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scale of B sharp

Ramsay
Getting Fifths as we ascend toward the number twelve they are in themselves the same, but with regard to their relationships they are quite different. Before and up to the twelfth fifth no scale has all the notes at the same distance above the first scale of the series. But after twelve, the thirteenth scale for example, B#, supposing the scale to be marked by sharps only, is a comma and a very small ratio above C; Cx is the same distance above D of the first scale; Dx the same above E; E# is the same distance above F; Fx the same distance above G; Gx the same distance above A; and Ax the same distance above B. So the scale of B# is just the scale of C over again at the distance of twelve-fifths, only it is a comma and the apotome minor higher; and each series of twelve-fifths is this distance higher than the preceding one. [Scientific Basis and Build of Music, page 30]

lastly it is altered again and becomes, by the power of 3 once more, F#,#, and serves in four keys. But this carries us beyond the horizon of our musical world of twelve keys; for in B#, the top of the tonic E, we have reached our twelfth fifth, and it here coalesces with C of the seventh octave, and closes the circle. This is the way that all notes become alternately altered, either by commas and sharps in the upward genesis of scales, or by commas and flats in the downward genesis, by the alternate powers of 3 and 5. In the upward genesis in this illustration, notes by the power of 5 serve in three keys, and those by the power of 3 serve in four keys. In the minors it is just the inverse on this by the Law of Duality. But no note serves for more than either three or four keys, as the case may be. [Scientific Basis and Build of Music, page 63]

Created by Dale Pond. Last Modification: Friday November 6, 2020 04:17:57 MST by Dale Pond.