re: Cents, etc.

There is a 60s era article by A. G. Pikler in the Journal of the Acoustic Society of America on this topic.

Logarithmic Frequency Systems <http://link.aip.org/link/jasman/v39/i6/p1102/s1>

A. G. Pikler

J. Acoust. Soc. Am.*39*, 1102 (1966)

The late composer Paul Beaver suggested 'Harmos," the cycle of 1728 in duodecimal notation. This is
a division of the semitone into 144 parts 12^2), the whole octave into 12^3.

There are also linear (Subharmonic series) power of 2 divisions of the octave into 512, 1024, 2048, 4096 parts and implemented on some synths, IIRC.

I have a paper in Xenharmonikon 15 entitled "Cents and Non-Cents: Logarithmic Measures of Musical Interval Magnitude,
pp 81-96, 1993. I propose the powers of two octave divisions in octal and hexadecimal notation, decimal harmos, and some base 20 divisions in both base-20 and decimal notation (no, I didn't use Maya-Aztec numerals, though one could).

--john