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

190 Treatment of Svara
fold⁸. The four⁴ beginning with ṣaḍja⁵ and madhyama⁶ are
twofold each, and the other ten are fourfold; thus, these
original series are forty-eight⁷ in all. (40-41)
The seven hundred and twenty⁸, already enumerated,
when multiplied by the original series make thirty-four thou-
sand five hundred and sixty, which forms the total number
of hexatonics⁹. (42-43a)
(cf. note 3 on 35b-36d), when one or more notes are dropped out of
these series in their original order for making permutational note-series,
these mūrcchanā-series in that modified form are called krama-s or
original series. The author, now onwards, is taking into account the
number of these original series in the hexatonic to monotonic series.
Now, if hexatonic note-series are to be formed out of the mūrcchanā-
series, the last note may be dropped in the process, in each case. Thus
we shall, in effect, have two types of note-series viz. inclusive of either
kākalī or antara or exclusive of either of them.
Fourteen mūrcchanā-s have been spoken of (vide verse 15 ante) in
both of the grāma-s. Out of these fourteen, two in each of the grāma-s
(i.e. four) begin with sa and ma and end in ni and ga respectively. In
their case only two alternate types are possible viz., śuddha (standard)
and antara-inclusive, and śuddha (standard) and kākalī-inclusive. The
rest of the ten mūrcchanā-s will have the usual four varieties. Thus we
have four hexatonic note-series, which are two-fold, making eight varie-
ties in all, and ten hexatonic note-series that are four-fold making forty
varieties in all. The total number of the original series, in this way,
comes to forty-eight. (40-41)
Seven hundred twenty permutational hexatonic note-series have
been enumerated (cf. verse 37 ante) for each mūrcchanā. In all forty-
eight mūrcchanā-series have been counted. Thus the total number of
the permutational hexatonic note-series is worked out (720 × 48 = 34560)
to be thirty-four thousand five hundred and sixty.
3. Viz in case ni is dropped, standard and antara-inclusive; and
in case ga is dropped, standard and kākalī-inclusive.
4. The four mūrcchanā-series.
5. The first mūrcchanā (uttaramandrā) of the ṣaḍja-grāma and the
fourth mūrcchanā (śuddhamadhyā) of the madhyama-grāma.
6. The fifth mūrcchanā (matsarīkṛtā) of the ṣaḍja-grāma and the
first (sauvīrī) of the madhyama-grāma.
7. (4 × 2 = 8) + (10 × 4 = 40) = 8 + 40 = 48.
8. 720 permutational hexatonic note-series, formed out of a given
combination.
9. That is, permutational hexatonic note-series, formed out of
48 hexatonic combinations or original series. This number
also includes the original-series (mūlakrama-s).
Section 4 : Grāma, Mūrcchanā, Kūṭatāna ...
7. औडुवकूटतान-सङ्ख्या
, अथ पञ्चस्वरान्ब्रुवे ।
गाद्यौ धाद्यौ निषादाद्यौ चतुर्भेदाः षडौडुवाः ॥४३॥
अष्टावन्ये द्विधेत्येवं चत्वारिंशदिमे क्रमाः ।
सविंशतौ शते तैश्च गुणिते ऽष्टौ शतानि तु ॥४४॥
चत्वारि च सहस्राणि सङ्ख्या पञ्चस्वरेष्विति ।
(7) The enumeration of the pentatonics : 43b-45b
Now, I am to describe the pentatonics.¹ The six
pentatonics² commencing with ga dha and ni are fourfold,
and the eight others are twofold; thus, these (original) series
are forty in all, which when multiplied by one hundred and
twenty³ bring the total number of the pentatonics⁴ to four
thousand and eight hundred. (43b-45b)
¹The pentatonic permutational note-series are formed by dropping
the last two notes of the mūrcchanā-series. In the two grāma-s we have
six series i. e., three in each beginning with ga, dha and ni in which
naturally neither ga nor ni is dropped. So these six series are fourfold;
but in the case of remaining eight series either ga or ni is dropped, and
so we can have only two types. That is how the total number of pen-
tatonic series is found to be forty, i. e. (6 × 4 = 24) + (8 × 2 = 16) = 24 +
16 = 40.

1. The pentatonic permutational note-series.
2. These six are identified to be from the mūrcchanā-s of the two
   grāma-s as under.
   | Commencing with the note | The mūrcchanā-s in the grāmas: Ṣaḍja-grāma (No.) | The mūrcchanā-s in the grāmas: Ṣaḍja-grāma (Name) | The mūrcchanā-s in the grāmas: Madhyama-grāma (No.) | The mūrcchanā-s in the grāmas: Madhyama-grāma (Name) |
   |---|---|---|---|---|
   | ga | 6th | Aśvakrāntā | 2nd | Hariṇāśvā |
   | dha | 3rd | Uttarāyatā | 6th | Pauravī |
   | ni | 2nd | Rajanī | 5th | Mārgī |
   (Chart 18)
   (Showing pentatonic series inclusive of ga and ni)
3. 120 is the number of permutational pentatonic note-series (kūṭa-
   tāna-s) formed out of a given combination or original-series.
4. That is permutational pentatonic, note-series formed out of 40
   pentatonic combinations or original series. The number also
   includes the original series (mūla-krama-s).