Pointers to Katapayadi formula needed

[Srinivasan Pichumani]

I believe that the kaTapayAdi sankhya dates back to 
Vararuci's times (?) at least ...

Don't have a direct citation to this scheme in
Vararuci's works themselves, but in the introduction
to the 1938 Adyar Library edition of 
	The Samgraha-cuda-mani of Govinda ; and, the Bahattara-mela-
	karta of Venkata-kavi / edited by S. Subrahmanya Sastri ;
	with a critical introduction in English by T.R. Srinivasa
	Ayyangar.
	LC# ML 338 .G74 (in our library !!!)
Vararuci's name is mentioned by T.R.Srinivasa Ayyangar,
and his rule regarding conjunct consonants is given -
in such cases, it is the convention to use the second part 
of the samyukta akShara for the sankhyA purposes.

Here is where, there are a few deviations from the rule
in the kanakAngi-ratnAngi nomenclature of Govinda e.g.
cakravAka, which yields 26, is the name of the 16th 
melakarta.

& This scheme was applied in musicology by Venkatamakhi, son of Govinda
& Dikshita (17th cent). The first official mention of this formula is
& found in his book "Caturtand.i Prakasika". 

Neither this formula, nor its use in numbering the
meLas, has been given in the caturdaNDi prakAs'ikA
proper.  Venkatamakhi only postulated a 72 meLa scheme,
with his indexing of the 16 svaras as 
    sa, ra, ri, ru, ga, gi, gu, ma, mi, pa, dha, dhi, dhu, na, ni, nu
and congratulated himself in a fairly up-beat manner on
this achievement ;-) remarking that even the forehead-eyed
S'iva can't change this...
    (na hi phAlalOcanOpi pragalbhate or something like that)

Next, he just mentioned the name of 19 meLas (many don't 
have their prefixes in order to fit in the kaTapayAdi
sankhya scheme), and their ordinal position in the 72 meLa
scheme, for which the constituent svaras, and not the sankhyA,
was the criterion in his scheme.

Of these meLas, only "simhArava" is mentioned by him as
his own creation.  The others were prevalent during his
times...  In later times, this meLa took the prefix
"des'i", in order to occupy the 58th position in the
kanakAmbarI-ratnAmbarI nomenclature for the 72 meLas. 

This nomenclature is given in the anubandha to the 
caturdaNDi prakAs'ikA, which has been definitely proven 
to be a later interpolation.

-Srini.