 In South Indian musical theory, one of the most famous explanations of the scalar system is that of Venkatamakhi developed in the 17th Century. The following is excerpted from B.C.Deva's Indian Music For simplicity's sake I have omitted Indian names for the pitches. The construction of the seventy two parent scales (janaka mela) is out of two tetrachords (anga). The octave is divided into to anga-s: the poorvanga (lower tetrachord) and the uttaranga (upper tetrachord) thus:
Poorvanga: C Db D Eb E F F# Uttaranga: G Ab A Bb B C For the nonce let us leave out F# and consider the varieties of the possible first tetrachords. They will be as under:
C Db D F C Db Eb F C Db E F C D Eb F C D E F C Eb E F By a similar process six kinds of upper tetrachords may be obtained:
G Ab A C' G Ab Bb C' G Ab B C' G A Bb C' G A B C' G Bb B C' By combining each of the poorvanga-s with every one of the uttaranga-s there can be constructed thirty-six janaka mela-s. One example is given below:
C Eb E F G Ab A C' C Eb E F G Ab Bb C' C Eb E F G Ab B C' C Eb E F G A Bb C' C Eb E F G A B C' C Eb E F G Bb B C' Now, in all the thirty-six janaka mela's, substitute F by F#. We then have another thirty-six, differing only in madhyama (Fourth). Totally there can thus be seventy-two scales. To summarize the conclusion B.C.Deva's chapter, assuming a scale can have a differing number of notes acending and descending, and assuming one wishes to keep those movements between five and seven notes, each of the parent scales can thus spawn 484 subsidiary ones, yielding 34,848 scales. Obviously, if one widens the scalar parameters further to include more or less notes in a scale, and admit microtones, (the Indian system admits 22 such sruti to the octave) the number of scales one has to explore becomes astronomical.
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