The History of Music. (Art And Science) Vol. I. From the Earliest Records to the Fall of the Roman Empire

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4 n 26.
H 27.
LaJ XI .s 28.
29.
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cc 218 THE HISTORY OP MUSIc!
The scale might be carried further, into quarter- tones, but it is unnecessary to print it, because there is a simple rule by which any one may tell what the interval will be, and it applies to the division of all "super-particular" ratios, or such as differ only by one degree. Nature makes no fractions, but doubles the numbers, and interposes the one and only intermediate number. Thus, in the above division of the
... Fifth, No." 3, which is in the ratio of 3 to 2 of CC, No. 2, she doubles the ratio, viz., 6 to 4, and interposes the inter- mediate 5. Then, in the next Octave, this Fifth is divided into 6 to 5 and 5. to 4, minor Third and major Third. A-U odd numbers are new sounds ; all even ones have before appeared in the Octave below. The numbers of the Harmonics are of importance in many ways. First, each indicates its proportion to the whole string, so No. 5 is a fifth part of the length, and No. 27 a twenty^seventh part, vibratiug twenty- seven times as fast as No.

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