> In algebraic terms, choose a neutral n between m and M. The total pitch > system will be i m + j M + k n, where i, j, k are integers. But the staff > system only has the pitches i' m + j' M. When taking the difference with the > staff note, reducing the degree to 0, and taking away the sharps/flat (a > multiple of M - m), there will result a multiple n - m or n - M.
a minor point: wouldn't it be clearer to use d (degree) and a (alteration) instead of M and m? d should be a second, i.e. M (or m), while a should be the augmented prime, i.e. M - m. then multiples of d gives the staff system (very roughly equivalent to the diatonic scale), linear combinations of d and a would give the usual chromatic system (all notes that can be notated with sharps and flats), and for microtonal and exotic music one should use (one or several) n. anyway, I'm a big fan of using such a system: I've tried Pythagorean and meantone MIDI-output by defining alterations, and MIDI was all right, but the score had all the naturals which weren't defined to be exactly zero (i.e. all except a); your system distinguishes nicely between pitch systems and tuning (thoretical pitch and its physical frequency). Pál _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org http://lists.gnu.org/mailman/listinfo/lilypond-devel
