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

212 Treatment of Svara
number of the square concerned¹³ and the resultant
written below that.¹⁴ This is considered to be the "permu-
tation-indicator" (khaṇḍameru).¹⁵ (65-66b)
squares is preceding, then the total of the last square of that series be
written in the last square (from right to left) of the succeeding series,
i. e., the 2nd. If however, there are two preceding series, then the total
of the last squares of both the series may be given below the zero in the
third square of the second series of six notes.
However, if there are many preceding series, then the total of the
figures given in their last squares may be added in the squares and
given below the respective zeros in the first series. For example, in the
column-square below the first zero, (1) is written, for the total given in
the last square of its preceding series is one. Then, in the next square
of the series below 2nd zero, we have 2 as the total of (1+1=2) the
last squares of the first and the second series. Again in the next square
of the series below the third zero in the fourth column, we have 6 as the
total of the last numbers of the first, second and the third series
(1+1+4=6). Similarly, the fourth square in the fifth column shows
24 as the total of the preceding last squares (1+1+4+18=24); and so
on That is how the figures of the second series are computed.
For computing the figures of the subsequent series (i. e., from
3rd to the 7th) another method is suggested which cuts short the above
process, for it would be cumbersome if applied further; and it consists
in multiplying the sum thus obtained in the squares of the second series
by the number of the respective column-squares thereunder. For
example, to fill in the first square (from the left) of the 3rd (horizontal)
series, we have figure 2 in the 2nd series above, and this being the 2nd
square from it, multiplying 2×2 we get 4. 2 represents the sum total
of the last squares of the preceding series' which is here multiplied by
the number of the square to be filled in. Similarly, to fill in the next
square in the same series (below ma), we have the figure 6 as the sum of
the last squares of the preceding series which is multiplied by 2 to
yield 12. Likewise, in the 4th vertical column (below ma) the last
13. The square concerned is the one in which the sum arrived at
is given and is to be counted vertically from top to bottom.
14. The square below the one in which the sum of the addition
referred to is given i. e., the last square in the vertical series.
15. Khaṇḍameru is a mathematical graph that indicates what is
known as naṣṭa and uddiṣṭa, the terms that are to be explained
presently. Both naṣṭa and uddiṣṭa are finally related to the
sequential extension of the note-series; thus this graph actually
works as the indicator of note-series.
Section 4 : Grāma, Mūrcchanā, Krama and Tāna 213
square of the 4th series bears the figure 18 in the graph. This is found
as per the same rule, i. e., 6 is obtained in the 2nd series of the same
column as the sum of the last squares of the preceding series which is
multiplied by 3, being the number of the square below the series (indi-
cative of the sum). Other figures can similarly be worked out. This
process can also be understood from the following two charts :
Computation of 2nd series of the indicator (The additive process)
No. of column | Total of the last squares of the preceding series | The figure obtained
square in question left to right | No. of series | Respective figures |
1 | 1 | 1 | 1
2 | 1,2 | 1+1 | 2
3 | 1,2,3 | 1+1+4 | 6
4 | 1,2,3,4 | 1+1+4+18 | 24
5 | 1,2,3,4,5 | 1+1+4+18+96 | 120
6 | 1,2,3,4,5,6 | 1+1+4+18+96+600 | 720
(Chart 24)
Computation of 3-7 series of the indicator
(The process of multiplication)
No. of series | Figure in the 2nd column square | Sl. No. of the square computed vertically from below the zero | Process of multiplication: Multiplication | Process of multiplication: Result | Process of multiplication: No. of the column squares filled
3rd | 2 | 2 | 2×2 | 4 | 3rd
4th | 6 | 2 | 6×2 | 12 | 3rd
| 6 | 3 | 6×3 | 18 | 4th
5th | 24 | 2 | 24×2 | 48 | 3rd
| 24 | 3 | 24×3 | 72 | 4th
| 24 | 4 | 24×4 | 96 | 5th
6th | 120 | 2 | 120×2 | 240 | 3rd
| 120 | 3 | 120×3 | 360 | 4th
| 120 | 4 | 120×4 | 480 | 5th
| 120 | 5 | 120×5 | 600 | 6th
7th | 720 | 2 | 720×2 | 1440 | 3rd
| 720 | 3 | 720×3 | 2160 | 4th
| 720 | 4 | 720×4 | 2880 | 5th
| 720 | 5 | 720×5 | 3600 | 6th
| 720 | 6 | 720×6 | 4320 | 7th
(Chart 25)