Thane writes: << The frequency ratio of 3^12 divided by 2^19 = 1.0136... is called the Pythagorean Comma, at least by music people. ... if you up 12 pure fifths from a note then go down 7 octaves, the resulting tone is little bit higher than the one you started out with. ... I don't know how the Shepard thing works but it might be related
I don't believe there is any relation at all between the Pythagorean comma and the Shepard tones phenomenon. The Shepard tones phenomenon occurs simply because if you play a note and simultaneously all audible notes that are an integer number of exact octaves above it, then as you travel (say) up the scale doing the same thing at each note, a listener gets the sense of a rising tone, but after an octave you reach exactly the same set of audible notes played at the start. --Dan