Re: CHAT: various infotaining natlang tidbits

Lars wrote:
>Are there actually intonation systems out there where you don't have
>any pitches in a 2:1 ratio at all? All the systems that I have seen
>described repeated themselves after an octave, but that may be an
>artifact of the descriptions --- and of course I haven't seen all
>systems.>
I haven't seen them all either, but I'd be willing to guess-- it would be a
pretty odd system that couldn't repeat itself at a higher or lower range!
When looking into alternative tunings last summer, I learned that pentatonic
scales were supposedly originally derived from a series of three ascending
fifth intervals (basically the black keys on the piano):  C#-G#, D#-A#,
F#-(C#, octave).  Like octave 2:1, the fifth is also easy to discover, 3:2.
(For reasons I forget, even in early Western music, the third, fourth and
sixth were often avoided.)