"You must learn to think one octave higher. Only then will you learn how implosion energy works."

If...[Alban] Berg departs so radically from tradition, through his substitution of a symmetrical partitioning of the octave for the asymmetrical partionings of the major/minor system, he departs just as radically from the twelvetone tradition that is represented in the music of Schoenberg and Webern, for whom the twelvetone series was always an integral structure that could be transposed only as a unit, and for whom twelvetone music always implied a constant and equivalent circulation of the totality of pitch classes.
george perleIn accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.
vitruviusOur music has sprung from the patient, incessant, and progressive penetration into the law of resonance, that is to say, from the successive exploitation of the octave , the fifth and the fourth (ninth to twelfth century), the third (thirteenth to sixteenth century), the seventh (seventeenth and eighteenth century), the major ninth , the augmented fifth , and the perfect eleventh (nineteenth and twentieth centuries) . . . . this evolution . . . . constitutes, at the same time, the only true justification of the musical art.
...the Carnatic music system is arbitrary in principle, even though some features may be conditioned by mathematical laws ....the only law of mathematics that Carnatic music adheres to is the law of doubling the frequency of the fundamental for the octave.