Re: Ocarena Tuning and "Octave Equivalence" question

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I'm glad you brought that point up. I've been using the ocarina patch in my
just-tuned MIDI chord files, because it appears to be the purest sounding
patch available, not jammed with overtones of its own. Add to that it
doesn't have vibrato, at least not on my card. When I made a MIDI chord of
the first 19 overtones, just tuned, the result sounded like the fundamental
being played on a loud oboe. When I used only the odd overtones, it sounded
like a clarinet.

* * * * *

For those of you who happen to be math geeks: I believe that the concept of
octave equivalence was really meant to be applied to the study of just
intonation "on paper". All it really refers to the concept of being free to
factor 2 in and out as convenient, since the octave can be assumed to be
already "just". I also believe that the matter of inversion in octave
equivalence depends on what you mean by an inversion. In studying just
intonation, I like to think of intervals in terms of the FIRST and the
SECOND note rather than the HIGHER and the LOWER note. If the first note is
a C and the second note is a G, you can call it a "fifth" (factor of 3)
without bothering about whether the G is a fourth below or a fifth above the
C. Values like 3/2, 3/4, or 12/256 can be written simply as 3. However, if
the second note is an F, it is considered a 4th and is a different interval
as far as octave equivance is concerned, since the factor of 3 is now in the
denominator.

Of course, in the actual hearing of music, octave equivalence wouldn't apply
well. One can plainly hear a difference of sound quality between a
well-ringable DGBF dominant 7th chord and an inversion like FGDB, which
sounds weak.

Billy