consistency

Though I'm really just starting to take a look at it, I seem to be
finding consistency a rather slippery concept to lineup with some
pretty general ways of going about things... for example: In something
as common as the standard JI major scale (1/1, 9/8, 5/4, 4/3, 3/2,
5/3, 15/8, 2/1), 26e, which is consistent through the 13-limit, would
seem to be inconsistent not only because of the 15/8, but also because
of the inconsistent (i.e. not the best ((LOG(N)-LOG(D))*(n/LOG(2))
approximation if N/D=32/27 and n=26) 7/26 32/27 between the 4/3 and
the 9/8... while on the other hand you have say the Pythagorean 1/1,
9/8, 81/64, 4/3, 3/2, 27/16, 243/128, 2/1, which would seem to be
entirely consistent in 5e despite the fact that 81/64 and 4/3 are both
approximated by 2/5, and that 243/128 and 2/1 are both approximated by
5/5... So I guess some of the things I'm wondering are these: Is
consistency more of a theoretically useful concept, or is it a really
musically detectable (or useful) phenomena... to what sorts of degrees
does the ear/brain ensemble of the conditioned and the innate tolerate
extrapolations of the 5e example, or take exception to (or notice)
extrapolations of the 26e example?

Dan

In a message dated 10/27/99 12:14:51 AM, stearns@capecod.net wrote:

<<So I guess some of the things I'm wondering are these: Is

consistency more of a theoretically useful concept, or is it a really

musically detectable (or useful) phenomena... to what sorts of degrees

does the ear/brain ensemble of the conditioned and the innate tolerate

extrapolations of the 5e example, or take exception to (or notice)

extrapolations of the 26e example?>>

Yes, interesting question.

I personally find scales with
wildly un-equal intervals (i.e. Thai scales, Balinese 'Pelog'
tunings) quite "noticable"... "spicey."

Wendy Carlos used a 15 TET scale on her "Tales of Heaven
& Hell" CD and has this to say: "... one of the most fascinating
and exotic scales around. It's also a thorny tuning to sing and
play in."

I like scales/tunings that "stand out"... that have "a life of
their own"... I am not the least afraid of a little "jarring effect"
in my music (ask John Chalmers). Maybe cuz I come to this from
a self-taught percussionist's background (I've played a lotta
odd found objects & created lotsa "sound-makers")... & cuz I have
done some of "circuit-bending" of thriftstore electronic toys (gonna
be soon doing some serious microtonally-scaled digital sampling).

zHANg

>Though I'm really just starting to take a look at it, I seem to be
>finding consistency a rather slippery concept to lineup with some
>pretty general ways of going about things... for example: In something
>as common as the standard JI major scale (1/1, 9/8, 5/4, 4/3, 3/2,
>5/3, 15/8, 2/1), 26e, which is consistent through the 13-limit, would
>seem to be inconsistent not only because of the 15/8, but also because
>of the inconsistent (i.e. not the best ((LOG(N)-LOG(D))*(n/LOG(2))
>approximation if N/D=32/27 and n=26) 7/26 32/27 between the 4/3 and
>the 9/8...

Dan -- I think you're misunderstanding the point of consistency. Consistency
does not apply to scales within an ET, it applies to consonant harmonies
within an ET. Intervals like 15/8 and 32/27 are not consonances within the
13-limit, let alone the 5-limit, so the quality of their approximation is
irrelevant. If you'd like to use 15/8 as a consonance, you're at the
15-limit at least, so 26-equal is inconsistent. Moreover, the 32/27 in the
"standard JI major scale" is more a defect than something you'd like to
accurately approximate.

Consistency is really intended as a check against the kind of errors Wendy
Carlos and Yunik and Swift made -- evaluating how well JI intervals are
approximated without bothering to check whether those approximations "fit"
with one another. Yunik and Swift liked 19-equal's approximations of
13-limit intervals, but those approximations are incompatible!