Yahoo Tuning Groups Ultimate Backup tuning Size of scale-steps in ETs

FROM: mclaren
TO: New Practical Microtonality List
SUBJECT: Number of tones per octave

Joseph Pehrson asked whether the size of
the individual scale step in an equal division
of the octave might not strike listeners as its
most important musical characteristic. This
suggestion apparently received savage response
from the internet addicts who currently
tyrannize the other tuning list, and who
consequently do not have time to actually
listen to or compose music in any of the tunings
they discuss.
In my hands-on experience composing with
equal temperaments from 5 through 53 and a few
beyond, the answer boils down to "It depends..."
This never satisfies the arrogant incompetent
ignorami on the tuning list, since they want all
musical experience encapsulated in a single neat
equation -- preferably an equation that doesn't
stretch their grade school mathematical abilities.
In the real world, however, the rest of the world's
musical cultures unanimously agree that mathematics
has no connection with music, and whenever you ask
any musician anywhere in the world other than
Europe/North America and India "Why do you use this
tuning?" the answer is *NEVER* "mathematics."
Typically you get answers like "It fits my rasa"
(Bali); "Tradition" (China); "Because a goddess
sang that song at the beginning of the world" (Japan);
"Because my guru taught it to me" (Thailand)...and so
on.
Since the responses of the people who have never
composed in or even heard the tunings they discuss
on the tuning list are contradicted so sharply by
musical reality throughout the non-Western world, we
must look elsewhere than mathematics or the harmonic
series for the answer to Joseph Pehrson's question.
----
In order of importance, the influences on the
listener's perception of an (equal tempered) tuning
are:
[1] The listener's cultural preconceptions. On a
scale of 1 to 10, this rates a 10. Depending on the
culture, tonal combinations which send one audience
into ecstasy impel other non-acculturated listeners
fleeing with their hands over their ears. Music forms
which sounds "natural" and "obvious" to acculturated
listeners strike listeners from outside the culture
as "noise" and "not even music."
[2] The musical style in which the tuning is
used. By employing a sparse polyphonic highly rhythmic
style with percussive timbres, 13/oct can be made to
sound almost entirely like 12 equal. By changing to
a bach chorale style with an organ timbre, 13/oct
can be made to sound like the Tuning From Hell.
[3] The interaction twixt the timbre and the
tuning and the ear/brain system's critical bandwidth.
The critical band, about 280 cents in width, is so
important that it impacts on all the ear's operations--
loudness perception, acoustical roughness, streaming,
just about everything. By changing the timbre of tones
electronically, tonal combination which sound unbearably
rough can be made to sound angelically smooth, and vice
versa.
[4] Whether or not the tuning contains recognizable
perfect fifths. Moran and Pratt showed in 1926 that the
psychophysical range of the p5th runs from about 680 to
720 cents, but in 9/oct it also runs down to 666.666 cents.
Fifths within this range (except for 9/oct and 18/oct as
2 pairs of 9s) will sound musically functional. p5ths
outside that range will not. This has some important
consequences for musical style and hte overall "sound"
of the tuning. For ETs sans recognizable p5ths (6, 8,
11, 13, 16, 18, 23) triads with near-harmonic-series
timbres sound like diminished chords moving by diminished
or agumented intervals -- not a strong recipe for
tonal closure or convincing stable harmonic progressions
that strongly establish a sense of tonality.
[5] The overall range of the ET. Beyond about 29 - 36
tones per octave, successive equal temperaments become
inditistinguishable from one another. That is to say,
if you play a piece composed in 31 equal in the closest
pitches in 34 equal, it's almost impossible to hear any
musical difference. If you do the same for (say) 41 and 43,
it IS impossible to reliably hear a difference.
Thus, Joseph Pehrson is onto something important in
stressing the overall size of the individual scale step
in a tuning. There is a crucial difference twixt tunings
larger than 23/oct -- they ALL boast recognizable p5ths.
Moreover, the "region of blurring" which begins around 31/oct,
renders nearby tunings largely impossible to distinguish
from one another.
These two properties mean that tunings beyond 23/oct
differ drastically from those below 23/oct. There is no
way of mistaking a very small ET from another nearby
one -- 5 and 6 equal sound radically different. Not so
51 and 56 equal, which sound essentially identical in
real music in the real world.
OF the ET tunings from 5 - 23 inclusive, a total of
6 out of that 19 (or about 1/3) have no recognizable
pths. Of the ET tunings from 23 equal to infinity 100%
have recognizable perfect fifths. That's a huge
difference, and it's easily audible even to a novice.
Since these things are easy to hear, it stands to
reason that the internet addicts who tyrannize the
other tuning lists by hurling insults and shouting lies
would be completely unaware of them. Naturally, you must
actually *LISTEN* to music in these tunings to hear
these things -- and that, the internet addicts who
tyrannize the other tuning list have no time for. Instead,
like Paul "All Math, No Music" Erlich and Dave "All
Idle Speculations, No Composition" Keenan, these
characters prefer to "correct" other people's posts
with "corrections" which turn out to be riddled with
errors, and laughably incorrect to boot to anyone who
has actually listened to or composed music in the tunings
concerned.
So the bottom line is that in the extremes, the
individual step has a tremendous influence on the
listener's perception of ETs. Mind you -- at the
*extremes*. As we move from 5/oct to 72/oct, there's
a drastic audible difference that anyone (except the
people who never compose or listen to microtonal
music on the other tuning list) can hear. However,
going from 31 to 32 equal is not taking this question
to extremes, and accordingly there will be little
difference twixt such tunings. Between 5 equal and
72 equal, yes -- between the ultra-small and utlra-large
scale step range, yes...but between, say, 27 and 29
equal, or 14 and 15 equal, no.
As always, it's more complex than you'd expect.
Fortunately for composers and listeners, and to the
eternal humiliation of the amusical numerologists
who tyrannize the other tuning list.
---------
--mclaren

Size of scale-steps in ETs

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