RE: Paul Hindemith & the harmonic series

Brian wrote,

>since the perfect fifth
>is 1/170 of an octave off from the harmonic-series
>value in 19-tone equal temperament, Yasser
>proscribed the use of that 19-tone interval.

That is not why. Yasser thought the consonant chord in 19-equal had to be
constructed as every other note in a 12-note scale in 22. The perfect fifth
in 19-tone equal is closer to its harmonic series value that the
approximations to the eleventh and thirteenth harmonics in Yasser's hexad.
Since the hexad did not include the twelfth harmonic of the same
fundamental, Yasser concluded that the "perfect fifth" would have to be
treated as a dissonance. Of course this is backwards, but necessary for
Yasser to preserve his numerological patterns. These patterns happen not to
be consistent with each other when the details of Yasser's proposed
"super-ultra-tonality" or 19-out-of-31 system are worked out.



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