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Uddiṣṭam Method

Adapted from Chapter 5 of 'Saṅgītaratnākara - A Study' by R.Rangaramanuja Ayyangar, 2nd Ed.

The method of Uddiṣṭam (that which is revealed) addressed the query that was the reverse of the one posed for the Naṣṭam method: which is the permutation step in a prastāra that has a specified rūpam. To illustrate this method, consider the query:

Which step in the laghu-pluta prastāra has the tāla rūpam of the form 'l-d-d-g'?

The Uddiṣṭam method involves a two stage procedure. The first stage simulates the derivation of the rūpam through the naṣṭam method and the second stage then works out the required permutation step.

1. Start with the saṅkyā series for this prastāra and tagged with the position markers m0 to m4 (steps a, b).

2. The first element in the specified rūpam is a guru (elements are numbered right to left). As noted in the earlier in the naṣṭam process, a guru is generated through a two-step reduction over m1 and m2, stopping at m3 (step c). Note the saṅkyā values at positions m1 and m2. These are 33 and 19 respectively.

3. Once an element is obtained, the markers would have been reset with marker m0 being placed at the point where the reduction stopped. All other markers would have been placed 1,2,4 and 6 positions to the left of new m0 (step d).

 a. 1 2 3 6 10 19 33 =60 b. m4 m3 m2 m1 m0 c. g d. m2 m1 m0

4. The next element in the specified rūpam is a druta. This would have been derived from a non-reduction over position m1. The markers would have shifted again (steps e, f).
 a. 1 2 3 6 10 19 33 =60 .. d. m2 m1 m0 e. d f. m2 m1 m0

5. The third element is again a druta produced through a non-reduction, repeating the process outlined in 4 (steps g, h).
 a. 1 2 3 6 10 19 33 =60 .. f. m2 m1 m0 g. d h. m1 m0

6. The final element is a laghu. This would have been obtained from a single-position reduction over m1 (step i). Again, note the saṅkyā value at m1. This is 1.
 a. 1 2 3 6 10 19 33 =60 .. h. m1 m0 i. l

The Uddiṣṭam method now proceeds to second stage. Add up the saṅkyā series values at all positions that yielded a rūpam element that was not a druta. Ignore the values at the druta determining steps as these do not carry any significance.The relevant values then are 33 and 19 from the guru determining step and 1 from the laghu determining step. Add up these values. 33+19+1=53. Subtract this number from the total permutation steps in the prastāra. 60 - 53 = 7. This, then, is the required permutation step.

Therefore, the tāla rūpam of the form 'l-d-d-g' is found in the seventh step of the laghu-pluta prastāra.

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