“The differences in the notes or the differences in the pitch of the notes are called intervals. We see that there are three kinds of intervals in the octave: 9/8, 10/9, and 16/15, which in whole numbers correspond to 405, 400, and 384. The smallest interval 16/15 occurs between mi and fa and between SI AND DO. These are precisely the places of retardation in the octave. Fragments: Seven

“In this manner twenty notes are obtained, eight of which are fundamental: do, re, mi, fa, sol, la, si, do; and twelve intermediate: two between each of the following two notes: do-re re-mi fa-sol sol-la la-si; and one between each of the following two notes: mi-fa si-do. “But in practice, that is, in music, instead of twelve intermediate semitones only five are taken, that is one semitone between: do-re re-mi fa-sol sol-la la-si. “Between mi and fa and between SI AND DO the semitone is not taken at all. Fragments: Seven

“What precisely does happen at the moment of the retardation of vibrations? A deviation from the original direction takes place. The octave begins in the direction shown by the arrow: “But a deviation takes place between mi and fa; the line begun at do changes its direction and through fa, sol, la, and si it descends at an angle to its original direction, shown by the first three notes. Between SI AND DO the second ‘interval’ occurs — a fresh deviation, a further change of direction. Fragments: Seven

“In an ascending octave the first ‘interval’ comes between mi and fa. If corresponding additional energy enters at this point the octave will develop without hindrance to si, but between SI AND DO it needs a much stronger ‘additional shock’ for its right development than between mi and fa, because the vibrations of the octave at this point are of a considerably higher pitch and to overcome a check in the development of the octave a greater intensity is needed. Fragments: Seven

“We have spoken earlier of the law of octaves, of the fact that every process, no matter upon what scale it takes place, is completely determined in its gradual development by the law of the structure of the seven-tone scale. In connection with this it has been pointed out that every note, every tone, if taken on another scale is again a whole octave. The ‘intervals’ between mi and fa and between SI AND DO which cannot be filled by the intensity of the energy of the process in operation, and which require an outside ‘shock,’ outside help so to speak, connect by this very fact one process with other processes. From this it follows that the law of octaves connects all processes of the universe and, to one who knows the scales of the passage and the laws of the structure of the octave, it presents the possibility of an exact cognition of everything and every phenomenon in its essential nature and of all its interrelations with phenomena and things connected with it. Fragments: Fourteen

“At this point in our reasoning it would be entirely right to raise the question: Why is one of the ‘intervals’ which is designated by the number 3 found in its right place between the notes mi and fa, and the other, which is designated by the number 6, found between sol and la, when its right place is between SI AND DO. Fragments: Fourteen