Thoughts on Brian M's Non-Octave Thoughts

(Gag! This is the third time I've written this message; CompuServe
Information Manager keeps kicking the bit-bucket on me. This message only
though. Weird...)

First of all, let me acknowledge right off that Brian has experience with
more nonoctave tunings than I do. My nonoctave experience is mostly limited to
88CET tuning, although my experience with 88CET is fairly significant.


Regarding coming close to an octave being sufficient to elicit the feeling of
octave equivalence:
I absolutely agree with that, but I'd like to add that it doesn't
necessarily mean that it will sound like a CORRECT octave. Best I've been
able to see, speaking in very overgeneralized approximations, an interval
within about 75 cents of an octave will sound like an octave rather than
having a musical meaning of its own. And if it's more than, say, 10 cents
off from a proper 2:1, it will sound pretty dreadfully out of tune. That
too is a big overgeneralization, and both of those generalizations apply
only to approximately-harmonic timbres.

On a related note, Paul E recently pointed out that neither he nor I have
been able to get a pitch-classing effect from a P12 (3:1). I may have
inadvertently misrepresented my findings there. That is certainly true
when it comes to compounding intervals by a twelfth, meaning that I haven't
been able to find much similarity between, for example, a major third and a
major fourteenth. I have, however, been able to get a sense much like that
of leading-tone resolution to other intervals, including the P5. In doing
that though, I have to avoid the tuning's closest representations of an
octave, because aluding to the octave almost immediately destroys the sense
the P5, or whatever, is the most "basic" interval.


Regarding Enrique Moreno's (or Brian's attribution of Enrique Moreno's) view
that using traditional interval nomenclature for non-octave tunings' pitch
relationships:
I can certainly see value in avoiding them. When I was in the throes of
devising my 88CET notation system, I initially devised an 88CET-specific
interval nomenclature, but later decided that there really wasn't a whole
lot of value to it, and that it was more likely to confuse than enlighten.
But certainly a strong case can be made for avoiding classifying some
intervals in terms of traditional nomenclature. 9:7 is probably in that
category, in that it somewhat stretches the boundary between thirds and
fourths. I find it to be more clearly a third than a fourth, but there are
certainly some contexts where it clearly has a fourth-like sound. One is
the scenario where you let a pickup note rise by a 9:7 into the opening
downbeat in a moderate-to-fast-tempo melody. That is probably a case of
social conditioning: it probably gives that fourth-like sensation (or it
often does for me anyway), because that's a VERY common melodic use for a
P4.

But that brings to mind the first of two caveats to accepting Enrique's
view that traditional nomenclature shouldn't apply to nonoctave tunings.
Is this sort of social conditioning (this sort of sensation is a third,
this sensation is a fifth, etc.) hopeless to try to overcome? It is
certainly deeply engrained.

My other caveat is that this sort of motivation for not applying traditional
interval nomenclature to non-octave tunings' resources is not in any
specific to non-octave tunings. Any tuning that 9:7s (again, as an example)
may benefit from avoiding classifying that interval as a third or a fourth.
If his concern in particular is that you need to come up with a new set of
interval nomenclature based upon the interval and its non-octave duplicates
(e.g., coming up with a name for the sensation of Pierce-Bohlen's 9:7 and
its 3:1-displaced equivalent, then I personally would be skeptical about
the value in that, because I have only managed to get a pitch-classing
effect from other intervals in very limited ways. But then again, that may
be partly due to the fact that, like Carlos' Alpha and Beta tunings, 88CET
doesn't really have a natural interval of repetition (although its 7:4,
3:2, 5:2, and 8:1, in order of decreasing preference, are good candidates).


Regarding Brian's question about how one goes about determining a non-octave
tuning's most consonant interval:
Brian approached the question, appropriately I'd say, in terms of what
intervals work for doubling. In that regard, I have found that intervals
that work for doubling are heavily dependent upon the intervals in the
original chord. In particular, most any interval that is "bland" compared
to the other intervals in the chord seems to work fairly well for doubling.
Even intervals as flavorful as a 5:2 seem to produce a quite satisfactory
doubling effect for chords whose harmonies are comparatively complex, like
7:6s or 11:9s for example.


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