There are 42 intervals exclusive of the octave interval with ratio 1:2. There are seven seconds of three magnitudes, so determined in the genesis of notes - two in the ratio of 15:16; two, 9:10; and three, 8:9. There are seven corresponding sevenths - two in the ratio of 8:15; two, 5:9; and three. 9:16. There are seven thirds - one in the ratio of 27:32; three, 5:6; and three, 4:5; and there are seven corresponding sixths - three in the [Scientific Basis and Build of Music, page 109]
It is very interesting to observe how the number seven, which is excluded from the genesis of the system of vibration, comes into view after the genesis is completed, not only in the seven seconds of the melodic scale, but also in the seven of each of the intervals. As there are seven days in the week, though the seventh was only after the genesis of creation was finished, so there are six intervals, but seven of each, as we have seen; and in each 7-fold group three magnitudes determined by the three genetic magnitudes of the seconds. There is much symbolic meaning in all this. Any of the intervals may be used in melody; in harmony also, either in simple or compound chords, they all have the honor of fulfilling a part; and even those, such as seconds and sevenths, which are less honorable in themselves, have great honor in compound chords, such as dominant sevenths and compound tonics, which fulfill exceedingly interesting functions in the society of chords. [Scientific Basis and Build of Music, page 110]
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