Similarity of scales.

We've seen a number of debates on whether 19-tET, or 22-tET, or whatever
is "like" the old familiar 12-tET. I think in part it comes down to what
you're looking at. I think that it would be improper for me to comment
on the general impression of what a piece in some unusual scale sounds
like, as I've never heard any full piece played in any temperaments other
than 12 or 7 (At least, I _assume_ the background music I hear in some Thai
restaurants is in 7-tET; I've been told that it is Thai traditional music,
and I've read that that is in 7-tET. But I haven't done a frequency scan
to make sure they weren't using Western instruments tuned to 12.)

But I've played scales generated on computers. And to my ear, Blackwood's
comment that a diatonic scale will sound "recognizable" if it follows the
standard pattern of 2 large intervals, one small, three large, and one small
seems correct. Now the only tempered scales that permit this are those
with 5x + 2y tones, with x > y > 0. This means 12, 17, 19, 22, 24, 26, ...
and certainly both 19 and 22 qualify. And in fact, if I play a 19-tET scale,
with "whole steps" of 158 moc (I'm using moc consistently; if you need to
convert to cents to visualize, multiply by 1.2) and "half steps" of 105 moc
for my intervals, it sounds to my ear so much like a standard major scale
that I'd never spot the difference unless I heard them played together.
The fact that the "half step" is MUCH more than half the "whole step" is
not obvious to my ears. (In fact, in the most common sort of JI scale, the
"half steps" are 93 moc and the "whole steps" are a mixture of 152 and 170
moc. So the fact that the "whole step" is less than double the "half step"
does make it somewhat "JI-like." But the point is that ALL these scales,
12-tET, 5-limit JI, 19-tET, etc., permit the construction of major [and
minor] scales of the same pattern.)

Now having said this, we can note that a 4:5:6 major triad is characterized
by three intervals: 5/4 (322 moc), 6/5 (263 moc), and 3/2 (585 moc). And
these are represented in 12-tET by 333, 250, and 583 moc, while in 19-tET
they are 316, 263, and 579 moc. It is possible that some ears hearing the
CHORD may get a different impression because the two thirds are closer
to JI while the fifth is further from JI. I don't know. I can't program my
computer to play the chords and I don't have a keyboard I can retune.

But I think that melodically, from what I've said, assuming that most tunes
consist of sequences from the diatonic scale up or down for large portions
of their scope, 19, 12, or 22 will sound all about the same. (If you write
a complex piece with much modulation, this may not be so. But a popular
song, for example, played in 19 will not sound unusual to ANYONE's ear unless
they have far better absolute sense of pitch than I have.)

Bruce R. Gilson
email: brg@netcom.com
IRC: EZ-as-pi
WWW: http://www.geocities.com/CapitolHill/3141

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