Reply to Xavier on Ave Verum analysis

Hi Xavier -- your analysis is interesting but appears a bit divorced from
reality in at least one respect. Rather that abruptly shifting by a comma at
a particular point in the score, in order to cancel the comma "pump", most
of us seem to agree that a fine ensemble will "hide" the comma through
gradual compromises and thereby avoid drift. Your approach assumes that all
melodic, as well as harmonic, intervals are simple-integer ratios; while
most harmonies are indeed amenable to this approach, melodies are involved
in motivic considerations and achieving a rough degree of intervallic
consistency between motivic statements can be a stronger consideration than
fixing all minor triads to 16:19:24, all dominant sevenths to 4:5:6:7
(personally I would only use 4:5:6:7 for a "tonic" (eg Mixolydian) seventh),
or even all major triads to 4:5:6. Both of these issues, especially the
former, speak against a strict JI approach like the one you're taking,
certainly for composers such as Mozart. By the way, what do you think
happens when major and minor triads link together, as in a minor seventh
chord or major seventh chord?