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R. @RangaTheDude
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A thread on kerala hand gestures or mudras used in vedic chanting. Madhyandina hasta mudras appear to be an independent tradition and is passed over right now.
According to Dr. Mannur Jatavedan Nambutiri, ŕşi vaikhānasa lead by parashurāma formulated the kerala style of japasvara and mātrāsvara for udātta and anudātta vedic svaras.
As per a text 'madhushiksha', the padapāțha of Rig veda is attributed to Ravana. This is from a quotation of the text in vedavikŕtivivaraņam by shrī P.M. Damidaran Nambutiripad. He also adds while commenting that hastamudrā tradition is explained by Ravana.
Why did the system of hastamudras arise? When the samhitā pāțha is broken into padas svaras change; sandhi is broken; words morph. Hasta mudras clarify what is going on.
For e.g. the samhitā reading "ajoşā vŕşabham patim". The ajoşā may contain dīrghasvarita or dīrghānta. Grammar is not initially taught to the pupils. But the hand gestures resolve the ambiguity. The student will understand when he learns it later.
The following shakhas employing hasta mudras in KL. Śākalya of Rig veda, taittiriya of Krishna Yajurveda and jaiminiya of sāmaveda. Taittiriya system is a subset of rig veda. The samaveda employs gestures for svaras and mātrās, employing the forearm extensively.
There are 30 types of mudras in RV tradition. Some are based on mātrās of a syllable - hrasvamudra for short vowel, dīrghamudra for long vowel. Some are based on place of articulation - oşțhya mudra, mūrdhanyamudra
To be continued...
Enumerating the list quickly with extra notes on mudras I find interesting (Disclaimer: I don't know kathakali)
1. hrasva mudra - gesture for short vowel. This can be overridden by other mudras like udātta. Hamsapaksha in kathakali.
2. ākāra mudra - for syllables ending in ā.
Patākā in kathakali.
3. Tālavyadīrgha - mudra for long palatal vowels ī and ū. Bāņa in kathakali.
4. Aikāra mudra - for syllable ai. Similar to 3 but little finger rotated.
5. Oşțhya dïrgha - mudra for long labial vowels ū, o, au. Mukuļa in kathakali.
6. Ukāra - mudra for short u. Kartarīmukha in kathakali.
7. Anusvāra - mudra for short anusvāra. Muşți in kathakali.
8. Dīrghānusvāra - for long anusvāra.
9. Hrasvavisarga - for short visarga; mudrākhya in kathakali
10. Dīrgha visarga- long visarga; sūcimukha in kathakali
Index finger moved slightly up and down if the visarga is preceded by ai or au.
11. Prathamānta mudra - mudra when a word ends in 'first' consonant of varga (k, ch, ț, t, p).
12. ghoşa mudra - text is confusing. It appears to be for voiced aspirates gha, jha, ďha, dha, and ha.
Apparently useful when samhitā is unaspirated but padapātha word is aspirated; e.g: dakshat in samhitā vs dhakshat in pada.
13. Svarapūrvaka takāra - dental t with preceding vowel. Hand is supine for short vowel and pronated for long vowel.
14. Missing
15. Mūrdhanya - retroflex
Mudra. Used in CV where C is retroflex ța varga, şa or ļa and C is short vowel or e. Also used for şya and şva unless there is a svarita on it. E.g. uruşya, kŕńuşva. Then it takes the hrasva mudra.
16. ti or tithi- mudra for syllables ending with ti or thi.Mŕgaśirşa in kathakali
17. Udātta - Marks udātta in a word of the mantra.
18, 19: nakāra and ņakāra mudras. IMO to clarify dental na vs retroflex ņa.
20. Akārasūchaka- I find this interesting. Mudra for a in doubtful sandhi. Examples:
Vidharmaņāyatraih RV 10.46.6 splits into vidharmaņā + ayatraih and
Not vidharmaņā + yatraih. The a in ayatraih ia indicated by the mudra.
Naijan RV 1.63.1 -> na + aijan and not ejan.
Yathohişe RV 8.5.3 -> yathā + ohişe and not ūhişe. Expected samhitā form should really be yathauhişe.
21. Mudra for repha, vikāra, prakŕti and utpatti.
Repha eg: punah. Padapāțha punar iti. The repha r in punar.
Vikāra or modification: indicates a change from retroflex to dental in padapāțha. dūđhyah -> duh dhyah; vŕşapāņāsah -> vŕşa pānāsah. Ņ becomes n.

Prakŕti - natural form. Clarifies initial gh, d, dh, n, r, ś or s is
Natural and not due to sandhi. E.g. RV 6.11.5 srug ghŕtavatī is sruk + ghŕtavatī and not hŕtavatī. gh is original in the word.
Utpatti - when a sound is added in padapāțha. RV 10.11.5 cit kambhanena -> cit + skambhanena. Additional s.
22. Vikāranişedha - mudra to denote the ABSENCE of modification from retroflex to dental in the padapāțha. E.g. praņeşat -> neşat in pp and not nesat.

23. Hrasvīkaraņa - when a vowel shortens in padapāțha. Vāvŕdhāte in samhita -> vāvŕdhate in pada.
24. Ūm iti - mudra shown when ūm iti occurs in padapāțha
25. Avagraha - mudra shown when a compound word in samhita splits in padapāțha. E.g. pra + śastaye.
26. Si mudra - shown when word ends with si, sī, se, sya or sva. Bhramara in kathakali.
Based on article written by Assistant professor K.P. Parvathy, VTB college, Mannampatta, Palakkad.
I notice it doesn't have all the 30. I omitted short notes on samaveda, yajurveda and kodanthiruppuli village style jaiminiya samaveda. The last one is not a nambudri style at all and has roots in TN.
Here is a sample of sarpa sāman in kodanthiruppuli style:
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