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

208 Treatment of Svarā Section 2 . Grāma, Mūrcchanā, ...
Thus, the method of forming the permutational calculus of note- (vi) Khaṇḍameru (permutation-indicator) : 63c-71
series has been explained in detail applying the rule to the tetratonic (1) The construction of the permutation-indicator: (63c-66b)
series for illustration. Similarly pentatonic, hexatonic and heptatonic Let there be seven series of squares¹ commencing with
series can also be worked out. Since this is a tedious process, a mathe- seven squares and ending with one², arranged one below
matical graph has been prepared to facilitate the recognition of note- The text of the verses 63c to 66b describes the method of drawing
series with reference to their serial number in the sequential order and the mathematical graph which is devised to indicate naṣṭa and uddiṣṭa.
their particular order of notes. Naṣṭa is a technical name of the musical problem in which what is given
is the number of the note-series in question, and what is to be found out
is its tonal form giving the order of notes in it; while uddiṣṭa denotes the
(vi) खण्डमेरुः musical problem in which the tonal form of the note-series is given and
its serial number is to be found out. This graph, called khaṇḍameru (per-

1. खण्डमेरु-निर्माणम् mutation-indicator), helps to solve these two musical problems jointly
   known as 'naṣṭa-uddiṣṭa'.
   सप्ताद्येकान्तकोष्ठानामधो ऽधः सप्त पङ्क्तयः ॥६३॥ The permutation-indicator is drawn by placing seven series of squares
   तास्वाद्यायामाद्यकोष्ठे लिखेदेकं परेषु खम् । having seven, six, five, four, three, two and one squares each in due order
   वेद्यतानस्वरमितान्न्यस्येत्तेष्वेव लोष्टकान् ॥६४॥ one below the other. The graph is thus formed into the following pattern.
   प्राक्पङ्क्त्यन्त्याङ्कसंयोगमूर्ध्वाधःस्थितपङ्क्तिषु । Permutation-indicator
   शून्यादधो लिखेदेकं तं चाधो ऽधः स्वकोष्ठकान् ॥६५॥
   कोष्ठसङ्ख्यागुणं न्यस्येत्खण्डमेरुरयं मतः ।
   [खण्डमेरु-कोष्ठकम् / Devanagari Permutation Table]
   | स | रि | ग | म | प | ध | नि |
   | :-: | :-: | :-: | :-: | :-: | :-: | :-: |
   | १ | ० | ० | ० | ० | ० | ० |
   | | १ | २ | ६ | २४ | १२० | ७२० |
   | | | ४ | १२ | ४८ | २४० | १४४० |
   | | | | १८ | ७२ | ३६० | २१६० |
   | | | | | ९६ | ४८० | २८८० |
   | | | | | | ६०० | ३६०० |
   | | | | | | | ४३२० |
   [English Permutation-indicator Table]
   | sa | ri | ga | ma | pa | dha | ni |
   | :-: | :-: | :-: | :-: | :-: | :-: | :-: |
   | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
   | | 1 | 2 | 6 | 24 | 120 | 720 |
   | | | 4 | 12 | 48 | 240 | 1440 |
   | | | | 18 | 72 | 360 | 2160 |
   | | | | | 96 | 480 | 2880 |
   | | | | | | 600 | 3600 |
   | | | | | | | 4320 |
   इति खण्डमेरुः Khaṇḍameru
   (Chart 23)

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1. Koṣṭha literally means a chamber or an inner apartment, a store-
   room or space surrounded by walls. Here it is used in the sense
   of an enclosed space which in this case is in the form of a square.
2. Only the commencing and the ending number of the squares is
   given. What is implied is that if the first series has seven squares,
   the last will have one i. e., the second will have six, the third will
   have five, the fourth will have four, the fifth will have three, the
   14