except the tonic and the other notes of
the melody.

I wish to emphasize that the melodic limen seems to be affected but very
little by cultural environment. The modern Arabs are a good example.
Under both native pythagorean and heavy Western influence, the modern
Arab theorists have adopted 24-tone equal temperament to describe their
native melody. (They have also copied the 53-tone equal from the West,
which from their point of view at least gives an approximation to the
1/3 tone.)

The typical Westerner finds 24-tone equal less notionally threatening to
his theoretico-musical worldview than 19-tone equal or some other
system, and the Arabs have been greatly influenced by the modern West,
even in such intimate matters as sexual mores and the like.
Nevertheless, beginning as long ago as Villoteau (1809), whenever Arab
singers are studied, the evidence is quite impressive that they use, in
enharmonic melody, a range of close intervals much better described by a
1/3 tone than by a 1/4 tone. Various Westerners, beginning with Ellis (a
person not known for a particularly open mind), have attacked these
results in all sorts of ingenious ways.

But the fact is that singers of whatever culture find melodic intervals
as close as 50 cents very difficult to sing, and tend to substitute a
somewhat wider interval. This is not a very pleasing subject to the
typical modern Western musician, who usually finds even the idea of a
melodic 1/4 tone, much less a melodic 1/3 tone, alien to his habits of
theoretical thought, and this in spite of the fact that our _own_
popular singers deliberately use 1/3 tones all the time, at least since
the 60's ? but so far as I can discover, do not use 1/4 tones except by
accident.

In short, so strong is the insidious hold of the 12-tone equal on the
modern academic Western musician, that he would rather pretend that the
Arabs use the mythical vocal 1/4 tone, because this seems to be more in
theoretical conformity with the 12-tone equal, than admit that they use
something much closer to the 1/3 tone, which anyone can sing, but which
leads directly outside 12-tone equal to 19-tone equal temperament. There
really do seem to now exist certain Western musicians whose ear-training
at the piano has succeeded so well, alas, that they prefer the 12-tone
equal even to just intervals.

But such are not the musicians that screaming crowds try to tear to
pieces in a frenzy of adulation. It is the rock vocalists, who, at least
incipiently, use the tonality of the 1/3 tone, who enjoy _that_ godlike
destiny, which Haydn, Mozart and Beethoven in their day likewise
enjoyed.

And this is very ironic, you know, because the music of a Haydn even now
might have a far greater popular following than it does have, were it
played not in 12-tone equal, nor yet in what Haydn used to compose at
his keyboard
(a selection from 55-tone equal, it appears) but in the tonality which
the rock vocalists are steadily making ever dearer to the masses - that
of the 19-tone equal. And as it happens, the 19 system is far closer in
harmonic effect to what most of the classical composers used (at least
down to Beethoven), than is the 12 system. Beethoven, by the way, played
in 19-tone equal is a treat indeed.


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From: "Bob Lee"
Subject: 19tet vs. meantone?
PostedDate: 17-12-97 07:23:39
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Bradford Catler played just intonation pedal steel in my cello concerto
Odysseus last May. It (the instrument) had the role of Night and it was
ideal in its application. Certainly, if one hears a different tuning (or
has set the significant places of newer tunings) it should be possible to
achieve it.

Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM


SMTPOriginator: tuning@eartha.mills.edu
From: gbreed@cix.compulink.co.uk (Graham Breed)
Subject: Re: 22-tone exhortations
PostedDate: 17-12-97 20:30:33
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"Bob Lee" wrote:

> I wonder if anyone here would care to speculate on how it would sound. In
> particular, would the harmonies ring as nicely as they do in my current
> (meantone?)temperment? Or should I expect it to sound a little rougher?

Bob,

I don't know how much bother is involved in tuning the pedal steel,
[I'll have a look at your page when I get a chance] but assuming it's
significantly less than a hammered dulcimer, I'd say just tune it up
and play around! That's the best way to learn, IMHO.

I'd strongly encourage you to approach it withOUT any expectations.
My first forays into tuning were so tainted, and it's taken me a bit
of effort to overcome my preconceived biases and just listen to what a
tuning has to offer. Whether you like it, and how much, and for what,
will depend on you and the music you want to make with it. And, don't
stop there!

You may, in fact probably will, find *several* tunings that you like
for different purposes. So, try them! Try a bunch! Try as many
tunings as you can think of, or as are feasable on your instrument,
even if you think they won't work for you. You could be right, but
you may be pleasantly suprised, or discover another path to run down.
You'll never know if you don't listen to them.

It can be a bit difficult, at least it was [and sometimes still is!]
for me, but think of it a Zen-like exercise -- it will eventually lead
to enlightenment. [And I'm the first to admit that "I'm not there yet"
and I've got a lot more tuning to do.]

Always beginning... tune on,

Steve

PS Welcome to the list :-)


SMTPOriginator: tuning@eartha.mills.edu
From: John Chalmers
Subject: Partch Dissertation refs
PostedDate: 17-12-97 21:35:07
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