Post: RE: Why ET-x?

>Excuse me if this question sounds a bit ignorant. I expected to find
>discussions mostly of just tuning issues on this list, but there seems to
be
>as much discussion of various ET scales. This puzzles me. We've been
stuck
>with a handful of pitch "islands," to use Brian Eno's term, for a few
hundred
>years now. Finally, technology is giving us keyboards with virtually
>continuous pitch possibilities, allowing us to produce music that is more
>consistent with natural principles (acoustics, psycho-acoustics, etc.).
Why
>continue exploring various equal temperaments? What is the value in it?
>Please understand, I'm not registering a complaint or leveling a criticism;
>I just don't know what the heck's the dang big deal with ETs. Myself, I'm
>glad to be rid of the dern varmints. But I'd be fascinated to see a good
>apology (justification) in favor of them.

>David J. Finnamore

Psycho-acoustics has told us that our ears have limited pitch resolution,
and that they develop short-term familiarity with a small set of specific
pitches and specific melodic intervals. In my opinion, the greater the
number of consonant harmonies you can make out of a small set of pitches and
melodic intervals, the better. In this regard non-just tunings definitely
win out over JI.

Examples:

1. A 7-note diatonic scale in JI has three melodic intervals and five
consonant triads. In meantone (or 12-, 19-, 31-, 50-tET), it has two melodic
intervals and six consonant triads.

2. Another example eluded to already is tritone substitution. It is useful
to have a half-octave, since it can represent 7:5 in some contexts and its
own inversion, 10:7, in others. Using common tones in a changing context is
an effective way to move to distant harmonies, but in JI, distant harmonies
will have at most one common tone. JI of course has no half-octave.

Another way of saying this is that Just Intonation has no "puns", or notes
taken in two different senses, and typical JI theory does not admit punning.
However, in creating intervals in JI, you will eventually come across some
very complicated ratios that are so close to simple ones that they will
function as consonances rather than dissonances. So the typical JI
small-integersnsonance / large-integersssonance approach falls flat on
its face. In ETs, as long as the ET is _consistent_ within the particular
harmonic limit you are trying to represent, _accurate_ enough to represent
it, and does not have notes too close to each other (34 is just barely OK in
this last respect), the dichotomy between consonance and dissonance is
unambiguous and you have all the benefits of extended harmony enjoyed by JI
of that harmonic limit (I speak of odd-, not prime-number, limits here).

Ultimately I have to agree that a continuous-pitch paradigm is most
desirable. However, individual musical ideas within such a paradigm are
likely to employ simple sets of fixed pitches, and some non-just tuning,
perhaps even an ET, might be the best way to work out harmonizations and
developments of a given idea. Combining all the ideas into a single
composition, however, may require us to demand completely flexible pitch.
Johnny Reinhard's compositions make this case even where simple-limit
harmonic considerations are not often dominant.

Here's my point of view: We have several hundred years of Western music in
12-tET, by, say, 100 great composers. Have the possibilities been exhausted?
Somewhat. Does the existing repertoire have enough diversity to provide a
lifetime of listening enjoyment of the most transcendent and sublime sort?
Many seem to feel that it does. Therefore, even a single new tuning system
should be enough for a composer to do a lifetime of work and, even if the
composer is of the first rank, the composer will not exhaust 1% of the
tuning's resources. Considering the range of expression contained in 12-tET
music, any single microtonal tuning will, by increasing pitch resources,
lead to an unimaginable new universe of moods and sensations. The technical
difficulty of mastering a single new tuning, even a new ET, in the current
educational environment, is plenty to expect of a composer whose main goal
is to express himself/herself in a new way.

David, Let's discuss more if you like this topic as much as I.

-Paul E.

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