Donald Francis Tovey
Tovey, Donald Francis, The Forms of Music, Meridian Books, The World Publishing Company, Cleveland and New York, 1967
VII. TEMPERAMENT AND JUST INTONATION
Even in pure sixteenth-century polyphony the ideal diatonic scale implies distinctions of intonation beyond the capacity of any mechanical instrument with a limited number of notes. In the Ionian mode or major scale of C the interval C-D is not the same kind of whole tone as the interval D-E, but differs as 8:9 from 9:10.
The normal position for the supertonic is a 'major tone' (8:9) above the tonic; but even so common a discord as the dominant seventh will set up a conflict, the dominant requiring its fifth to be as 9:8 above the tonic, while the seventh will want to make a true minor third from a supertonic in the position of 10:9. Such conflicts are about very minute distinctions, but every discord produces them if it is dwelt upon. . . . .[p64]
. . . Bach decided that it was better to have all keys equally out of tune than to have some keys intolerable. . . . . [p65]
XI. THEORETIC POSSIBILITIES OF THE FUTURE
Harmony has not yet found a place for so simple a natural phenomenon as the seventh note of the harmonic series. . . no fewer than three (besides the octave of No. 7) are outside our system, Nos. 7 and 13 being much flatter than the notes here written, and No. 11 much sharper. . . .
Schönberg rightly says that der Einfall, the inspiration that comes without theorizing, is the sole criterion of musical truth; and perhaps some composers may have Einfälle so convincing in their use of Nos. 7, 11, and 13 as to compel us to build new instruments for them. . . . The string quartets of Haba have not as yet made quarter-tones sound convincingly unlike faulty intonation. We must not blame our ears, which often appreciate much smaller measurements. The just intonation of a Wagner opera would comprise some thousand notes to the octave. The question is not how many notes we use in the long run, but how small a direct measurement is of interest to us. . . .[p70-71]
December 4, 2003