http://www.medieval.org/music/world/carnatic/dikshitar.html
(best summary reference)
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see
https://sites.google.com/site/cmhm4me/home/melakartha-keyboard
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There are 72 mela-kartha ragams. ( parent ragams)
If we adopt HM notation,
S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 S
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as many as 40 of these parent ragams break the rule that r should be followed by g etc,
If a pattern like r1 r2 in successive notes occur, it is vivadhi ragam.
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If we reject them, we will get 32 parent ragams only. ( these are non-vivadhi)
They do not contain vivadhi combinations.
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My contention is that both Thyagaraja and muthuswami Dikshithar, preferred non-vivadi melakartha ragams.
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Which are such non-vivadi parent ragams?
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Let us first see the non-vivadhi with suddha madhyamam ( M1).
There are 16 ragams
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1) todi
2) dhenuka
3) natakapriya
4) kokilapriya
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5) vakulabaranam
6) mayamalavagowla
7) chakravakam
8) suryakantham
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9) natabairavi
10) keerravani
11) karaharapriya
12) gowrimanohari
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13) charukesi
14) sarasangi
15) harikambodhi
16) sankarabaranam
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( non-vivadi under M2) -PRATHI MADHYAMAM
1) bhavapriya
2) subpanthuvarali
3)shadvidhamargani
4) suvarnaanbi
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5)namanaratani
6) panthuvarali
7) ramapriya
8) gamanasrama (poorvikalyani)
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9) shanmugapriya
10) simmendramadhyamam
11) hemavathi
12) dharmavathi
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13) rishabapriya
14) lathangi
15) vachaspathi
16) kalyani
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