In music theory, the cycle or circle of fifths (or circle of fourths) is the relationship among the 12 tones (or pitches) of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space. Wikipedia, Circle of Fifths
Ramsay
The number 3 is the creative power in music, producing fifths, but it is under the control of the Octave prime - the number 2. It is the supreme octave which forms a boundary by making twelve fifths and seven octaves unite in one note. Within this horizon lies the musical system in its threefoldness - major, minor, and chromatic. [Scientific Basis and Build of Music, page 35]
There are very few things in music which have not change written upon them. TWELVE and THREE, however, are stable. There is nothing that will disturb the propriety of the circle of twelve fifths, as in the tempered system of music; for, although the mathematical-intonation indulges in thirteen keys, the thirteenth is simply the first of a new cycle of twelve.
The working model of three fifths is that which possesses musical life-powers; and these life-powers go with it wherever it goes, and they go with nothing else. [Scientific Basis and Build of Music, page 74]
If the minors are to be developed by sharps in an ascending series of fifths, then the mathematical process must be, as in the majors, by multiplying the top of the dominant by 3 and by 5, and they will then follow the majors. But the Genesis must first necessarily be produced by the descending process. [Scientific Basis and Build of Music, page 84]
See Also
circle of twelve fifths
fifth
Laws of Music
seven octaves
twelve fifths