88CET #12: Experimental Chord-Finding

Probably the easiest and most productive, but least predictable, way to find
new chords in 88CET is simply by experimentation. Most of the really surprising
chords I've located thus far have come from mere experimentation, and really
don't match any of the above formulas, except in fragments.

As in traditional tunings, an easy way to locate potentially interesting
88CET chords is to start with a chord from a known formula and change a few
intervals around. One scenario that often produces interesting results is
turning a perfect fifth within a chord to tritone or a minor sixth. That also
often produces interesting chord variants in traditional tuning, but 88CET has
subtly different-sounding tritones and minor sixths from most traditional
tunings.

When locating 88CET chords from scratch, you often have to work with what I
jokingly refer to as "landmines". This again refers to the problem of avoiding
those false perfect consonances. Consider the task of experimentally choosing a
chord in isolation, without regard to voice-leading with the chords around it.
Before you choose any chord tones, all pitches are available. As soon as you
choose one pitch, that pitch lays down landmines at pitches 13, 14, 22, and 27
88c steps above and below that pitch. If the resultant chord steps on those
pitches, it's dead! So you have to choose pitches other than those. As soon as
you choose another such pitch, it too lays down its own landmines.

One of the most important aspects to bear in mind from this regards
chord-tones thirds apart, and the landmines for the false twelfth and
double-octave, and to a lesser degree the sharp false-octave. With the
landmines for each single tone a fourth and a fifth apart, and those between
notes thirds apart, the choices available for tones in those pitch ranges
dwindle rapidly. This can often lead to widely-spaced chords.


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Dave Hill's legendary tape series Introduction to Nontraditional Harmony,
demonstrates the effects of temperament (12-tone equal-temperament in
particular) similarly. In the case of the major thirds, he lays down a the
root, adds the third, then adds in the P5, and procedes to inversions of that
chord. Throughout that whole time he let's the third slide back and forth
between just and 12-equal pitches. He does similar demonstrations with 6:5
minor and 7:6 subminor thirds.

Last I heard, the the Just Intonation Store sells Dave Hill's lecture demo.


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