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

186 Treatment of Svara
in four groups in each of which the notes ma, ga, ri and sa respectively
are constant, while the position of other notes keeps on changing. This
gives us the clue to find out the number of possible permutations.
Similarly the 120 permutations of the pentatonic series, 720 of the
hexatonic series and 5040 of the complete series can be worked out
easily. Another principle involved in these calculations is that the
number of permutations of the preceding series denotes the number of
times each note of the succeeding series can be kept constant. Thus, for
example, the permutations of the two-note-series are 2, therefore in the
three-note-series all the three notes can be kept constant twice, leading
us to (2 × 3 = 6) six permutations in all. Likewise, in the four-note-
series, each note can be kept constant for 6 times since the preceding
three-note series has six permutations, leading us to (4 × 6 = 24) twenty-
four permutations in all. That is how the pentatonics are 5 × 24 = 120,
the hexatonics are 6 × 120 = 720, and the complete series are
7 × 720 = 5040.
3. अपूर्णकूटतान-निर्माणम्
,अथापूर्णान्प्रचक्ष्महे ।
एकैकान्त्यान्त्यविरहाद्भेदाः षट् षट्स्वरादयः ॥३५॥
एकस्वरो ऽत्र निर्भेदो ऽप्युक्तो नष्टादिसिद्धये ।
क्रमा अकूटतानत्वे ऽप्युक्तास्तेषूपयोगिनः ॥३६॥
(3) The formation of the incomplete permutational
note-series : (35b-36)
Now, we are to describe the incomplete (permutational
note-series). In each (of the mūrcchanā-s) six varieties are
formed, viz. hexatonic¹ etc. by successively dropping the
last note step by step. Although the monotone has no sub-
The incomplete permutational note-series are formed by the simple
device of dropping the last note from seventh to the second; thus, by
dropping the seventh we get a hexatonic tāna, by dropping the sixth we
get a pentatonic tāna, by dropping the fifth we get a tetratonic note-
series, by dropping the fourth we get a tri-tone note-series, by dropping
the third we get bi-tone series and by dropping the second we get the
mono-tone: these are the six varieties.

1. Hexatonic, i. e., having six tones, the other varieties being
   pentatonic, tetra-tonic series, tritone-series, bitone-series and
   monotone-series.
   Section 4 : Grāma, Mūrcchanā, Krama and Tāna 187
   varieties, it is also counted for the working of naṣṭa.² The
   original-series (krama-s³) which are unrelated to the permu-
   tational note-series have also been included as they will be
   useful with regard to them. (35b-36)
   The number of note-series in each of them will now be described.
   The terms naṣṭa and uddiṣṭa will shortly be explained in their proper
   context, but for the time being the author has pointed out the reason
   for enumerating the mono-tone as a note-series even though it can have
   obviously, no varieties. Similarly, the krama-s or the mūrcchanā-series
   (precisely called here as, the original-series) too have been enumerated
   for technical reasons which will soon be clear.
2. अपूर्ण कूटतानानां सङ्ख्या
   स्युः षाडवानां विशत्या सह सप्त शतानि तु ।
   औडुवानां तु विशत्या सहितं शतमिष्यते ॥३७॥
   चतुःस्वराणां कूटानां चतुर्विंशतिरीरिताः ।
   त्रिस्वराः षड् द्विस्वरौ द्वावेकस्त्वेकस्वरो मतः ॥३८॥
   (4) The enumeration of the different permutational
   note-series : 37-38
   The hexatonic series formed are seven hundred and
   twenty¹, and the pentatonic series are one hundred and
   Ārcika literally means relating to the Ṛgveda (Ṛc + veda). Ṛc is a
   hymn, and the hymns employed in the performance of sacrifices, it
   seems, were sung in the monotone, though the accent system was also
   there with its three accents viz., udātta (raised), anudātta (unraised) and
   svarita (intermediate note). 'K' also says, "Yajñaprayogeṣu ṛcamekasvara-
   śrayatvāt, tatsambandhād ārcikaḥ" i. e., hymns while they are employed in
   (2. Naṣṭa will be explained later.
3. Krama in this context refers to the original (mūla) form of the
   mūrcchanā-s in their ascent i. e., ‘sa ri ga ma pa dha ni’ for
   uttamamandrā. However, the term mūrcchanā-series applied to the
   392 series spoken of vide 19-20 ab ante is not precisely appli-
   cable in the context of the calculation of permutational note-
   series, the krama-s for which may consist of six to one notes
   each in the original order of the mūrcchanā-series concerned.
   Thus, the krama-s in this context have been rendered as the
   original series, as the author himself names them as mūla-
   krama-s somewhere else (verse 40 of this section).
4. This includes the original series (krama-s) as well.