ET vs JI

Carl Lumma wrote:

> I've always viewed these "commas" as making modulation
> more interesting. But many disagree. Partch's chapter in
> Genesis of a Music is really great about this point (the one
> with the letter from Fox-Strangeways). Boy that chapter
> is really a thrill!

> Basically, what I got from this chapter is that modulation is
> best defined simply as switching the 1/1, and that common
> tones, while playing, of all things, perhaps the most important
> role in the use of modulation, are not necessary in its definition
> or execution. And perhaps, that a theory of modulation may
> be constructed where tones separated by a comma can still be
> considered "common"!

I've written about this same passage in my book. Partch describes
three ways of modulating, assuming two chords which possess
a "common tone":

1) Making the "common tone" consonant with the first chord and
dissonant with the second.

2) Making the "common tone" dissonant with the first chord and
consonant with the second.

3) Making the "common tone" actually two different tones which
are close by in frequency (differing by said "comma") and
which are each consonant with their respective chords.

His conclusion, with which I agree, is that all three methods can
be used to effect a modulation in just-intonation, giving a richness
and subtlety of expression which is _utterly non-existent_ when
utilizing the 12-Eq scale to present the same musical passage.

I have some interesting observations of my own in this regard,
involving not full-fledged modulation, but rather short-term
tonicization:

1) I have tried sequencing Mozart's 40th Symphony in several
different versions, using ratios that were 5-limit, 7-Limit and
19-Limit. 5-Limit sounded best, 7- and 19- were both OK, but
when tonicization was effected by a common-tone related by
7, it didn't sound right. It sounded to me like the tonality veered
off into a weird key that was microtonally "off". This argued
against the applicability of 7 in Mozart's music.

2) In my own "Incidental music to 'Invisible Haircut'", I use
tonicizations
which have 19 as a factor in the common-tone. This piece has
a jazz/ blues flavor, and I find that the 19-limit tonicizations work
well (they certainly provide a richness that the bland 12-Eq version
lacks completely). This may, however, be because 19/16 is so
close to the 12-equal "minor 3rd" that the _interval of modulation_
is not so strange to my ears. I'll grant that it's possible that, had
I
used it in the tonicization, 7 may have sounded just as strange in
this piece as in Mozart.

3) I sequenced some of Satie's "Sarabande No. 1" in just-intonation,
and found that tonicizations involving 7 sounded "off" here too,
tending to corroborate what I said in #2.

My original point was that no matter how well any equal temperament
represents whatever ratios, there's no substitute for the richness
and subtlety of expression which is possible when using ratios
themselves. Numbers can be compared in all sorts of different
patterns and combinations, and when these numbers represent
_easy-to-hear_ musical relationships, the variety of musical
relationships is correspondingly expansive. I'll grant that equal
temperaments are easy to hear in melodic terms, but, aside from
the ratios they imply well or badly, they don't have much
significance from a _harmonic_ standpoint.

Part of the problem I have with 12-Eq serial music is that I just
can't hear many of the supposed relationships in the music that
have been pointed out by theorists. I will admit the possibility that
things that are happening in music that are numerically related
but are not consciously audible may still have some kind of effect
on our nervous system, but at our present state of theoretical
knowledge, I think it's best if we deal in terms of what can
demonstrably be _heard_.

I think a large part of the reason Schoenberg stuck with the
12-Eq scale was because he realized intuitively that within the
vastly expanded resources of his implied 13-Limit, were he to
work in just-intonation, the number-play involved could quickly
become a bottomless pit from which his musical inspiration would
never again emerge into the light of day. Then again, I also
think he wanted to make use of the ambiguities made possible
by a comparison of so many close ratios on the one hand and
their nearby 12-Eq equivalents on the other.

My whole idea of primes having distinct qualities is useful
compositionally when, for example, using a precisely-tuned
81/64 "Pythagorean major 3rd" or 9/7 "septimal major 3rd"
instead of the usual 5/4 "just major 3rd", or when sliding
around between them, as good blues singers do, to create
a specific effect that 5/4 just doesn't give.

I refuse to accept an equal-temperament because it makes
modulation "easy" or (excuse me while I laugh) "possible".
Part of the reason JI composers use JI is because, within
a restricted JI scale, modulation to a new key brings a
whole new set of intervallic relationships into play, giving
each key its own distinct "flavor", far more pronounced
in their differences than anything a well-temperament can
do.

The only reasons I can see for accepting any equal-temperament
is that it is easier to play on most instruments, and, as I stated
in another post to this issue, the study of the interplay between
JI and ET in the same piece is becoming more and more interesting
to me.

Joseph L. Monzo
monz@juno.com


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