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The Positive Sciences of the Ancient Hindus c6.s1: Section 6. The Notes of the Diatonic Scale: Determination of Their Relative Pitch

The Positive Sciences of the Ancient Hindus c6.s1

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Section 6. The Notes of the Diatonic Scale: Determination of Their Relative Pitch

c6.s1.2

The pitch of a note is inversely proportional to the length of the wire (तन्त्रीतनुस्वरो ज्ञेयः तद्दर्ध्यव्यस्तमानतः—क्षेत्रलीलावती, quoted by Mr. Devala in his "Hindu Musical Scale").

c6.s1.3

The pitch of the fundamental note to that of its octave is as 1 : 2 (मध्यस्थानस्यः षड्जः द्विगुणसमः—रागविबोध, quoted by Mr. Devala).

c6.s1.4

The pitch of the fourth note (F) to that of the fundamental (C) is as 4 : 3 (उभयोः षड्जयोर्मध्ये मध्यमं स्वरमाचरेत—संगीतपारिजात, quoted by Mr. Devala).

c6.s1.5

The vibrations of the fifth note (G) to those of the fundamental (C) are as 3 : 2 (त्रिभागात्मकवीणायां पञ्चमः स्यात्तदग्रिमे ।—संगीतपारिजात, quoted by Mr. Devala).

c6.s1.6

Concord (सम्वादित्व) is either perfect or imperfect. The ratio of perfect concord is 3 : 2 ; that of imperfect concord, 4 : 3 (स-प-स-म मुख्याः संवाद्निः स्वराः रक्तसंश्रयाः प्रायः—रागविबोध, quoted by Mr. Devala) ; *e.g.* if D be the Vâdî, A would be a Samvâdî ; if E be the Vâdî, B would be a Samvâdî : in each case a perfect concord. The pitch of D is determined from that of G, and the pitch of A from that of D, in each case, by the rule of perfect concord.

c6.s1.7

Determination of the pitches of E and B (after Mr. Devala). This may be done in either of the following ways :—

c6.s1.8

(1) E may be determined from A, and B from E, by the rule of perfect concord. This would give 303¾ as the value of the pitch of E, and 455⅝ as that of the pitch of B, if the pitch of C be taken as 240 ; *or*

c6.s1.9

(2) E may be determined from C by reduction of the fifth harmonic by two octaves, a sort of imperfect concord ; and then B may be determined from E by the rule of perfect concord. This would give 300 for E, and 450 for B, if C be taken as 240.

c6.s1.10

Mr. Devala, in his investigations with the "Sonochord," finds that Hindu musicians (and Sanskrit writers on music) adopted the latter values for E and B, as they tested their notes by harmonics (मेरुगतस्वयम्भूस्वरपंक्तिप्रामाण्येन—रागविबोध, quoted by Mr. Devala). The Hindus therefore followed just intonation.

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