“Let us again take the ASCENDING OCTAVE, that is, the octave in which the frequency of vibrations increases. Let us suppose that this octave begins with one thousand vibrations a second. Let us designate these thousand vibrations by the note do. Vibrations are growing, that is, their frequency is increasing. At the point where they reach two thousand vibrations a second there will be a second do, that is, the do of the next octave. “The period between one do and the next, that is, an octave, is divided into seven unequal parts because the frequency of vibrations does not increase uniformly. 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

“In a descending octave, on the other hand, the greatest ‘interval’ occurs at the very beginning of the octave, immediately after the first do and the material for filling it is very often found either in do itself or in the lateral vibrations evoked by do. For this reason a descending octave develops much more easily than an ASCENDING OCTAVE and in passing beyond si it reaches fa without hindrance; here an ‘additional shock’ is necessary, though considerably less strong than the first ‘shock’ between do and si. Fragments: Seven

“As it is known from the law of octaves mi cannot pass independently into fa in an ASCENDING OCTAVE; an ‘additional shock’ is necessary. If an ‘additional shock’ is not received the substance mi 192 cannot by itself pass into the full note fa. Fragments: Nine