88CET #19: Timbral Considerations

Orchestrational considerations are something of a mixed bag; some traditional
orchestrational notions apply equally well to 88CET, but others are better
rethought a bit. Some need to be rethought for concrete, physical reasons, and
others need to change strictly for aesthetic reasons.

As for the aesthetic reasons, some timbres just aren't all that exciting in
88CET. Classical guitar sounds I have found to be less interesting than
harpsichord for example. That was sad to accept for me, having played classical
guitar for many years. Piano sounds about as good in 88CET as in any tuning.
Even though I've used flute sounds successfully for variety in my 88CET
compositions, there are better instrument sounds to use for 88CET. Clarinets
and brass instruments probably work best of all. Saxophones and bowed strings
generally work fairly well too, although not as spectacularly well as brasses.

There is an amusing footnote to these instrument choices: Some of the
instruments that sound best in 88CET cannot be constructed physically in 88CET
tuning. Notably, winds use the lower-harmonic vibrational modes to extend their
range. That is harmonics like single- and double-octaves and twelfths which lie
outside the 88CET system. It's far more difficult to get a tube to "overblow"
in the seventh- and eleventh-harmonic modes. On the other hand, I've given some
thought to the purely-cylindrical flute's tendency to overblow to a flat octave,
to create an 88CET flute as an instrument that play 13 steps per
quarter-tone-flat-octave.

In the realm of the concrete physical issues are organ timbres. Does adding,
for example, a four-foot flute rank to an eight-foot diapason rank in a
nonoctave tuning produce a richer timbre, or just a false note (the octave) that
doesn't exist in the tuning system? Best I can tell, the answer is more likely
that it'll sound like a false note not in the tuning. With such strong
power-of-two harmonics, you almost invariably create those dreadful false
perfect consonances. Instrument timbres with modest-to-normal levels of
octave-harmonics don't pose any such concerns though.

Of course the case of a timbre's partials creating harmonies not present in
the tuning system is certainly not unique to nonoctave tunings. The seventh and
eleventh harmonics don't fit into the usual 12TET system, and the fifth harmonic
is not represented very accurately. The big difference is that we're creating
false consonances with very basic, and thus frequently louder, harmonics than
before. It is therefore a bigger concern in a non-octave tuning than in an
octave-based tuning, but is a concern in either. This of course doesn't rule
out writing for individual ranks, but the lack of the free-form doubling damages
the organistic quality of the music.

In the vein of less basic physical concerns, certain instruments' overtone
structures seem to lend themselves to certain chords over others, as is the case
in most any tuning. I haven't studied this topic extensively, but I have
noticed an especially strong example of this: The 6:7:10 chord seems more
discordant than the 6:7:9 subminor triad on timbres with weak even harmonics,
whereas the reverse seems to be true on timbres where even harmonics are about
the same strength as odd. I'm sure that there are many other examples of this
sort of phenomenon, and those wishing to investigate it may want to start with
this example.


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As John (C) briefly aluded here, graphical methods can place frets,
toneholes, lengths of bars, or most any other physical dimension to pretty
decent precision.

In the case of 12TET, once you precisely calculate whatever dimensions you're
interested in for the square root (tritone), the square root of that (minor
third), and the product of the two (minor sixth), you've got a 4TET scale. You
can graph those points and "french curve" in the rest of the notes' dimensions
to pretty decent accuracy. Certainly far greater accuracy than the "lipping"
range of a wind instrument.

Fixed pitch instruments like the bells mentioned here would have a little
error here and there, but not a whole lot more than you get from typical
well-temperament schemes. (Now of course the "error" from ET in well
temperament schemes are intentional and desirable, but I'm sure you get my
point.)


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