Ramsay
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]
subdominant also moves by semitonic progression to the middle of the dominant, and so, like the simple chords, they are brought into continuity. When the subdominant follows the dominant, the top of the dominant is lent to the root of the subdominant, and they come to have also a note in common; and the middle of the dominant moves by semitonic progression to the top of the subdominant; and thus resolving continuity is established between them. [Scientific Basis and Build of Music, page 112]
With perfect duality of response does resolution of chords go on in the minors. When the tonic chord follows the subdominant one, they have for their note in common A, i.e., in the key of A; and the middle of the subdominant moves by semitonic progression to the top of the tonic. When the tonic chord follows the dominant one, the top of the tonic and the root of dominant E is a note in common, and the top of the dominant goes by semitonic progression to the middle of the tonic. These simple chords are thus linked together exactly with the same degree of continuity as the simple chords of the major. When the tonic chord follows the compound subdominant, this compound chord, like the compound dominant in the major, has two semitonic progressions - one to the top and one to the middle of the tonic - and they have one note in common. When the compound dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus a note in common is created, and the middle of the subdominant moves by semitonic progression to the root of the dominant. When the compound subdominant follows the dominant, the top is lent to the root of the subdominant, creating a note in common between them, and the root of the dominant goes to the middle of the subdominant in semitonic progression. This is the way of Nature. The unbroken continuity of her ways is perfectly illustrated in the linked sweetness and kinship of chords in a key; or when one key passes by modulation to another key; and that through all the chords and all the keys. We shall see wondrously more of this when we come to the study and contemplation of the Chromatic System of Chords. [Scientific Basis and Build of Music, page 112]
See Also