The Music of Hindostan c9.s2.46

c9.s2.46

Each partial forms with its neighbour in the series an interval represented by a ‘super-particular’² fraction, and these intervals are the ultimate facts of music. They immediately combine to form new intervals as quotients: thus, 2/1 ÷ 3/2 = 4/3, that is, the power of hearing the Octave and Fifth carries with it the power to hear the Fourth as well. Further, 3/2 ÷ 4/3 = 9/8; that is, the hearing of the Fourth and Fifth involves the appreciation of the major Tone. This means that in order to discriminate the major Tone it is not necessary to have an ear fine enough to hear the 8th and 9th partials, which also give it (because they are partials of the 2nd and 3rd partials), but it can be apprehended directly as the ‘difference’ (strictly, quotient of) an Octave and two Fifths.