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

184 Treatment of Svara
A mūrcchanā is said to be complete when it has seven notes, and it
is considered incomplete when it has less than seven notes i.e. from six
to one; although one note does not make a series, but that is theoretical.
Actually, when one or more 'notes are omitted from a mūrcchanā, it
becomes a tāna (as already explained in the comments on 19-20b ante),
a note-series. But, here, the author is talking in terms of incomplete
mūrcchanā-s (as well) giving rise to permutational note-series, because
such note-series are derived from the mūrcchanā-series, and not because
on this account, they continue to be mūrcchanā-s. It has already been
said that Bharata has used the expression mūrcchanā-tāna for hexatonic
and pentatonic combinational note-series.
We have already come across the fourfold classification of mūr-
cchanā-s and this is a twofold classification viz. complete and incom-
plete. Now, the purport of the text is that, a mūrcchanā, whether
complete or incomplete, becomes a permutational note-series if the
normal order of its notes is disturbed, and in that case even a descend-
ing movement to a certain extent is no bar. It may be pointed out that
ordinarily the notes of the mūrcchanā-series (krama-s) from which the
note-series are derived are in the ascending order.
2. पूर्णकूटतानानां सङ्ख्या
तत्सङ्ख्यामभिदध्महे ॥३२॥
पूर्णाः पञ्च सहस्राणि चत्वारिंशद्युतानि तु ।
एकैकस्यां मूर्च्छनायां कूटतानाः सह क्रमैः ॥३३॥
षट्पञ्चाशन्मूर्च्छनास्थाः पूर्णाः कूटास्तु योजिताः ।
लक्षद्वयं सहस्राणि द्व्यशीतिर्द्वे शते तथा ॥३४॥
चत्वारिंशच्च सङ्ख्याता
(2) The enumeration of the complete permutational note-
series : (32d-35a)
We calculate their number as follows. Including the
mūrcchanā-series (krama-s) there are five thousand and forty
(5040) complete permutational note-series in each of the
Mataṅga has spoken of five thousand thirtythree permutational
note-series, and Śārṅgadeva has added the seven mūrcchanā-series to
this number, for each of the fiftysix mūrcchanā-s does have seven series
of its own. Dattila also does not include the seven mūrcchanā-series
(krama-s) in the total number of permutational note-series, but that
Section 4 : Grāma, Mūrcchanā, Krama and Tāna 185
mūrcchanā-s. Thus, the total number of the complete permu-
tational note-series subsisting in the fiftysix mūrcchanā-s comes
to two lakh eightytwo thousand and two hundred forty
(2,82,240). (32d-35a)
makes no difference in principle. The number 5040 is arrived at in
the following manner :
With 1 note the number of possible permutational series of
of the notes will be 1 × 1 = 1
With 2 notes ,, ,, ,, ,, 1 × 2 = 2
With 3 ,, ,, ,, ,, ,, 2 × 3 = 6
With 4 ,, ,, ,, ,, ,, 6 × 4 = 24
With 5 ,, ,, ,, ,, ,, 24 × 5 = 120
With 6 ,, ,, ,, ,, ,, 120 × 6 = 720
With 7 ,, ,, ,, ,, ,, 720 × 7 = 5040
To demonstrate let us take items with 2 and 3 notes to begin
with :—

1. Two-note-series : sa ri, ri sa
2. Three-note-series : sa ri ga } group A with ga constant
   ri sa ga }
   sa ga ri } group B with ri constant
   ga sa ri }
   ri ga sa } group C with sa constant
   ga ri sa }
   Now, it will be observed that the two-note-series is a simple one
   and does not involve any complicated procedure in the working out of
   the different permutations as in the case of the three-note-series, and
   much more so in all the subsequent series. The permutations in the
   three-note-series are so arranged that an attempt is made as a rule to
   keep the last note of the series constant as long as possible. This is
   demonstrated in the four-note-series worked out hereunder.
   S. No. Group A Group B Group C Group D
3. sa ri ga ma sa ri ma ga sa ga ma ri ri ga ma sa
4. ri sa ga ma ri sa ma ga ga sa ma ri ga ri ma sa
5. sa ga ri ma sa ma ri ga sa ma ga ri ri ma ga sa
6. ga sa ri ma ma sa ri ga ma sa ga ri ma ri ga sa
7. ri ga sa ma ri ma sa ga ga ma sa ri ga ma ri sa
8. ga ri sa ma ma ri sa ga ma ga sa ri ma ga ri sa
   It will be observed that on the basis of the above principle, the
   24 permutations of the four-note series have been classified and arranged