Scale Taxonomy in the कर्नाटकी पद्धती

The कर्नाटकी पद्धती is often claimed to be faithful to the music of ancient (pre-Islamic) India. In some respects this is reflected even today in the musicological terms used. Specifically, terms like शुद्ध, चतुःशृति, षट्शृति, etc. have a provenance in the २२-शृति model of मुनि भरत् documented in the नाट्यशास्त्र and in the संगीत्-रत्नाकर् by शारंग्देव्. I've always thought that the use of this terminology in the कर्नाटकी पद्धती was somewhat curious. But before I elaborate on what I mean, it is worth taking a quick look at the षड्ज् ग्राम् of मुनि भरत्.

Recovering the षड्ज् ग्राम्

According to the नाट्यशास्त्र, the षड्ज् ग्राम् is defined by the allocation of the २२ शृतिs (whatever the term शृति means) into an octave as ४/३/२/४/४/३/२:

नि - - - स - - र - ग - - - म - - - प - - ध - नि

This is also the division in the चतुर्दंडीप्रकाशिका of व्यंकतमुखी (1560 A.D.) indicating continuity with the tradition of the नाट्यशास्त्र. The names given by व्यंकतमुखी to these स्वर्s were:

०० - शुद्ध निषाद् / पंचशृति धैवत्
०१ - कैशिक निषाद् / षट्शृति धैवत्
०२ - काकली निषाद्
०४ - षड्ज्
०७ - शुद्ध ऋषभ्
०९ - शुद्ध गाँधार् / पंचशृति ऋषभ्
१० - साधारण् गाँधार् / षट्शृति ऋषभ्
११ - अंतर् गाँधार्
१३ - शुद्ध मध्यम्
१६ - वराळी मध्यम्
१७ - पंचम्
२० - शुद्ध धैवत्
२२ - शुद्ध निषाद् / पंचशृति धैवत्

[The modern terminology however uses चतुःशृति ऋषभ् (शृति ८) and चतुःशृति धैवत् (शृति २१) in place of the पंचशृति versions. This has the advantage of avoiding १-शृति intervals between notes in a मेल्. The मध्यम् terminology is also different. It is not clear to me when this change took place.]

The शुद्ध scale above (i.e. षड्ज् ग्राम्) corresponds to the काफ़ी mode of the modern हिन्दूस्तानी पद्धती when referred to the षड्ज् based tonality. [However, in the निषाद् based tonality, it really represents the बिलावल् mode.]

In the षड्ज् ग्राम्, the intervals between the notes are either ४, ३, or २ शृतिs. Clearly the २-शृति intervals are akin to modern semitones, and the ४-शृति intervals to modern tones. For the purposes of the current discussion the exact numerical sizes of the intervals don't matter.

Discussion on the notes

With reference to a षड्ज् based tonality, the (३-शृति) शुद्ध ऋषभ् of the षड्ज् ग्राम् represents an interval larger than a २-शृति 'semitone'. However, present-day कर्नाटकी पद्धती definitely employs a शुद्ध ऋषभ् which is a 'semitone' away from the षड्ज्. In other words, contemporary practice seems to no longer have any relation with theory. It appears that the modern शुद्ध ऋषभ् is more representative of a २-शृति interval.

The षट्शृति ऋषभ् presents its own problem. When this note is used in a मेल्, the choice of the following गाँधार् is then restricted to the अंतर् गाँधार् which however forms a १-शृति interval with the षट्शृति ऋषभ्. १-शृति intervals are meant to be avoided in theory because of their alleged dissonance. Choosing the next higher शृति for the गाँधार् is also not possible because that location forms a १-शृति interval with the शुद्ध मध्यम्. This suggests that the षट्शृति ऋषभ् cannot be a viable note in the modern कर्नाटकी पद्धती.

Redefining the notes

Given what has been said above, the whole note naming in the कर्नाटकी पद्धती needs to be revisited. The only rule to be followed is that two adjacent notes cannot be closer than २-शृतिs. Thus, the शुद्ध ऋषभ् can be no lower than the २-शृति position. This puts the शुद्ध गाँधार् at the ४-शृति position. Similarly, the highest गाँधार् cannot be higher than the ७-शृति position which puts the highest ऋषभ् at the ५-शृति position. The ऋषभ् then can range from the २-शृति to the ५-शृति position while the गाँधार् can range from the ४-शृति to the ७-शृति position. Similar considerations apply to the positions of the धैवत् and निषाद्.

The individual positions for each स्वर् are then better identified by the following qualifiers: शुद्ध, तीव्र, तीव्रतर्, and तीव्रतम्.

Final Taxonomy

Based on all the discussions above, a new taxonomy for the notes in the कर्नाटकी पद्धती is proposed:

०० - षड्ज् (S)
०२ - शुद्ध ऋषभ् (r1)
०३ - तीव्र ऋषभ् (r2)
०४ - तीव्रतर् ऋषभ् (r3) / शुद्ध गाँधार् (g1)
०५ - तीव्रतम् ऋषभ् (r4) / तीव्र गाँधार् (g2)
०६ - तीव्रतर् गाँधार् (g3)
०७ - तीव्रतम् गाँधार् (g4)
०९ - शुद्ध मध्यम् (m1)
१० - तीव्र मध्यम् (m2)
११ - तीव्रतर् मध्यम् (m3)
१२ - तीव्रतम् मध्यम् (m4) [Unused]
१३ - पंचम् (P)
१५ - शुद्ध धैवत् (d1)
१६ - तीव्र धैवत् (d2)
१७ - तीव्रतर् धैवत् (d3) / शुद्ध निषाद् (n1)
१८ - तीव्रतम् धैवत् (d4) / तीव्र निषाद् (n2)
१९ - तीव्रतर् निषाद् (n3)
२० - तीव्रतम् निषाद् (n4)

The possible options for the ऋषभ् and गाँधार् give 10 'genera':
r1 g1
r1 g2
r1 g3
r1 g4
r2 g2
r2 g3
r2 g4
r3 g3
r3 g4
r4 g4

The possible options for the मध्यम् and पंचम् give 3 'genera' (assuming that P must be present):
m1 P
m2 P
m3 P

The possible options for the धैवत् and निषाद् give 10 'genera':
d1 n1
d1 n2
d1 n3
d1 n4
d2 n2
d2 n3
d2 n4
d3 n3
d3 n4
d4 n4

In all, this gives 10 * 3 * 10 = 300 'genera' in all. Each of them is a valid candidate 'मेल्'.