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

206                      Treatment of Svara                              Section 4 : Grama, Murchhana, ...
the rest (of the notes in the series) be left behind$^5$ according                      Permutational calculus of the tetratonic series
to the original order; such is the 'permutational calculus'$^6$
(prastāra). (62-63b)

Sl. No.	Note-series with ma as the fourth	Sl. No.	Note-series with ga as the fourth	Sl. No.	Note-series with ri as the fourth	Sl. No.	Note-series with sa as the fourth
1	sa ri ga ma	7	sa ri ma ga	13	sa ga ma ri	19	ri ga ma sa
2	ri sa ga ma	8	ri sa ma ga	14	ga sa ma ri	20	ga ri ma sa
3	sa ga ri ma	9	sa ma ri ga	15	sa ma ga ri	21	ri ma ga sa
4	ga sa ri ma	10	ma sa ri ga	16	ma sa ga ri	22	ma ri ga sa
5	ri ga sa ma	11	ri ma sa ga	17	ga ma sa ri	23	ga ma ri sa
6	ga ri sa ma	12	ma ri sa ga	18	ma ga sa ri	24	ma ga ri sa
permutation-series, no relationship is to be repeated. Moreover, the
author has ordained that the two notes can be interposed only once in
a series. Thus, ri cannot be placed below sa as that relationship is
already available on the top; therefore, ri will now be related to ga, and
ga will be placed before ri; ma will follow ri in accordance with the
series overhead and sa will be in its own position as per the original
order. Thus we shall get sa ga ri ma
(iv) To form the fourth series sa will be placed below ga, ri and
ma will follow it as per the overhead series (i. e. the third series) and ga
will be placed behind sa. Thus we get ga sa ri ma.
(v) To form the fifth series, as per the rule, ga should be placed
below sa (in the fourth series), but if sa is interposed with ga what we
get is sa ga ri ma, which we already have in the preceding section of this
permutational calculus. So ga will be related to ri and interposed with
it. The rest of the notes will follow, yielding ri ga sa ma.
(vi) To form the sixth series ri will be placed below ga (in the
fifth series) and interposed with it; the rest of the notes will follow as in
the overhead series. Thus we get, ga ri sa ma.
It will be observed that hitherto the position of ma is unaffected,
because we have six varieties in the tritone series. We cannot form any
more series without affecting the position of ma.
(vii) To get the seventh series we have to place ga below ri and
interpose with it. But that will result in the series ri ga sa ma which has
already been formed. Similarly ga cannot as well be related to sa, for
that will result in the series ri sa ga ma which is already formed. So, ga
will now be related to ma, and what we get is sa ri ma ga.
Now, we can form five other series on the above pattern, in which
we shall have ga in the fourth place. And so also we can form six other
series with ri in the fourth place and six more with sa in the fourth
place. That is how twentyfour note-series are formed into the permuta-
tional calculus of the tetratone note-series which is presented in the
following order:

5. 'Behind' the placement of the preceding note i. e., to the left of it on the paper.
6. Prastāra is defined as the extension of the series of note-series in a particular permutational sequence, which has been explained above.
   (Chart 21)
   The process of formation is briefly presented in the following chart
   as per the rule stated in the text, and demonstrated up to seventh note-
   series as explained above.
   The process of formation of the permutational calculus of the
   tetratonic series
   | Sl. No. of the note-series | Notes transposed | Series obtained | Remarks |
   | :--- | :--- | :--- | :--- |
   | 1st series | ............ | sa ri ga ma | This being the 1st series no series precedes it and there is no transposition of notes. |
   | 2nd series | sa for ri | ri sa ga ma | |
   | 3rd series | ri for ga | sa ga ri ma | |
   | 4th series | sa for ga | ga sa ri ma | |
   | 5th series | ga for ri | ri ga sa ma | |
   | 6th series | ri for ga | ga ri sa ma | |
   | 7th series | ga for ma | sa ri ma ga | |
   (Chart 22 a)
   If the notes are 1, 2, 3, 4 we get the following picture of the first six series :
   | No. of series | sa ri ga ma | Remarks |
   | :--- | :---: | :--- |
   | 1st series | 1—2—3—4 | Original order |
   | 2nd series | 2—1—3—4 | 1 transposed for 2 |
   | 3rd series | 1—3—2—4 | 2 transposed for 3 |
   | 4th series | 3—1—2—4 | 1 transposed for 3 |
   | 5th series | 2—3—1—4 | 3 transposed for 2 |
   | 6th series | 3—2—1—4 | 2 transposed for 3 |
   (Chart 22 b)