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

Left Page (Page 202)

202 Treatment of Svara
The number of repetitions

Sl. No.	Description of series	No. of repetitions	Break up if any	Remarks
1.	Complete original series	392	56 x 7 = 392	i. e. mūlakramas or krama-s
2.	Incomplete original series	179	$\left.\begin{aligned}48 + 40 + 32 + 26

• 22 + 11 = 179\end{aligned}\right}$ | Hexatonic, pentatonic, tetratonic, tritonic, bitonic and monotone series respectively. |
  | 3. | Repeated note-series | 4081 | $\left.\begin{aligned}63 + 593 + 3425
  = 4081\end{aligned}\right}$ | śuddhamadhyā, mārgi pauravi respectively |
  Total number of repetitions : 392 + 179 + 4081 = 4652
  (Chart 19b)
  The correct number of permutational note-series
  | | | |
  | :--- | :---: | ---: |
  | Total number of note-series | ... .. | 3,22,582 |
  | Total number of repetitions | (-) | 4,652 |
  | Correct number of note-series | ... ... | 3,17,930 |
  (Chart 19c)
  (iv) प्रतिमूर्च्छनं कूटतान-सङ्ख्याज्ञानोपायः
  , ज्ञानोपायो ऽत्र कथ्यते ।
  अङ्कानेकादिसप्तान्तानूर्ध्वमूर्ध्वं लिखेत्क्रमात् ॥६०॥
  हते पूर्वेण पूर्वेण तेषु चाङ्के परे परे ।
  एकस्वरादिसङ्ख्या स्यात्क्रमेण प्रतिमूर्च्छनम् ॥६१॥
  (iv) Determining the number of permutational forms in the note-series of each mūrcchanā : 60b-61
  Now, the method of determining them¹ is herewith described : Let the numbers one to seven be written (verti-
  Since the number of permutations making for the note-series enumerated above is enormous, a mathematical device has been devised to determine the number of a particular permutation of a given form

1. This refers to the permutational note-series i. e., the kūṭatāna-s.

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Right Page

Section 4 : Grāma, Mūrcchanā, ... ...
cally) one over² another in consecutive order. Every succeeding³ number multiplied by the preceding⁴ one respectively points out the number of note-series such as monotone etc., in each mūrcchanā. (60b-61)
in a particular series and also the particular form of a certain permutation in a particular series, given its proper number. This device is called khaṇḍa-meru, which will be explained subsequently.
Presently the author is trying to explain the method of working out the precise number of the note series or the permutational form of a particular series of notes such as monotone, bitone, tritone series and so on in each mūrcchanā.
The text directs us to write numbers commencing from one upto seven, one over the other i. e., vertically. These numbers incidentally would represent the particular note-series such as monotone, bitone, etc. Keeping in view the directions of the text the numbers would be written from the bottom to the top. 'S' too interprets the text as such.
Number of permutational forms in different note-series in each mūrcchanā

Sl. No.	Note-series	Suggested multiplication	Number of the permutational form
7	Heptatonic	7 x 720 =	5040
6	Hexatonic	6 x 120 =	720
5	Pentatonic	5 x 24 =	120
4	Tetratonic	4 x 6 =	24
3	Tritonic	3 x 2 =	6
2	Bitonic	2 x 1 =	2
1	Monotone	1 x 1 =	1
(Chart 20a)
However, for the sake of convenience an inverted graph is presented below commencing with the monotone from the top. To apply the text, the figures in the first vertical row in column 3 be taken as the succeeding numbers and the figures of the respective previous series in column 4 may be taken as the preceding numbers.

2. This expression does not suggest that the numbers are not to be written serially, for that direction has explicitly been given immediately in the text, it only implies that they are not to be written horizontally as usual.
3. The successive note.
4. The preceding resultant i. e., the number of the permutations of the previous series.