Re:PHI

William Lyman Young self-published a thin oversize booklet entitled
"Report to the Swedish Royal Academy of Music on the Discovery of Two
Classcal Scales and their Natural Keyboards" in 1961. I saw a copy in
the Stanford University Music Library back when. In it he mentions
scales of 10 and 14 tones generated by cycles of "sectional" sixths
which are intervals of 833 cents in 36-tet (25 degrees).

His new scales are scales of 10 and 14 tones in 24-tet. Essentially,
they are tandem copies of the pentatonic and diatonic scales in 12,
compressed by 1/2 and concatenated (2323223232 and 22122212212221). They
are not MOS and are not very successful scales. As I recall, he claimed
they were generated by the half-fifth. Young designed a 24-tone
keyboard for them also.

Young also dabbled in tetrachords and came up with a 13-limit diatonic
genus 12/11 x 13/12 x 44/39, his "exquisite 3/4 tone Hellenic Lyre."

--John