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

204 Treatment of Svara
Number of permutational forms in different note-series in each mūrcchanā

Sl. No.	Note-series	Suggested multiplication	Number of the permutational form
1	Monotone	1 × 1 =	1
2	Bitonic	2 × 1 =	2
3	Tritonic	3 × 2 =	6
4	Tetratonic	4 × 6 =	24
5	Pentatonic	5 × 24 =	120
6	Hexatonic	6 × 120 =	720
7	Heptatonic or complete	7 × 720 =	5040
(Chart 20b)
In other words, every successive note in a given series has as many
possibilities of permutation as those of all the notes of the preceding
series put together. That is how the number of the permutations of
the preceding series, when multiplied by the number of notes in the
successive series results in the total number of the permutations of the
succeeding series.
(v) कूटतान-प्रस्तारः
क्रमं न्यस्य स्वरः स्थाप्यः पूर्वः पूर्वः परादधः ।
स चेदुपरि तत्पूर्वः पुरस्तूपरिवर्तिनः ॥६२॥
मूलक्रमक्रमात्पृष्ठे शेषाः प्रस्तार ईदृशः ।
(v) The formation of the permutational calculus (prastāra) : 62-63b
Having established the original order¹, every² preceding note has to be placed below the succeeding one. If
Now, the author is explaining the procedure for forming, what
may be called the 'permutational calculus' (prastāra), that is, he is

1. 'sa ri ga ma pa dha ni' is the original order of the seven notes.
   The word krama which has been rendered as 'the mūrcchanā
   series' or sometimes as the original series has a different shade
   of meaning here, though essentially the connotation of the
   word remains the same. If it is a tetratonic series the order
   would be 'sa ri ga ma' for it, and so on. Thus, in this context,
   krama implies the original combinational order of notes of a
   given note-series. But for the sake of convenience we are to
   use the expression "original order" corresponding to the Skt.
   mūlakrama.
2. The repetition of the term 'pūrva' in the text has been effected
   through this expression, since that is the import of the text.
   Section 4 : Grāma, Mūrchhanā, Tāna and ...
   that³ becomes the succeeding note, the preceding one may
   be advanced keeping the subsequent⁴ notes afterwards; and
   describing the method of placing the notes of various types of note-
   series such as complete, hexatonic etc., in a particular and progressive
   sequence of notes, giving all the possible permutations of the series.
   The essential formula consists in the rule that, while forming the 'permu-
   tational calculus' (prastāra) the notes of the series may, in the first
   instance, be placed in their original order, which may be considered to
   be the first note-series. In order, further to derive the other possible
   permutations the preceding note in each of the series has been placed
   below the succeeding note.
   The question is, 'what to do about the remaining notes'?, and the
   author himself explains that the notes following the succeeding note will
   have to be placed after the note transposed, and the notes preceding it
   will be placed before it in their original order. This much is the action
   that is to be taken.
   The next series, and all the other possible series will be formed
   by applying the above rule to their preceding series. The application
   of the rule is demonstrated by the commentators as under with respect
   to the permutational calculus of the tetratonic series.
   (i) The first series is of the original order viz. sa ri ga ma.
   (ii) To form the series the preceding note viz. sa is to be written
   below the succeeding note, viz. ri. The subsequent notes ga and ma
   will be written after (or in front of) ri as in the overhead line (i. e., the
   preceding series), and ri will naturally be placed before i. e., behind it;
   thus what we get is ri sa ga ma.
   (iii) To form the third series, the second series may be taken as
   the top. Now as per the rule, ri may be placed below sa which will
   result in the series sa ri ga ma, a repetition of the original order. The
   purpose of the permutational calculus being the forming of different
   The implication derived by 'K' is that this action can be taken
   only once in each of the note-series of a particular sequential
   order.
3. The pronoun 'that', according to 'S', refers to the preceding
   note i. e., in the first step. This is the second step being
   explained and accordingly the preceding note of the first step
   becomes the succeeding note of the second step.
4. The subsequent notes are the ones that follow the action taking
   place among the preceding notes with reference to the previous
   note-series.