An Archaeological Dig into the Mathematical Foundations of Western Music

I owe this link to B.K. This is not an account of a physical "dig" but of a mathematical exploration. One indication of its scope can be found in one of its subtitles: "The Seventeen Tones of Western Music - Really!" (Or eighteen, to complete the octave as derived in a particular way, as therein sharps are not the same as flats. This is the basis in fact of much of present Middle Eastern modality, including Jewish modality in the ancient Middle Eastern coummunities.)

One reason why I doubt Mr. Benton's conclusions as to the basis of Western music is that while the biblical modes in Suzanne Haik-Vantoura's chant vary all the tones save the stable E and B in one mode or another, one need not go beyond the just-tuned 12-tone (or 13-tone) scale to account for all the accidentals involved... at least not so far as I have yet perceived in actual test. It would be impractical to try an 18-tone vocal scale given the limited ranges of the instruments (ten or twelve strings, according to Josephus) that supported that chant.

- John Wheeler (יוחנן רכב)