सङ्गीतरत्नाकर: प्रथम भाग (शार्ङ्गदेव - स्वरगताध्याय सविस्तार व्याख्या व अनुवाद सहित)

222 Treatment of Svara
4. खण्डमेरुत एकस्वरादितानानां सङ्ख्या-परिज्ञानोपायः
तानस्वरमितोध्वर्धःपङ्क्तिगान्त्याङ्कमिश्रणात् ।
एकस्वरादितानानां संख्या संजायते क्रमात् ॥७१॥
(4) The number of permutational note-series in each of the
series as shown by the permutation-indicator : (71)
The number of note-series in monotone¹ etc. is com-
puted by adding up the figures of the last column-squares²
The note-series indicator does not merely show the indicated note-
series and the 'missing note-series', but it also informs us with regard to
the total number of note-series in each of the different types such as
heptatonic, hexatonic, monotonic, etc.
As many notes there are in a given note-series (e. g. seven in the
complete and one in the monotone series) so many end-squares of these
columns will be taken into consideration and figures indicated by them
when added up would in their sum-total indicate the number of note-
series in that type.
The following chart shows the working of this relationship.
The number of note series in each type derived from the
permutation-indicator

The final note of the series in its original order	Name of the type of the series	Column squares: No. of cols.	Column squares: No. of square	Figures of the last column sqs.: S. No. of last col sq.	Figures of the last column sqs.: Figure indicated	Sum total of last squares: Figures added	Sum total of last squares: Total
sa	Monotone series	1	1	1st	1	1	1
ri	Bitonic "	2	2	2nd	1	1+1	2
ga	Tritonic "	3	3	3rd	4	1+1+4	6
ma	Tetratonic "	4	4	4th	18	1+1+4+18	24
pa	Pentatonic "	5	5	4th	96	1+1+4+18+96	120
dha	Hexatonic "	6	6	5th	600	1+1+4+18+96+600	720
ni	Complete or heptatonic "	7	7	7th	4320	1+1+4+18+96+600+4320=5040	5040
(Chart 27)

1. In each type of the permutational note-series such as mono-
   tone, bitone, hexatonic, complete, etc.
2. The squares at the bottom and of the vertical series arranged
   into the columns of the permutation-indicator.
   Section 4 : Grāma, Mūrcchanā, Krama and Tāna
   corresponding respectively³ to the notes in the series.⁴ (71)
   It will be observed that every total incorporates the total of its
   antecedent squares. Thus, in effect, to find out the total number
   of note-series of a particular type what may essentially be taken into
   account is the figures indicated in the squares just below the zero and
   the last squares of the respective columns, as the squares immediately
   below the zero indicate the total number of the preceding series. For
   example, the total number of the complete permutational note-series is
   found to be 5040, but this figure is composed of the figures shown in the
   squares immediately below the zero of the 7th column as the 7th. square
   i. e., 720+4320=5040. So also the figure 720 is composed of
   120+600=720.
   Incidentally, this shows that the zeros placed in the first squares
   of the columns are symbolic of the figures indicated into the last squares
   of the antecedent columns and are therefore identical with them. That
   is how the zeros become significant.
   It may now be observed that the Khaṇḍameru i. e., the permuta-
   tion-indicator has a three-fold function viz., (i) to find out serial
   number of the note-series indicated, (ii) to discover the tonal form of
   a given number of note-series, and (iii) to ascertain the total number
   of note-series in each of the seven types of permutational note-series.
   (vii) शुद्धतान-नामानि
3. षड्जग्रामस्थ-षाडव-शुद्धतानाः
   अथात्र शुद्धतानानां नामानि व्याहरामहे ।
   अग्निष्टोमो ऽत्यग्निष्टोमो वाजपेयश्च षोडशी ॥७२॥
   पुण्डरीको ऽश्वमेधश्च राजसूयस्ततः परः ।
   इति स्युः षड्जहीनानां सप्त नामान्यनुक्रमात् ॥७३॥
   स्विष्टकृद्बहुसौवर्णो गोसवश्च महाव्रतः ।
   विश्वजिद्ब्रह्मयज्ञश्च प्राजापत्यस्तु सप्तमः ॥७४॥
   3 & 4. Each column is indicative of a note i. e., the first column
   square for sa, the second for ri and so on. So the figures
   of these last column-squares only have to be taken into
   account, the notes pertaining to which go to constitute the
   series in question. Series denotes the note-series.