The Music of Hindostan c9.s1.63

c9.s1.63

which is proved in every book on Higher Algebra. The number of cents is 3986 times this expression, that is, number of cents corresponding to m/n is 3986 × 2 × .43429 (m-n)/(m+n) + ⅓ ( (m-n)/(m+n) )³ + ⅕ ( (m-n)/(m+n) )⁵ + that is, 3462 × (m-n)/(m+n) + 1154 × ( (m-n)/(m+n) )³ + 692 ( (m-n)/(m+n) )⁵ + in ratios, their quotients). Columns VI and VII are adjustments proposed by Mr. Clements on the strength of observations taken by Mr. Deval of Poona on a dichord: his two tertian intervals are a Fourth apart, and his two septimal, a Fifth. [Septimal intervals are derived from the septimal seventh; 7/4 = 969 cents.]