31/21

I really like ascending into these Harmonic depths. First of all Paul, I
won't dispute your quip concerning Carl's ear, but it's quite a journey from
31/21 to 300000000000001/200000000000001 even though the ear cannot come
along. I seem to remember a cartoon "Scientists Probing Blind with
Instruments" from Utopia or Oblivion by Buckminster Fuller. The Harmonic
usage is very important. If we are only concerned about aural feedback then
Paul is definitely correct in his perceptions, but if we are dealing in the
nature of the surrounding Harmonic territory and exact measurements then
Carl's argument for consonance definitely wins the day. The beauty of
Harmonics, of which Tuning is a branch, prescribes collections of interval
relationships in a variety of disciplines. Paul, if I am leading to the
absurdities you mentioned I guess it's intentional.

Infinity/1 . . . 0/0 . . . 1/Infinity

Lambdoma Matrix

Monochord


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