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A challenge to create "x/16" harmonic series tunings and scales

🔗djtrancendance <djtrancendance@...>

2/2/2009 8:00:05 PM

One thing that is obvious, is that the latest version of my tuning
uses x/16 formatted values of the harmonic series (17/16,18/16,etc.)

And...12TET itself can be estimated fairly well by x/16 formatted
fractions as I showed in my "proof of 12TET" example.

The point is not to say my scale is "great", but that it seems to
reveal how x/16 format fractions can work pretty well even as opposed
to other JI harmonic series fractional formats such as x/15.
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My tuning allows 9-note scales that sound fairly consonant (at
least to my ears).
So here is a (hopefully quite productive) challenge :-)

Make
A) A tuning composed of x/16 format notes
B) A 9-note scale within that tuning (meaning, 9-notes 2/1 PER OCTAVE)
that can be transposed (IE moved up 1 note and still sound in key NOT
limited by the overly technical definition of transpose which involves
maintaining exactly the same intervals that applies to TET tuning)
within said above tuning.

And, of course, post it to this thread (preferably in fractional
format). :-)
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I figure at least someone here will be able to take what I have
learned to create something better than my scale...maybe even good
enough to be widely adopted. Hopefully this challenge will yield
something beautiful...