Donald Francis Tovey

Tovey, Donald Francis, The Forms of Music, Meridian Books, The World Publishing Company, Cleveland and New York, 1967

HARMONY

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]