Thyagaraja Swami 's kritis are about 700 according to sangeethapriya site.
http://www.sangeethapriya.org/tributes/thyagaraja/dl_krithis.html
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The list of kritis can be sorted on the basis of ragams.
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Then I found that there are about 140 ragams having only one or two kritis.
Some of these 'single-kriti' ragams-kritis are very famous and nice.
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I had also read that Thyagaraja Swami preferrred the first 32 meLakarta scales. even for these rare ragams.
To verify, I tried to list the single kriti ragams , alphabetically and note their parent scale.
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This is the work in last two days.
If the column in right side is yellow, then, it is a suddhamadhyamam scale
If it is cyan, then, it is pathimadhyamam scale
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I observed that Thyagaraja Swami has carefully chosen, only such MK scales even in SuddhaMadhyama set, where there are no vivadi swaras.
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The non-vivadi scales are numbered
8 to 11, 14 to 17, 20 to 23, 26 to 29 ,only.
(16 scales).
My contention is that we can totally avoid notation like R3,G3 , D3 and N3.
if we follow the Trinity's choice of ragams.
----------------------
We can then follow
S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 S
as in Hindusthani music.
https://sites.google.com/site/4carnaticmusic/home/00-carnatic-music/melakartha-keyboard
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Even for swara-singing , there is no problem , as a raga based on a non-vivadi sampoorna meLa ragam , will not touch any vivadi swaram.
( am I right?)
===================================
I have used a pdf book named RARE RAGAS HANDLED BY THYAGARAJA,
=================================
and re-arranged the material.
28
Eesamanohari
HARIKAMBODHI
38
hinolavasantam
NATABAIRAVI
66
latAngi-63
LATANGI
Navaneetam is a rāgam in Carnatic music It is the 40th Melakarta rāgam (parent scale) in the 72 melakarta rāgam system of Carnatic music. It is called Nabhōmaṇi in Muthuswami Dikshitar school of Carnatic music
120
121
takka
tivravahini
MAYAMALAVAGOWLA
SHADVIDHAMARGANI (46)
122
123
umabaranam
udayaravichandrika
HARIKAMBODHI
UDAYARAVICHANDRIKA
1)AndAli
2)AndhOlikA
3)Bhavapriya
4)Bhinnashadjam
5)BhupAla
6)BhushAvaLi
-----------------
7)chAyAtarangiNi
8)ChAyanATa
--
9)Isa-manOhari
10)JhankAradwani
----------------------------
11)Kannada ----------------------------
12) KannadagouLa MMI*
13)ShuddhabangALa MMI *
====================
14) ShuddhadEsi
----------------------------
15) Takka
16) Vegavahini
17) Vijaya-vasanta
============================
18) abhEri
--
19)abhOgi
------------------------------
20)ahiri
--------------------------------
21) amritavAhini
-----------------------------
22)bahudAri
----------------------------
23) bangAla
=======
24) bindumAlinin
25) bouLi
26) brindAvanasAranga
27) chUrnika
----------------------
28)chakravAka
29) chandrajyOti
------
30)bhavAbharaNam
31) charukEsi
32) chittaranjani
33) dIpika
34) devAmritavarshini
35) devakriya
36) dhEnuka
37) divyamani
38) gAnavardhini
39) gambhIravANi
40) ganamUrti
41) gangEyabhUShaNi
42) garudadwani
-------------
43) gouLa
44) gourImanOhari
45) gundakriya
46) gurjari
47) hinolavasantam
48) jayamanOhari
------------------
49)jayanArAyaNi
50) jayantaSrI
51) jayantasena
52) jenjUti
53)Jingala
54) jujAhuli
55) kAmavardini
56) kAntAmani
57) kApinArAyaNi
58) kEsari
59) kIrvAni
60) kOkiladwani
61) kOkilapriya
62) kOkilavarAli
63) kOlahalam
64) kaikavasi
65) kalAkAnti
66) kalAnidhi
67) kalAvati
68)
69) kalgada
70) kamalAmanOhari
-----------------------
71) kanakAngi
72) karnAtaka-bEhag
73) kiranAvali
---------
74) latAngi
75) mAlavi
76) mAnavati
77) mAraranjani
78) mArgahindOlam
79) mAruvadhanyAsi
80) malavaSrI
81) manOhari
82) manOranjani
83) manasAmarthyavardhani
84) mandAri
85) mangalakaishiki
86) manirangu
87) manjari
88) nAdavarAngini
-------------------------
89) nAgAnandini
90) nAgaswarALi
91) nArAyaNi
92) nAsikAbhUShaNi
93) naBhOmani
94) nalinakAnti
95) navanItam
96) navarasakannada
-------------------
97) pUrNachandrika
98) pUrNalalita
99) pUrNashadjam
-----------
100) phalamanjari
101) phalaranjani
102) pharaju
103) pratApavarALi
104) rAgapanjaram
105) rAmapriya
106) rUpavati
107) ramAmanOhari
108)
109) rasALi
110) ravichandrika
111) revagupti
112)RishaBhapriya
113)sAlaga-Bhairavi
114) sAramati
115) sUlini
116) sUryakAnta
117) sarasAngi
118) sarasvati
119)sarasvati-manOhari
120) shanmukhapriya
=
121) siddhasEna
122) simhavAhini
123) sindhurAmakriya
===
124)supOShini
125) supradIpa
126)swarAvaLi
127) swaraBhuShaNi
128) tIvravAhini
129)udayaravichandrika
130) umABharana
131) vAchaspati
132) vAgadhIswari
-------------------------------
133)vIravasantha
134) VakulABharaNa
135) vanaspati ,
==
136) varamu
136) vasantha-Bhairavi
--------------------
137) vasantha-varaLi
138) vijayaSrI
139) vivardhani
140)amritavarshiNi
==========================
TOTAL 140 RAGAMS