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224                    HAND-BOOK OF ACOUSTICS.
dissonances, we find a predominance of the unfavourable positions of the major and minor chords. Thus that expression which modern music endeavours to attain by various discords and an abundant introduction of dominant Sevenths, was obtained in the school of Palestrina by the much more delicate shading of various transpositions of consonant chords. This explains the deep and tender expressiveness of the harmony of these compositions, which sound like the songs of angels with hearts affected but undarkened by human grief in their heavenly joy. Of course such pieces of music require fine ears both in singer and hearer, to let the delicate gradation of expression receive its due, now that modern music has accustomed us to modes of expression so much more violent and drastic."
"The great majority of Major Tetrads in Palestrina's ' Stabat Mater' are in the positions 1, 10, 8, 5, 3, 2, 4, 9, and of minor tetrads in the positions 9, 2, 4, 3, 5, 1. For the major chords one might almost think that some theoretical rule led him to avoid the bad intervals of the Minor Tenth and the Thirteenth. But this rule would have been entirely useless for minor chords. Since the existence of combinational tones was not then known, we can only conclude that his fine ear led him to this practice, and that the judgment of his ear exactly agreed with the rules deduced from our theory.
" These authorities may serve to lead musicians to allow the correctness of my arrangement of consonant chords in the order of their harmoniousness. But anyone can convince himself of their correctness on any justly intoned instrument. The present system of tempered intonation certainly obliterates somewhat of the more delicate distinctions, without, however, entirely destroying them."
Triads in their closest distribution.
Major Triads are smoother or more harmonious than Minor Triads, because their differential tones form part of the chord, which is not the case with the Minor Triads.
A triad is not equally smooth in its three positions ; arranged in the order of their smoothness, we have for Major Triads,
1st (c) position or 2nd inversion, as: Dc, Sc, Fc.
2nd (a)          ,, normal triad, ,, Da, Sa, Fa.
3rd (6)          1st inversion, ,, Db, Sb, Fb.