Thaat Scales: Bhatkhande’s Base Forms & Beyond

 

Foundational forms: What are Bhatkhande’s ‘thaat scales’? How should they be applied to raga study, and how can we extend these classifications? And how do other global traditions conceptualise their ‘reference scales’?

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• Raga Index: Home •

—Bhatkhande’s Ten Thaat—
Kalyan • Bilawal • Khamaj • Kafi • Asavari
Bhairavi • Bhairav • Marwa • Poorvi • Todi
• How to use the scales •
—Further Foundational Forms—
• ‘Dartboard’ of 32 sampurna scales •
• Why the ‘unfilled’ thaat sequences? •
• Melakarta, merukhand, & more •
• Global ‘foundational scales’ •

What are thaat? The concept originates with theorist V.N. Bhatkhande (1860-1936), who proposed ten ‘reference scales’, each with 7 swaras, designed to help classify the ragascape (Thus, the common translation of ‘parent scale’ is misleading: the ragas long predate the scales!).

 

 

Some ragas fit exactly into a particular thaat (e.g. Yaman & Kalyan thaat), or can be described neatly enough (e.g. Vachaspati: ‘Kalyan thaat komal ni’) – although many more defy easy summarisation (e.g. Jog & Lalit). Next: the scales themselves, with audio clips on my santoor:

• Kalyan thaat •

S-R-G-M-P-D-N-S

1-2-3-#4-5-6-7-8
(Lydian Mode)
Exact: Yaman, Shuddha Kalyan
Enclosed: Bhupali, Deshkar, Jait Kalyan, Adbhut Kalyan, Noor Sarang, Hansadhwani, Hindol, Pahadi, Kesari Kalyan, Malashree, Raj Kalyan, Shankara

• Bilawal thaat •

S-R-G-m-P-D-N-S

1-2-3-4-5-6-7-8
(Major Scale)
Exact: Bilawal, Tilak Kamod, Nat, Bihari, Dagori, Gagan Vihang, Hem Bihag, Chaya Malhar, Hemant, Mand, Maluha, Manjari Bihag, Savani, Swanandi
Enclosed: Bhupali, Durga, Pahadi, Hansadhwani, Kaushik Dhwani, Bhinna Shadja, Nat Kamod, Shuddha Malhar, Jaldhar Kedar, Deshkar, Shankara, Rasaranjani, Jait Kalyan, Kesari Kalyan, Adbhut Kalyan, Bhavani, Malashree

• Khamaj thaat •

S-R-G-m-P-D-n-S

1-2-3-4-5-6-b7-8
(Mixolydian Mode)
Exact: Khamaj, Jhinjhoti, Gaoti, Sakh, Kambhoji, Khambavati, Kalashri
Enclosed: Bhupali, Durga, Megh, Gorakh Kalyan, Kalavati, Jansammohini, Rageshri, Bhavani, Deshkar, Jait Kalyan, Durgawati, Pahadi, Madhumad Sarang, Malashree, Jaldhar Kedar, Shuddha Malhar, Narayani

• Kafi thaat •

S-R-g-m-P-D-n-S

1-2-b3-4-5-6-b7-8
(Dorian Mode)
Exact: Kafi, Bageshri, Bhimpalasi, Shahana, Desi, Dhanashree, Hussaini Kanada, Mudriki Kanada, Raisa Kanada
Enclosed: Durga, Dhani, Megh, Abhogi, Shivranjani, Gorakh Kalyan, Bhavani, Durgawati, Gaudgiri Malhar, Madhumad Sarang, Jaldhar Kedar, Manavi, Shuddha Malhar, Narayani, Nayaki Kanada, Suha Kanada, Sundarkauns

• Asavari thaat •

S-R-g-m-P-d-n-S

1-2-b3-4-5-b6-b7-8
(Aeolian Mode)
Exact: Darbari, Kaunsi Kanada, Adana, Jaunpuri, Sampurna Malkauns
Enclosed: Malkauns, Megh, Dhani, Gopika Basant, Gaudgiri Malhar, Madhumad Sarang, Nayaki Kanada, Pancham Malkauns, Shobhawari, Suha Kanada

• Bhairavi thaat •

S-r-g-m-P-d-n-S

1-b2-b3-4-5-b6-b7-8
(Phrygian Mode)
Exact: Bhairavi, Bilaskhani Todi
Enclosed: Malkauns, Dhani, Bhupali Todi, Bairagi, Bairagi Todi, Saheli Todi, Gunkali, Gunakri, Gopika Basant, Pancham Malkauns

• Bhairav thaat •

S-r-G-m-P-d-N-S

1-b2-3-4-5-b6-7-8
(Double Harmonic Scale)
Exact: Bhairav, Kalingada, Gauri, Prabhakali
Enclosed: Jogiya, Bibhas, Devranjani, Gunakri, Gunkali, Bangal Bhairav, Zeelaf, Malashree, Triveni, Reva

• Marwa thaat •

S-r-G-M-P-D-N-S

1-b2-3-#4-5-6-7-8
(Lydian b2)
Exact: Puriya Kalyan, Shree Kalyan, Dakshinatya Basant, Baradi
Enclosed: Marwa, Puriya, Sohini, Hindol, Hansa Narayani, Malavi, Malashree

• Poorvi thaat •

S-r-G-M-P-d-N-S

1-b2-3-#4-5-b6-7-8
(Lydian b2 b6)
Exact: Shree, Puriya Dhanashree, Basant, Gauri Basant, Purva, Jaitashree, Tankeshree
Enclosed: Bibhas, Din ki Puriya, Hansa Narayani, Malashree, Reva, Triveni

• Todi thaat •

S-r-g-M-P-d-N-S

1-b2-b3-#4-5-b6-7-8
(Lydian b2 b3 b6)
Exact: Todi, Multani, Annapurna
Enclosed: Bhupali Todi, Gujiri Todi

• Applying the Scales •

As mentioned above, thaat are not, literally speaking, ‘parent’ scales (after all, the ragas came first!). They are more like ‘reference forms’, intended to aid with the organisation of ragascape knowledge. A few starting points for effective use:
  • Sequential riyaz exercises: Designed to span a general spread of ‘raga-relevant combinations’, thaat scales are an efficient setting for scale-based riyaz drills: e.g. running a generic pattern such as ‘Sa–Re–Ga–Ma, Re–Ga–Ma–Pa…’ through each thaat in turn (e.g. Kalyan: SRGM, RGMP, GMPD… vs. Bhairav: SrGm, rGmP, GmPd…). Also see ‘merukhand‘ below.
  • Generative creation: While not themselves formulated as ‘parent scales’, thaat can definitely be used to help spark the creation of new forms – and also to catalyse fresh questioning around the deeper tendencies of the swarascape (e.g. Why does Todi thaat enclose so few ragas? Why is the ‘Ma–ni‘ sangati mainly found in Carnatic imports? Does the Lalit-flavoured ‘double Ma, varjit Pa‘ combo actually function more like a ‘komal Pa‘? And which ‘alternate thaat’ might be possible? Read on…)
—Contributions of Bhatkhande (Sanskriti)—
“Bhatkhande realised that [vs. Carnatic ragam], Hindustani ‘parent scales’ were far fewer in number. This was partly due to aesthetic convention, which frowned upon the frequent juxtaposition of pitches…He added a rule to deal with this: each scale shall have just one note from the pairs [rR, gG, mM, dD, nN], to eliminate many of the half-tones…He called each of these scales a ‘thaat’ (‘manner, style’), and…with inductive argument, identified 10 thaats as being in common use, each named after an important raga…” (via Ramesh Gangoli)

BlackLineNARROWER

—Search the Raga Index—

• Also see the RAGATABLE •

• Beyond Bhatkhande’s Thaat •

Which other ‘fundamental scales’ are possible?

Then ten scales above – chosen by Bhatkhande for their classificatory utility – are only a fraction of the total potential set. So, how many are possible? As per his original formulation, all scales must be:

Given these axioms, we can calculate our set size (a process also carried out by Bhatkhande himself, and several others since). While we have 7 swaras to arrange, 2 are immovable (Sa, as the root, and Pa, as per tradition). The remaining 5 each offer a ‘higher/lower’ binary (‘komal/shuddha‘ for rR–gG–dD–nN, and ‘shuddha/tivra‘ for mM). Following this through in ‘decision tree’ fashion equates to [25=] 32 scales. See this process visualised on my ‘dartboard’ below!

 

–Dartboard: 32 Sampurna Scales–
‘Decision tree’ of scales, arranged as per the Carnatic melakarta:

(e.g. #9: ‘SP+MnGDR’ = SRGMPDnS = Vachaspati)

–Wheels: 32 Sampurna Scales–
The ‘results’ of our ‘dartboard decision tree’:

(n.b. dotted lines indicate ‘mirror symmetry‘)

–Corresponding Ragas–
(Click on swara sets to listen!)
[1] SRGMPDNS: Kalyan thaat
[2] SrGMPDNS: Marwa thaat
[3*] SRGMPdNS: (‘Kalyan komal dha‘)
[4] SrGMPdNS: Poorvi thaat
[5] SRgMPDNS: Madhuvanti
[6*] SrgMPDNS: (‘Todi shuddha Dha‘)
[7] SRgMPdNS: Simhendra Madhya.
[8] SrgMPdNS: Todi thaat
[9] SRGMPDnS: Vachaspati
[10] SrGMPDnS: Rampriya
[11*] SRGMPdnS: (‘Charukeshi tivra Ma‘)
[12*] SrGMPdnS: (‘Shree komal ni‘)
[13] SRgMPDnS: Madhukant
[14*] SrgMPDnS: (‘Ahiri tivra Ma‘)
[15*] SRgMPdnS: (‘Darbari tivra Ma‘)
[16*] SrgMPdnS: (‘Todi komal ni‘)
[17] SRGmPDNS: Bilawal thaat
[18] SrGmPDNS: Bhatiyari Bhairav
[19] SRGmPdNS: Nat Bhairav
[20] SrGmPdNS: Bhairav thaat
[21] SRgmPDNS: Patdeep
[22*] SrgmPDNS: (‘Patdeep komal re‘)
[23] SRgmPdNS: Kirwani
[24*] SrgmPdNS: (‘Bhairavi shuddha Ni‘)
[25] SRGmPDnS: Khamaj thaat
[26] SrGmPDnS: Ahir Bhairav
[27] SRGmPdnS: Charukeshi
[28] SrGmPdnS: Basant Mukhari
[29] SRgmPDnS: Kafi thaat
[30] SrgmPDnS: Ahiri
[31] SRgmPdnS: Asavari thaat
[32] SrgmPdnS: Bhairavi thaat
(See my ‘Thaat: Sampurna 32‘ category for all matching ragas)

• ‘Unfilled’ raga sequences •

Why are some scales ‘missing a raga’?

Of the 32 scales above, only 23 clearly match with known ragas (as far as I can trace…). So, why have the other 9 possibilities seemingly gone unused? Which ragas are they closest to, or expressible in terms of? And where else do these sequences turn up across the wide world of music?

 

Explore these ‘unfilled sampurna scales‘ below, along with some brief analysis (mainly derived via search-querying my Ragatable spreadsheet, as well as just staring at the swara-wheels in search of quirks and familiar features). n.b. I assume that at least a couple will already have matching ragas out there somewhere (…share your insights!)

 

(Wheels: the 9 ‘unfilled’ scales)

–Unfilled #3 (SRGMPdNS)–

• S-R-G-M-P-d-N-S •

Analysis: No other ragas appear to be only one ‘double-swara‘ away (i.e. produced by ‘doubling’ any one of #3‘s chal swaras, e.g. ‘S-R-G…’ > ‘S-rR-G…’). However, on further searching, it appears that the Carnatic Latangi been borrowed by a scattering of prominent Hindustani performers: including Nikhil Banerjee, Hariprasad Chaurasia, & Pravin Godkhindi. Thus, its ‘unfilled’ status can probably be revoked (…I’ll add it to the Megalist soon!).

 

–Unfilled #6 (SrgMPDNS)–

• S-r-g-M-P-D-N-S •

Analysis: Could be seen as a ‘shuddha Ni only’ version of Niranjani Todi, or perhaps more usefully, as an ‘all-vikrit‘ poorvang combined with an ‘all-shuddha‘ uttarang (i.e. rgM are all ‘altered’, while PDN are not) – essentially, a ‘Todi-low, Yaman-high’ concoction. 4 of the 7 swaras are imperfect (rgPD: a ‘whole-toned rectangle’), and no ragas in the current Index are just one ‘double-swara shift’ away – and neither can any be formed by removing only one of its swaras. The equivalent South Indian scale (Suvarnangi: ‘the golden-bodied one’) is also said to have no active murchanas in its own tradition, hinting at a high degree of geometric isolation.

 

However, during another round of foraging for rare ragas, I came across a recording with this exact swara set entitled ‘Madhu Multani‘ on Abhirang’s treasure-trove of a channel, taglined as “a blend of Madhuvanti and Multani” (seemingly a one-off experiment by the artist: I can’t trace any other recordings, and the only YouTube comment describes it as “apparently the only Hindust[ani] raga fitting into Suvarnangi mela for which audio is available…”). And, a few weeks later, I encountered another exact SrgMPDNS raga, again recorded only once: ‘Bhimsen‘, adapted directly from the Carnatic Suvarnangi by Mahesh Mahadev (“named after Bhimsen Joshi (‘Bhim-‘) and Miyan Tansen (‘-sen’)…it [omits] Re and Dha in the ascent”). So, in a literal sense, our #6 scale is not ‘unfilled’ in the North: although neither of its ragas have yet developed any self-sustaining lineage.

 

–Unfilled #11 (SRGMPdnS)–

• S-R-G-M-P-d-n-S •

Analysis: Probably best summarised as an ‘all-raised’ poorvang plus an ‘all-lowered’ uttarang (i.e. RGM are set to their highest positions, while dn are both komal) – like a ‘poorvang-uttarang’ combination of either ‘Yaman–Bhairavi‘ or ‘Vachaspati–Charukeshi‘ (n.b. both these raga-pairs are their own ‘murchana counterparts’: see Bilawal & Charukesi sets). Features the rare ‘tivra Ma, komal ni‘ sangati – and also a highly distinctive ‘whole-tone run’ (dnSRG: ‘2-2-2-2’), shared by Charukeshi, Imratkauns, and Sehera.

 

Intriguingly, 5 of the 7 swaras are imperfect (RGMPn), and 4 are ‘detached‘ (RGMn: i.e. with no swara 7 semitones above or below): in both cases, the mathematical maximum for a 7-note, 12-tet scale – suggesting that this interval pattern (along with its murchanas, including ‘unfilled #22‘ below) is, in some sense, the hardest possible sampurna canvas for creating ‘strong’ resolutions, as the only descending ‘Perfect 5th sangati‘ on offer is the ‘achal‘ Pa>Sa, present by default in all sampurna scales. Despite this, the Carnatic Rishabhapriya enjoys a respectable level of popularity, and can certainly generate its own strange shades of melodic magic (e.g. a fantastic rendition by Mandolin Srinivas). Still unrecorded in the North (as far as I can make out), although the challenges of its ‘maximally unresolving’ geometries may yet tempt intrepid performers…

 

–Unfilled #12 (SrGMPdnS)–

• S-r-G-M-P-d-n-S •

Analysis: Also expressible as ‘Malay Marutam add tivra Ma’ – although no ragas appear to be only one ‘double-swara‘ away. Ian Ring’s All the Scales database notes that Western textbooks have titled it the ‘Harsh Major-Minor‘ in reference to its geometric disbalances: 4 of the 7 tones (GPdn) are imperfect, and 2 (the tritonally-separated Gn) are ‘detached‘ – again, creating significant challenges around melodic resolution. As yet untraced in Hindustani music, although Abhirang has recorded a trio of near-prakriti ragas: the double-Ma ‘Lalit Kesari‘ (SrGmMPdnS: “created by [Rampur-Sahaswan vocalist] Hafiz Ahmed Khan…a blend of Lalit and Bhairavi“), plus ‘Vaishnavi‘ and ‘Mandhari‘ (both derived from Carnatic scales via, respectively, “omitting Pa in Namanarayani [=SrGMdnS]” and “omitting Dha in Ramapriya [=SrGMPnS]”).

 

–Unfilled #14 (SrgMPDnS)–

• S-r-g-M-P-D-n-S •

Analysis: Few Hindustani ragas lie close by (even the promisingly-named Ahiri Todi, despite our scale’s low-high split of ‘Todi+Ahiri‘) – likely due to its 4 imperfect swaras (rPDn) and the disbalancing Ma–ni sangati. The rare Salagavarali, devised by S.N. Ratanjankar, is a ‘no-Ma‘ near-match (SrgPDnS) – especially when sung by Jitendra Abhisheki, who includes slight shades of tivra Ma to compete the scale. Subbha Rao’s Raga Nidhi Vol. 4 (1966) discusses the freshly-created Salagavarali as “popularised by Ratanjankar…according to him it belongs to the 46th melakarta Shadvidamargini, [which] corresponds to a raga called ‘Khatma‘ in Hindustani sangeet“. While I can’t yet trace anything else about the lineage of this mysterious ‘Khatma’, the general direction of these experiments definitely warrants deeper exploration of our SrgMPDnS scale. Fittingly for our quest, ‘Shadvidamargini’ translates as ‘one with the path to a hundred forms of knowledge’.

 

–Unfilled #15 (SRgMPdnS)–

• S-R-g-M-P-d-n-S •

Analysis: Another fundamentally disbalanced form – arguably, the scale’s most distinctive ‘regularity’ is in how its 4 imperfect tones are arranged as a neatly equilateral ‘augmented triangle‘ (RMn: 4-4-4). Initially, the closest Hindustani match I could find was Madhukali, a barely-recorded invention of scholar and vichitra veena master Lalmani Mishra which differs only in its use of double-Ni (also nearby: the Ga-less Saraswati Kanada, dha-less Madhura Palasi, and ni-less Kanchanangi). Ocean of Ragas names two ragas as an exact match for the SRgMPdnS swara set – ‘Godhani’ and ‘Asakali’ – but all Godhani renditions I can find fit with Bilawal thaat instead, and I can’t trace a Raag Asakali in the wild at all (save for misspellings of ‘Asa Kafi‘).

 

More promisingly, Subbha Rao’s Raga Nidhi Vol. 4 (published in 1966) mentions that the Carnatic Shanmukhapriya – long popular in the South – had recently attracted some Northern interest. One of the few Hindustani takes I could find is by Dagarvani-trained sarodiya K. Sridhar, from a 1986 concert in Stockholm, who mines its odd contours to great effect (sometimes even hinting at a Pa-murchana: producing the scale of #24 below). Plus, Purbayan Chatterjee’s sitar solos in the scale on Shankar Mahadevan’s intriguing fusion track Shanmukhapriya: The Mystic (also featuring Snarky Puppy star Michael League on bass!). Still, despite its Southern strength, the scale is yet to develop a truly independent Hindustani lineage.

 

–Unfilled #16 (SrgMPdnS)–

• S-r-g-M-P-d-n-S •

Analysis: It also offers several handy murchanas, as a ‘missing member’ of the Kedar set, and has only two imperfect swaras (Pn) – while its reversal gives the ‘Major Scale b5‘. To me, this scale can be seen as the ‘final komal step’ in an imaginary ‘Kalyan > Marwa > Poorvi > Todi‘ chain – i.e. ‘start with all swaras set to their highest positions, then make one more of them komal each time, jumping in ascending 5ths from re’ (SRGMPDNS > SrGMPDNS > SrGMPdNS > SrgMPdNS > SrgMPdnS). These geometric proximities afford it a curious place in the raga universe: taking a heavyweight low-high split of ‘Todi–Bhairavi‘, while also being just a single swara-shift from both these ragas (…could it work as a ‘missing link’ between them? Either way, it is true that ‘#16 is to Yaman as Bhupali Todi is to Bhupali‘, in the sense of the formers being ‘all-komal’ versions of the latters: so maybe #16 should be called something like ‘Kalyani Todi‘?).

 

  • Side quest: following the ‘chal chain’: Given the ‘flattening pattern’ outlined above (‘flatten in order of ascending generic 5ths, starting from re’: i.e. ‘R>D>G>N‘), the next implied step (‘N>M‘) would lead to lowering the tivra Ma: producing ‘SrgmPdnS’, i.e. the ‘all-komal‘ Bhairavi (and thus traversing both numerical extremities of the dartboard: #1. Kalyan, #32. Bhairavi). After this, the next upward 5th-jump is the tritonal ‘M>S‘ – and, since Sa cannot be flattened, the resulting scale ends up ‘re-rooted’: as a ‘flat Sa’ just equates to raising all other swaras by the same amount: giving ‘SRGPdDNS‘ (‘Shankara double-Dha‘, or ‘Hansadhwani add double-dha’). This ‘shifting circle’ is completed with a final step of ‘S>P‘, introducing a ‘komal Pa‘, i.e. reintroducing the original tivra Ma (=’SRGMdDNS‘: or ‘Raj Kalyan double-dha’). [How long until you get back to the exact recurrence of the original scale form? Or if you do similarly with a different interval generator? Or go backwards around the swara wheel? Let me know!]

 

Jairazbhoy, having followed a similar 32-thaat derivation process, also discusses the scale – basing his analysis on the disbalance of ‘melodic gravities’ exerted by Pa and Sa (The Rāgs of North Indian Music, 1971, p.85): “Having argued that [SrgMPdnS] could have arisen in Indian music, we must now attempt some explanation for its absence in the current repertoire…In one respect, the scale [is] musically unstable…From the consonance-dissonance charts, the most dynamic [‘resolution-begging’] notes in the octave are the komal re, tivra Ma, komal dha, and komal ni. The re and ni demand resolution [to Sa], while the Ma and dha demand resolution [to Pa]. When Pa is a secondary drone, the demand for resolution on it is intensified. Three of these dissonant notes [rMd] are in the hypothetical thaat: as there is no Ni, only the re resolves in the Sa, while both Ma and dha demand resolution on the Pa. As a consequence…the Pa has a strong tendency to usurp the place of the Sa and lead to a plagal inversion” [n.b. this Pa-murchana produces SrgmMdNS: Mangal Todi]. He adds, “There would also be a very strong tendency to introduce shuddha Ni; both as a leading note in ascent, and to provide symmetry in the descending conjunct tetrachords. From the standpoint of balance…there [is] a strong tendency to introduce shuddha ma, and move the scale back to Bhairavi” [I guess all its swaras have been scattered into plenty of Mishra Bhairavi renditions, albeit non-exclusively].

 

–Unfilled #22 (SrgmPDNS)–

• S-r-g-m-P-D-N-S •

Analysis: In some senses the most surprising ragascape omission, given its robust ‘SmP triangle’, palindromic structure, and A-list poorvang–uttarang combination of ‘Bhairavi–Yaman‘ (=’all-komal low, all-shuddha high’). Also relatable to other famous palindromic forms: either ‘Bhairav komal ga shuddha Dha’ (i.e. shifting Bhairav’s G-d ‘one semitone closer to Sa’, thus retaining the original Sa–Ma symmetry), or ‘Kafi komal re shuddha ni’ (the same idea, but shifting R-n towards Sa instead). On the other hand, the SrgmPDNS scale (along with its murchana counterpart #11) contains 5 imperfect and 4 detached swaras: the maximum possible for a 7-note scale. Still, I’m surprised that I can’t yet trace any ragas which are only a ‘double-swara‘ away (i.e. produced by ‘doubling’ any one of #22‘s chal swaras, e.g. ‘S-r-g…’ > ‘S-rR-g…’) – although Abhirang’s Carnatic-borrowed ‘Kinnareshapriya‘ is a nearby ‘no-ma‘ relative (SrgPDNS). Ripe for exploration!

 

–Unfilled #24 (SrgmPdNS)–

• S-r-g-m-P-d-N-S •

Analysis: Aside from #22, the only ‘unfilled’ scale to have a shuddha ma – and again easily summarizable in terms of ultra-famous ragas, with a poorvang–uttarang of ‘Bhairavi–Todi‘ – as well as being a single swara-shift from both Bhairav and Kirwani (also expressible as ‘Jogiya add komal ga’, ‘Viyogavarali add Pa’, or, maybe most fittingly, ‘Devata Bhairav with komal ga only’). Its three imperfect swaras are arranged in an equilateral ‘augmented triangle‘ (gPN: 4-4-4 semitones), and only shuddha Ni is ‘detached‘ (and given Ni’s inherent function as an ‘unresolved’ as a leading-tone to Sa, it is probably the least consequential of all ‘detached’ swaras). My intuition is that experiments with the scale have probably been ‘subsumed’ into the Mishra Bhairavi framework (…just add komal Ni) – although a ‘Jogiya add komal ga’ angle could allow for unique impressions.

 

–General Observations–
From the above, several trends emerge…
  • 7 of the 9 scales take a tivra Ma: perhaps unsurprising, given the inherent strengths of the ‘S-m-P‘ sangati (=’a perfect 5th above and below Sa’), beloved across global music for its palindromic solidity. The presence of ‘tivra Ma but no Pa’ presents particular challenges when it comes to melodic resolution…
  • In fact, 5 of the 7 ‘as-yet-unfilled’ scales have the Ma–ni sangati, while the other two have ma–Ni…
  • Imperfect and ‘detached’ tones are common:
  • Only one has a familiar ‘reversal’ (#24 with Bhatiyari Bhairav: although #22 is palindromic, i.e. forms its own reversal). Due to the prevalence of the ‘MP’ pairing, all but the final two scales become non-sampurna when reversed: as ‘MP’ becomes the awkward ‘mM with no Pa’ (also see my ‘komal Pa’ raga category). In particular, the ‘mM-n’ sangati is vanishingly rare in the wild…I can only find one such ‘double-Ma, komal ni only’ raga: Ahir Lalit).

• Melakarta & Merukhand •

A couple of proximate theoretical constructs…

–The Carnatic Melakarta–

As discussed above, my ‘sampurna dartboard‘ draws heavily from the design of the South Indian ‘melakarta’: the predominant classification system used in Carnatic ragam. The melakarta taxonomises 72 different 7-note scales in similar ‘decision tree’ fashion – separating them by interval variant to form a dense-yet-logical ‘wheel’ structure:

—Melakarta Wheel: 72 Janaka Scales—

(Interval order: ‘Ma > Ri/Ga > Da/Ni’)

How does the melakarta differ from its Hindustani equivalent? As you can see, the wheel above is far more intricate than my dartboard, spanning more scales and many other curiosities. Most notably:
  • The melakarta has 72 scales (vs. our 32): This is due to the broader note-naming flexibilities of the South Indian system. In Hindustani music, each of the 12 specific swara positions is occupied by only one ‘note-letter’ (i.e. ‘SrRgGmMPdDnN‘) – whereas in Carnatic ragam, 4 of these positions can take either of two alternate names (shuddha Re: ‘Ri/Ga‘, komal ga: ‘Ru/Gi‘, shuddha Dha: ‘Di/Na‘, & komal ni: ‘Du/Ni‘). In other words, the Carnatic Ga & Dha each offer three positions (‘Ga/Gi/Gu‘ & ‘Da/Di/Du‘), vs. the Hindustani two (‘ga/Ga‘ & ‘dha/Dha‘):

  • It underpins a logical raga-naming system: In contrast to the general mess of Hindustani raga nomenclature, many of South India’s core set of 72 ‘janaka’ ragam are titled after their positions on the melakarta. To do this, they make use of katyapayadi: an ancient mnemonic practice based on encoding numbers into a sequence of Sanskrit syllables (totalling 33, including ‘Ka-Ta-Pa-Ya-Di‘). For example, the first two syllables of ‘Charukeshi‘ (‘Cha‘ & ‘Ra‘) correspond to the katyapayadi for ‘6’ and ‘2’, which are then combined in reverse order to reveal the raga’s position on the wheel (#26: ‘S-R2-G3-M1-P-D1-N2-S’ = SRGmPdnS). Go into more depth via the Carnatic Student site (“To memorize the kaṭapayādi, recite the entire series aloud: ‘Ka Kha Ga Gha Ṅa Ca Cha Ja Jha Ña; Ṭa Ṭha Ḍa Ḍha Ṇa Ta Tha Da Dha Na; Pa Pha Ba Bha Ma; Ya Ra La Va Śa Ṣa Sa Ha’...”)
  • Melakarta are more like actual ‘parent scales’: As mentioned above, Bhatkhande’s thaat scales were derived from study of the Hindustani ragascape (i.e. the ragas are the ‘parents’ of the scales). However, the Carnatic melakarta has often played a more ‘generative’ role, providing direct inspiration to performers and composers in their quest for new melodic forms – in contrast to our ‘unfilled thaat‘ above, all melakarta scales seem to have readily-traceable recordings, while some sources cite numerous historical figures who wrote songs in all 72 scales: including the great Muthuswami Dikshitar (“in the ‘asampurna mela‘ system which was prevalent during his time”), as well as Mangalampalli Balamuralikrishna (“by the age of 15 he had…composed songs in all the melakartas. The book, Janaka Raga Kriti Manjari, was published in 1952″), Kotishvara Iyer (“the first to compose the 72 melakarta in Tamil: all these songs are in praise of Subrahmanya [Hindu god of war]”), and his grandson Yazhpanam Viramani Iyer (“the Tirumayilai Karpakambal Kirtanaiga [was] published in 2000: all of the songs are in praise of Karpakambal” [‘Goddess of the Wish-Yielding Tree’, an avatar of Parvati]…”).
  • The melakarta includes ‘non-melodic’ cultural associations: While the dartboard above is merely an ‘intervallic decision tree’, the Carnatic equivalent also features specific symbolic identifiers, in the form of 12 chakram divisions (the red ring above), linked to a range of ancient cultural associations. Each contains exactly 6 ragam (72/12=6), which, due to the wheel’s particular interval hierarchy (‘Ma > Ri/Ga > Da/Ni’), differ from each other only in their placements of Dha & Ni (which each take 3 positions: 3*2=6 ragam per chakram):
  1. Indu (“the moon…of which we have only one”)
  2. Netra (“the eyes, of which we have two”)
  3. Agni (“the three forms of divine fire”)
  4. Veda (“the four Vedas [Rig-, Yajur-, Sama-, & Atharva-]”)
  5. Bana (“the five arrows of Manmatha, God of Love”)
  6. Rutu (“the six grishma [seasons] of the Hindu calendar”)
  7. Rishi (“the saptarishi [seven great sages]“)
  8. Vasu (“the ashtavasu [eight fire deities] of Hinduism”)
  9. Brahma (“the nine [chosen] forms of the deity”)
  10. Disi (“the ten directions [N/S/E/W, NE/NW/SE/SW, up/down]”)
  11. Rudra (“the eleven deities of divine storm winds”)
  12. Aditya (“the twelve avatars of Vishnu’s Vamana incarnation”)

–Merukhand: Unique Sequences–

Another North Indian swara-sequencing technique, known as ‘merukhand’ (or ‘khandmeru’: literally ‘divisional analysis’) – involves deriving all possible ‘unique sequences’ from a given swara-set. This is calculated via the ‘factorial’ of the swara count (denoted, with pleasing spark, as ‘n!‘). Merukhand’s axioms are fairly similar to those of the dartboard, except with the goal of denoting how many sequences are possible in any order (vs. just ascending sampurna forms). For example:

  • 3 swaras: 3! = 3*2*1 = 6 (SRG, SGR, RSG, RGS, GSR, GRS)

This process involves an exponential increase in complexity:

Thus, practical use of the system is typically limited to the seven sapta swara (…more akin to the dartboard). As per Amir Khan, perhaps the most prominent merukhand aficionado: “My father made me practise the 5040 taan patterns which are possible through permutation [of] the 7 notes…for 22 years…Even [with] akaar, you should be clear which note you are singing…Due to this practice, I can do any number of variations…”).

 

Khan adds: “Later, I realised that out of these 5040 patterns, only 168 are useful“. This figure (exactly 30 times smaller) is primarily because many intervals between different swara-pairs are of identical pitch-distance (e.g. S>P, r-d, M-N are all 7-semitone leaps, despite occupying different specific positions). In his own explanation, “For knowledge of swaras, and for riyaz, practice of aroha–avroh is the first step. In our system, there are 360 alankars [phrase-shapes] and 5040 paltas [sequences]. To remember all of them is very difficult, if not impossible. Therefore, I have prepared 168 swara mailas [‘combinations’]“.

 

Learn more about the Ustad’s thinking in the interview below (turn subtitles on), and go deeper into how he applied these ideas to raga via Ibrahim Ali’s excellent Amirkhani Khayal: e.g. “To maintain the importance of nyas…Khan only considered those permutations in which no harm was done to the raga if a pause was laid on the final note. In Bageshri, he applied Pa in both aroha and avroh, but didn’t pause on it. Similarly, maintaining the role of komal re in Ahir Bhairav when improvising with ‘SrGm’, using permutations of ‘SGmr, SmGr, SrGm, SGrm, GmrS’…these phrases were applied very emotionally during alap“.

 

—Merukhand Interview (Amir Khan)—
“There is something called ‘khandmeru’: it has 5040 taans, starting [SRGMPDNS] and ending [SNDPMGRS], with no repetitions. In my childhood, I knew them all by heart. This gave me a lot of help: now, I can go wherever I want to. But the entire set of 5040 is too much to remember. So I created a ‘simplified subset’ of 168 taans, chosen for their practical uses (I even gave them to Vilayat Khan, whether he agrees I don’t know!). They particularly help in vilambit, as I can apply the same sur in multiple ways with these ‘stock variations’, giving scope and variety…” (Amir Khan)

–Global ‘Foundational Scales’–
How do other cultures use ‘base scales’?
  • T: In

–Further Learnings–
Onward links for my fellow swara-sequencing explorers…
  • Vishnu Narayan Bhatkhande (1860-1936): In my reckoning, the ‘Chatur-pandit’ exerted more influence on actual performance practice than virtually any other global music theorist of the past couple of centuries. Learn about his life in the video below, as well as via Ramesh Gangoli, and also Sriram V in The Hindu (“He qualified in law, and set up practice at the High Court of Bombay….[later] he began to ponder over the fact that Hindustani music did not have a structured curriculum…He travelled far and wide across North India, collecting information about the way music was taught in the various gharanas. He then moved South, coming to Madras in 1904…”).
—Bhatkhande Memorial Lecture (Ashok Da Ranade, 1998)—
“[Bhatkhande] lost both his wife and daughter after short illnesses…having a profound effect on him. He never married again, never gave further ‘hostages to fortune’, and devoted an increasing proportion of his mental life to musical contemplation. True to his promise to his father, he never sought to be a performer…His bent was more for acute observation, analysis, and synthesis. This, naturally, led him to musicology…” (Ramesh Gangoli)

  • Header images: My haphazard geometric renderings of the 32 scales (InDesign/Photoscape X)
  • Audio samples: Recorded on my santoor (tuned to A440 12-tet, Sa=D), lightly mastered in Ableton (with added drones)

 

[MORE TO FOLLOW]

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• Hindustani Raga Index •

An open-ended project seeking to bring North Indian raga closer to all who approach with open ears. Combines direct input from dozens of leading Hindustani artists with in-depth insights from music history, global theory, performance practice, cognitive science, and much more! [out 2023]

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George Howlett is a London-based musician, writer, and teacher (guitars, sitar, tabla, & santoor). Above all I seek to enthuse fellow sonic searchers, interconnecting fresh vibrations with the voices, cultures, and passions behind them. See Homepage for more, and hit me up for Lessons!

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