as the savage state. The savage is the sunken state of man, consequent on falling away from God by distrust and disobedience, and the loss of paradisial converse with Him. We may presume that music in the beginning, when the first human pair sang out with unbroken voices the joy of their hearts, was in the scale to which mankind, risen and restored by God's mercy, have returned. Our last days are thus become like the first again; and the lost dominion of Nature has returned, in the Incarnate One, into the hands of mankind. [Scientific Basis and Build of Music, page 79]
In compound chords there are no new notes created; they are found by combining the notes of the simple chords. The dominant sevenths, major and minor, are compounded by adding one from the subdominant.
All the inverse and reciprocal orders in music, whether of notes or chords, are produced by the law of Duality, and this gives them inevitably their symmetrical form.
The simple natural scale is the fifth; the compound natural scale is the octave; the harmony scale, or chord-scale, is the three fifths; the great genetic scale is six octaves; for, like the six creation days, it takes the six octaves to give birth to the elements of which the wondrous structure of our music is built up; the birthplace of B, the seventh of the octave scale, is the sixth octave of the great genetic scale. The area of the twelve major and twelve minor scales is twelve fifths or seven octaves, the twelfth fifth being a comma and the apotome minor in advance of the seventh octave. This is a quantity so small that it can be ignored in real music; and the two notes, say E# and F, joined to close the circle of this horizon of our music world. E# is the top of the twelfth fifth, and F is the top of the seventh octave; and they are practically, though not exactly mathematically, the samenote. Illustrations of this will be found among the plates of this work. [Scientific Basis and Build of Music, page 79]
The simplest condition of quantities and motions is in a string where half the length is double the vibrations. Next in the order of simplicity is a
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