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’?
• Raga Index: Home •
—Bhatkhande’s Ten Thaat—
—Further Foundational Forms—
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 •
(Lydian | Mechakalyani)
Reverse: SrgmMdnS | Negative: 3-2-2-3-2 | Imperfect: 1 (Ma) | Detached: none | Symmetries: mirror (ga—Dha) | Murchanas: Bilawal set | Quirks: ‘maximal‘
Exact: Yaman, Shuddha Kalyan | Enclosed: Bhupali, Deshkar, Jait Kalyan, Adbhut Kalyan, Hansadhwani, Hindol, Pahadi, Kesari Kalyan, Malashree, Raj Kalyan, Shankara
• Bilawal thaat •
Reverse: SrgmPdnS | Negative: 3-2-3-2-2 | Imperfect: 1 (Ni) | Detached: none | Symmetries: mirror (Re—dha) | Murchanas: Bilawal set | Quirks: ‘maximal‘
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, Shuddha Malhar, Jaldhar Kedar, Deshkar, Shankara, Rasaranjani, Jait Kalyan, Kesari Kalyan, Adbhut Kalyan, Bhavani, Malashree
• Khamaj thaat •
Reverse: SRgmPdnS | Negative: 2-2-3-2-3 | Imperfect: 1 (Ga) | Detached: none | Symmetries: mirror (re—Pa) | Murchanas: Bilawal set | Quirks: ‘maximal‘
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 •
(Dorian | Kharaharapriya)
Reverse: SRgmPDnS | Negative: 2-3-2-2-3 | Imperfect: 1 (Dha) | Detached: none | Symmetries: mirror (Sa—Ma) | Murchanas: Bilawal set | Quirks: ‘palindromic‘, ‘maximal‘
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 •
(Aeolian | Natabhairavi)
Reverse: SRGmPDnS | Negative: 2-3-2-3-2 | Imperfect: 1 (Re) | Detached: none | Symmetries: mirror (ma—Ni) | Murchanas: Bilawal set | Quirks: ‘maximal‘
Exact: Darbari, Kaunsi Kanada, Adana, Jaunpuri, Jungala, Sampurna Malkauns | Enclosed: Malkauns, Megh, Dhani, Gopika Basant, Gaudgiri Malhar, Madhumad Sarang, Nayaki Kanada, Pancham Malkauns, Shobhawari, Suha Kanada
• Bhairavi thaat •
(Phrygian | Hanumatodi)
Reverse: SRGmPDNS | Negative: 3-2-2-3-2 | Imperfect: 1 (Pa) Detached: none | Symmetries: mirror (Ga—ni) | Murchanas: Bilawal set | Quirks: ‘maximal‘
Exact: Bhairavi, Bilaskhani Todi, Darjeeling | Enclosed: Malkauns, Dhani, Bhupali Todi, Bairagi, Bairagi Todi, Saheli Todi, Gunkali, Gunakri, Gopika Basant, Pancham Malkauns
• Bhairav thaat •
Reverse: SrGmPdNS | Negative: 4-1-3-3-1 | Imperfect: 3 (Pa, dha, Ni) | Detached: none | Symmetries: mirror (Sa—Ma) | Murchanas: Bhairav set | Quirks: ‘palindromic‘ • ‘centred‘
Exact: Bhairav, Kalingada, Gauri, Prabhakali | Enclosed: Jogiya, Bibhas, Devranjani, Gunakri, Gunkali, Bangal Bhairav, Zeelaf, Malashree, Triveni, Reva
• Marwa thaat •
(Lydian b2 | Gamanasrama)
Reverse: SrgmMdNS | Negative: 4-1-2-3-2 (e.g. Sundarkauns) | Imperfect: 2 (re, Pa) | Detached: none | Symmetries: none | Murchanas: Deepavali (on Pa)
Exact: Puriya Kalyan, Shree Kalyan, Purva, Baradi | Enclosed: Marwa, Puriya, Sohini, Hindol, Hansa Narayani, Malavi, Malashree
• Poorvi thaat •
Reverse: SrGmMdNS | Negative: 4-1-4-1-2 | Imperfect: 2 (Pa, dha) | Detached: none | Symmetries: none | Murchanas: Basant set
Exact: Shree, Puriya Dhanashree, Basant, Gauri Basant, Jaitashree, Tankeshree | Enclosed: Bibhas, Din ki Puriya, Hansa Narayani, Malashree, Reva, Triveni
• Todi thaat •
Reverse: SrGmMDNS | Negative: 4-2-1-4-1 | Imperfect: 2 (ga, Pa) | Detached: none | Symmetries: none | Murchanas: Todi set
• 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.
- Ragascape organisation: Many ragas can be neatly summarised via comparison to their ‘nearest thaat’ (e.g. Ahiri: ‘Kafi komal re‘, Jansammohini: ‘Khamaj no ma‘, or Dev Gandhar: ‘Asavari double-Ga‘). Similarly, a raga’s thaat designation can give clues as to its melodic behaviour (e.g. Bhupali Todi is enclosed by both Todi and Bhairavi thaat: but performers will prioritise the phraseologies of the Todi raganga).
- 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 did Bhatkhande include all possible sangatis except ‘Ma–ni‘, and why does this combination scarcely exist outside 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)
—Search the Raga Index—
• 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:
- Heptatonic (=7 specific swaras)
- Sampurna (=all 7 sapta swara)
- In aroha order (i.e. no vakra)
- Achal Pa (remains ‘immovable’)
- Sruti-invariant (no microtones)
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–
(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‘)
(Click on swara sets to listen!)
 SRGMPDNS: Kalyan thaat
 SrGMPDNS: Marwa thaat
 SrGMPdNS: Poorvi thaat
 SRgMPDNS: Madhuvanti
 SrgMPdNS: Todi thaat
 SRGMPDnS: Vachaspati
[11*] SRGMPdnS: (‘Charukeshi tivra Ma‘)
 SRGmPDNS: Bilawal thaat
 SrGmPDNS: Bhatiyari Bhairav
 SRGmPdNS: Nat Bhairav
 SrGmPdNS: Bhairav thaat
 SRGmPDnS: Khamaj thaat
 SrGmPDnS: Ahir Bhairav
 SRGmPdnS: Charukeshi
 SrGmPdnS: Basant Mukhari
 SRgmPDnS: Kafi thaat
 SRgmPdnS: Asavari thaat
 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!)
–Unfilled #3 (SRGMPdNS)–
- Jod: ‘Yaman‘s poorvang + Todi‘s uttarang’
- Proximate: ‘Kalyan komal dha’, ‘Poorvi shuddha re’, ‘Nat Bhairav tivra Ma’, ‘Simhendra Madhyamam shuddha Ga’
- Reverse: S-r-G-mM-d-n-S (=none)
- Murchanas: Bhatiyari Bhairav (on Pa)
- Carnatic: Latangi (mela #63)
- Jazz: 1-2-3-#4-5-b6-7-8
• 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)–
- Jod: ‘Todi‘s poorvang + Yaman‘s uttarang’
- Proximate: ‘Todi shuddha Dha’, ‘Puriya Kalyan komal ga’, ‘Madhuvanti komal re’
- Reverse: S-r-g-mM-D-N-S (=none)
- Murchanas: (none found)
- Carnatic: Suvarnangi (mela #47)
- Jazz: 1-b2-b3-#4-5-6-7-8
• 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)–
- Jod: ‘Yaman‘s poorvang + Bhairavi‘s uttarang’
- Proximate: ‘Charukeshi tivra Ma’, ‘Vachaspati komal dha’
- Murchanas: ‘Unfilled #22‘ (on Pa)
- Reverse: S-R-G-mM-d-n-S (=none)
- Carnatic: Rishabhapriya (mela #62)
- Jazz: 1-2-3-#4-5-b6-b7-8
• 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: i.e. with no swara 7 semitones above), and 4 are ‘detached‘ (RGMn: i.e. with no swaras 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)–
- Jod: ‘Marwa‘s poorvang + Bhairavi‘s uttarang’
- Proximate: ‘Poorvi komal ni’, ‘Basant Mukhari tivra Ma’, ‘Rampriya komal dha’
- Reverse: S-R-G-mM-d-N-S (=none)
- Murchanas: (none found)
- Carnatic: Namanarayani (mela #50)
- Jazz: 1-b2-3-#4-5-b6-b7-8
• 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)–
- Jod: ‘Todi‘s poorvang + Kafi‘s uttarang’
- Proximate: ‘Ahiri tivra Ma’, ‘Madhukant shuddha Re’, ‘Rampriya komal ga’
- Reverse: S-R-g-mM-D-N-S (=none)
- Murchanas: (none found)
- Carnatic: Shadvidamargini (mela #46)
- Jazz: 1-b2-b3-#4-5-6-b7-8
• 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)–
- Jod: ‘Madhuvanti‘s poorvang + Bhairavi‘s uttarang’
- Proximate: ‘Asavari tivra Ma’, ‘Madhukant komal dha’, ‘Simhendra Madhyamam komal ni’
- Reverse: S-R-G-mM-D-n-S (=none)
- Murchanas: ‘Unfilled #24‘ (on Pa)
- Carnatic: Shanmukhapriya (mela #56)
- Jazz: 1-2-b3-#4-5-b6-b7-8
• 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, sitarist Purbayan Chatterjee’s 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)–
- Jod: ‘Todi‘s poorvang + Bhairavi‘s uttarang’
- Proximate: ‘Todi komal ni’, ‘Bhairavi tivra Ma’
- Reverse: S-R-G-mM-D-N-S (=’Bilawal komal pa‘)
- Murchanas: Kedar (on re), Jogeshwari Pancham (on ga), Mangal Todi (on Pa)
- Carnatic: Bhavapriya (mela #44)
- Jazz: 1-b2-b3-#4-5-b6-b7-8
• 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 a theoretical ‘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: listen below). 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 named something like ‘Kalyani Todi‘?).
- Side quest: following the ‘chal chain’: Given the ‘flattening pattern’ outlined above (‘flatten in order of ascending 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 then transformed with a step of ‘S>P‘, introducing a ‘komal Pa‘, i.e. reintroducing the original tivra Ma (=’SRGMdDNS‘: or ‘Raj Kalyan double-Dha‘). At this point, there is no ‘next perfect 5th’ to flatten (which, in this case, would be M>r), thus ending the sequence. [To extend this concept: which combinations of ‘starting points’ and ‘jump vectors’ would eventually lead to an exact recurrence of the original scale form? Share your insights!]
Jairazbhoy, having followed a similar 32-thaat derivation process, also discusses the SrgMPdnS scale – basing his analysis on the disbalance of ‘melodic gravities’ exerted by Pa and Sa (The Ragas of North Indian Music, 1971, p.85): “Having argued that it 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)–
- Jod: ‘Bhairavi‘s poorvang + Yaman‘s uttarang’
- Proximate: ‘Patdeep komal re’, ‘Ahiri shuddha ni’, ‘Bhatiyari Bhairav komal ga’
- Reverse: S-r-g-m-P-D-N-S (=itself, i.e. ‘Palindromic‘)
- Murchanas: ‘Unfilled #11‘ (on ma)
- Carnatic: Kokilapriya (mela #11)
- Jazz: 1-b2-b3-4-5-6-7-8
• 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, 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)–
- Jod: ‘Bhairavi‘s poorvang + Todi‘s uttarang’
- Proximate: ‘Bhairavi shuddha Ni’, ‘Bhairav komal ga’, ‘Todi shuddha Ma’, ‘Kirwani komal re’
- Reverse: S-r-G-m-P-D-N-S (=Bhatiyari Bhairav)
- Murchanas: ‘Unfilled #15‘ (on ma)
- Carnatic: Dhenuka (mela #9)
- Jazz: 1-b2-b3-4-5-b6-7-8
• 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’ 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.
We can now sort our 32 thaat into three approximate categories: Bhatkhande’s chosen set (10), other ‘raga-filled’ thaat (13), and our ‘unfilled’ scales (9). While these bounds are somewhat arbitrary (particularly between ‘filled’ and ‘unfilled’), we can still observe some broad geometric trends:
- 7 of the 9 ‘unfilled’ scales take a tivra Ma: perhaps unsurprising, given the strengths of the ‘Sa–ma–Pa‘ sangati (=’a perfect 5th above and below Sa’), beloved across global music for its palindromic solidity (see global scales below). The presence of tivra Ma presents particular challenges around melodic resolution (as noted in the analysis of #16): lying a tritone from Sa, and greatly strengthening the role of Pa as a resolution point (whereas shuddha ma cannot be imperfect or detached, as all ragas must contain Sa). For similar reasons, tanpuras are often tuned Sa-ma, but never Sa–Ma (…well, almost never: see Abhirang’s Tivrakauns & Abdul Latif Khan’s rendition of Hindol).
- 5 of the 7 ‘still-unfilled’ scales have the ‘Ma–ni’ sangati: the only swara-pairing which is entirely absent from Bhatkhande’s ten (in fact, I’ve only come across four 7-swara ragas with ‘tivra Ma only, komal ni only‘: Vachaspati, Hemavati, Madhukant, & Rampriya). As discussed by Jairazbhoy, the ‘Ma–Pa–ni’ combination can tempt the ear into hearing a scale as its own Pa–murchana, as the hemitonic ‘Ma>Pa’ is a more emphatic resolution than the 2-semitone ‘ni>Sa’: emphasised by the fact that all such ragas will take a Sa-Pa tanpura tuning. Underlying this is a cross-cultural tendency to hear the higher note of a hemitonic pair as the ‘home tone’ (‘Ma–Pa‘).
- Imperfect and ‘detached’ tones are unusually common: Due to the ‘circle of 5ths’ generation of our 12-semitone scale, all non-chromatic ragas must contain at least one ‘imperfect’ tone (i.e. one with no available swara 7 semitones above it). However, our ‘unfilled’ scales contain more than usual: while Bhatkhande’s 10 thaat have an average of 1.5 ‘imperfect’ swaras each, the 13 ‘filled’ sequences average over 3 each (~3.07), and the ‘unfilled’ scales over 3.5 (~3.66). Similarly, ‘detached’ swaras (i.e. with no swara 7 semitones above or below) are vastly overrepresented: in fact, none of Bhatkhande’s 10 contain any detached swaras (making me suspect that he may have held this as an explicit selection axiom), and the 13 ‘filled’ thaat have only 16 between them (~1.23 each) – the same total as across the 9 ‘unfilled’ scales (~1.77 each). Scales #11 and #22 (murchanas of each other) both contain 4 detached swaras: the mathematical maximum for any 7-note 12-tet scale – as well as the maximum allowable 5 imperfect swaras. At the other extreme, the oddity of #16’s ‘unfilled’ status is highlighted: having only 2 imperfect and no detached swaras.
- Only one unfilled scale has a familiar ‘raga reversal’ (#24 with Bhatiyari Bhairav: although #22 is palindromic): mainly as the prevalent ‘Ma–Pa’ becomes non-sampurna when reversed (‘MP’ flips to the rare ‘mM & no Pa’ (see Lalit and my ‘komal Pa’ category). While this concept of ‘reversal‘ is of less consequence than the other modes of analysis, a near-total absence of ‘reverse congruents’ is still unusual enough to mention: implying a general awkwardness of intervallic shape.
• 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:
—The Melakarta: 72 Janaka Scales—
(Interval order: ‘Ma > Ri/Ga > Da/Ni’)
How does the melakarta differ from its Hindustani equivalent? As you can see, it is far more intricate than my dartboard, spanning more scales and other curiosities. Most notably:
- The melakarta has 72 scales (vs. 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 tones 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 Hindustani positions for R/g & D/n each have two ‘enharmonic’ Carnatic names (see below). Refer to Shivkumar Sharma‘s Southern-imported Rasikpriya rendition for an demonstration of these differences in action (mela #72, or S-gG-m-P-nN-S: effectively ‘Yaman tivra Re & 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, with numerous historical figures writing 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″), plus 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: in praise of Karpakambal” [‘Goddess of the Wish-Yielding Tree’, an avatar of Parvati]).
- The melakarta includes ‘non-melodic’ cultural associations: While my dartboard 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 combine to give 6 unique ragam per chakram):
- Indu (“the moon…of which we have only one”)
- Netra (“the eyes, of which we have two”)
- Agni (“the three forms of divine fire”)
- Veda (“the four Vedas [Rig-, Yajur-, Sama-, & Atharva-]”)
- Bana (“the five arrows of Manmatha, God of Love”)
- Rutu (“the six grishma [seasons] of the Hindu calendar”)
- Rishi (“the saptarishi [seven great sages]“)
- Vasu (“the ashtavasu [eight fire deities] of Hinduism”)
- Brahma (“the nine [chosen] forms of the deity”)
- Disi (“the ten directions [N/S/E/W, NE/NW/SE/SW, up/down]”)
- Rudra (“the eleven deities of divine storm winds”)
- 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:
- 3 swaras: 3! = 6
- 4 swaras: 4!= 24
- 5 swaras: 5! = 120
- 6 swaras: 6! = 720
- 7 swaras: 7! = 5040
- 8 swaras: 8! = 40,320
- 9 swaras: 9! = 362,880
- 10 swaras: 10! = 3,628,800
- 11 swaras: 11! = 39,916,800
- 12 swaras: 12! = 479,001,600
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, and in Vijay Bakshi’s Practical Application of Merukhand – and go deeper into how Khan applied these ideas to raga via Ibrahim Ali’s excellent Amirkhani Khayal: “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…giving scope and variety.” (Amir Khan)
–Global ‘Foundational Scales’–
How do other cultures use ‘base scales’?
• Indonesian gamelan •
As covered in my Murchanas article, the bronze-gong percussion traditions of Bali and Java derive much of their repertoire from ‘sequential subsets’ of two fundamental scales, known as ‘Pelog’ (‘fine, beautiful’) and ‘Slendro’ (possibly named for a far-removed incarnation of Indra, the Hindu god of sky, lightning, and storms). Both are heavily microtonal, with some positions deviating far from their raga equivalents:
- ‘Pelog‘: ~S-r-g-m-P-dD-S (srutis: r/m/D higher, g/P/d lower)
- ‘Slendro‘: ~S-R-m-P-n-S (srutis: R/P higher, m/n lower)
Gamelan composition often utilises ‘pseudo-melodic fragments’ of these scales, known as ‘pathet’ – e.g. only 5 of Pelog’s 7 tones are used in ‘Pathet Nem’ (1-2-3-5-6), while ‘Pathet Barung’ uses tones 2-3-5-6-7 – although Pelog’s 4th tone (an ‘ati tivra‘ shuddha ma) may feature as a kind of ‘free-use accidental’. On the abstract level, gamelan has very different conceptions of ideas such as ‘scale’ or ‘root’, mostly shaped by the constraints of physical circumstance: once cast, metal gongs and chime bars cannot be retuned, meaning that ensembles are essentially ‘locked in’ to whichever scalar framework they are built around.
(Cent-values of Pelog & Slendro: Objective Harmony)
—Tabuh Pisan (Pelog subset)—
“In Balinese music, there is a basic rhythmic structure that excites me. It involves creating a continuous pulse by the interlocking of two independent and separate parts, which have rests or silences in between. The interlocking of simple separate parts to produce a flowing continuity is a distinctly Balinese feature: which appears in their gamelan music, at a very, very high speed. This is ensemble virtuosity of a totally different sort than African music…in which you have two different rhythms conflicting and overlaying.” (Steve Reich: read more in my Global Instrument Tunings article)
• Japanese traditions •
Like Indian raga, Japanese classical music comprises many disparate strands: spanning Buddhist temple chant to the instrumental songs of the Imperial Palace, alongside a plethora of folk-derived forms and other localised innovations. Consequently, several ‘fundamental sequences’ have been employed over the centuries, often taking a ‘pentatonic-plus-two’ shape (i.e. five tones at their core, plus two optional extras).
As usual, English-language scholarship contains plenty of conflicting information regarding the note-sets of these scales. For the most part, this is down to the fact that Japanese melodic concepts don’t really match with our ideas of ‘scale’: operating more like a mix of ‘note collection’, ‘tuning framework’, and ‘murchana set’. For example, while the ‘Yo scale’ may be notated as S-g-m-P-n-S or S-R-m-P-D-S, it is best understood as the ‘general interval sequence’ underlying both (a rootless, repeating ‘…3-2-2-3-2…’: see Bhupali murchana set):
- ‘Ryo‘: S-R-G-P-D-S [+M/N]: (~Bhupali [/Kalyan]): Of uncertain origin, but thought to be among Japan’s oldest patterns – matching, in a common transposition, the Major Pentatonic (a truly trans-cultural sequence)
- ‘Ritsu‘: S-R-m-P-D-S [+g/n]: (~Durga [/Kafi]): Another ancient scale, possibly a Japanese modification of Chinese folk ideas – which can be used in conjunction with Ryo to form mixed sequences known as ‘Hanryo-Hanritsu’.
- ‘Yo‘: S-g-m-P-n-S [+R/d]: (~Dhani [/Asavari]): Underlies the early evolution of both shomyo (Buddhist chant) and gagaku (classical court song: first officially recognised by the Imperial Bureau of Music in 702 A.D.).
- ‘In‘: S-r-m-P-d-S [+g/n]: (~Gunakri [/Bhairavi]): Originally prominent on the koto (multi-bridge zither) and shamisen (3-string lute). Alternately titled ‘Miyako-bushi’, or ‘Sakura’ (‘cherry blossoms’) after a famous composition.
- ‘Hirajoshi‘: S-R-g-P-d-S: (~’Shivranjani komal dha’): Adapted from shamisen by Yatsuhashi Kengyo (1614-1685), the father of ‘modern’ koto (hira-choshi: ‘tranquil/regular tuning’). Also borrowed into Hindustani music as ‘Japaneeya’.
- ‘Insen‘: S-r-m-P-n-S: (~Bairagi): Likely formed through combining portions from the In and Minyo sequences (Srm+PnS), rising to prominence in the music of the Imperial courts around the same era as Hirajoshi’s adoption.
- ‘Ryukyu‘: S-G-m-P-N-S (~’Bilawal no Re/Dha’): A major-flavoured scale named for its popularity in the Ryukyu island chain, thought to have exerted influence on Polynesian and other Pacific Ocean traditions via Okinawan folk song.
Despite Delhi and Tokyo being separated by almost 6,000km, strands of Subcontinental influence are apparent in Japanese classical music. Apart from Buddhism’s beginnings in the Kingdom of Magadha (circa 600 B.C.E.), Indian-origin devotional chants are believed to have reached Japan via China, helping to shape the ‘old music’ gagaku compositions of the pre-Tang era (~618 A.D.) – as hinted at by the number of raga-matches above. Learn more in Aishik Bandyopadhyay’s intriguing Comparative Study of Indian Ragas and Japanese Scales, as well as the work of Tim Hoffman, a longtime ‘raga-shakuhachi’ innovator.
—Shakuhachi Masterpieces (1990)—
“The shakuhachi was used by ‘komuso‘: priests who begged or sometimes spied while wandering the streets playing the flute incognito, their heads covered by special wicker basket hats. With the changes that had occurred in Japanese society, many former warriors no longer carried their swords…One curious side-effect was the appearance of a shakuhachi tucked in the back of one’s belt: for use as a musical device, or as a club…” (Britannica)
• European ‘church modes’ •
Starting around the 6th century, European liturgical traditions began to develop a style known as ‘plainsong’, based on unaccompanied vocal recitation of Latin religious texts. Absent of polyphony or meter, these chants drew from a variety of sources, ranging from Roman and Galician church music to the tetrachordal systema teleion of Ancient Greece.
Despite the relative diversity of its roots, plainsong quickly began to coalesce around a central melodic framework (in part due to specific decrees issued by religious authorities). Now known as the ‘ecclesiastical modes’, this system was originally based on four ‘authentic’ and four ‘plagal’ (‘Hypo-‘) scales, with the latter derived by shifting the roots of the authentic scales four positions lower in the same sequence (e.g. the ‘Dorian’ and ‘Hypodorian’ utilise the same note-set, but the Dorian’s low perfect 5th is the Hypodorian’s ‘new base tone’). The names were chosen by Hucbald, a 9th-century French monk, based on his own highly speculative interpretations of Mediterranean history (e.g. the Aeolia, Ionia, Lydia, Phrygia, and Doris regions are located in modern-day Turkey).
- ‘Dorian‘: S-R-g-m-P-D-n-S (~Kafi):
- ‘Hypodorian‘: S-R-g-m-P-d-n-S
- ‘Phrygian‘: S-r-g-m-P-d-n-S (~Bhairavi)
- ‘Hypophrygian‘: S-r-g-mM-d-n-S
- ‘Lydian‘: S-R-G-M-P-D-N-S (~Kalyan)
- ‘Hypolydian‘: S-R-G-m-P-D-N-S
- ‘Mixolydian‘: S-R-G-m-P-D-n-S (~Khamaj)
- ‘Hypomixolydian‘: S-R-G-m-P-D-n-S
Again, these sequences do not match neatly with our modern ideas of ‘scale’. Most importantly, each has particular tones designated as the ‘finalis’ (‘melodic endpoint’: loosely akin to vishranti) and the ‘tenor’ (‘dominant tone’, to be elongated or emphasised: see deergha & vadi). In absolute terms, the finalis of each ‘authentic’ mode is also the finalis of its ‘plagal’ counterpart (e.g. the Dorian’s ‘Sa‘ is the Hypodorian’s ‘ma‘: just as Asavari is the 5th murchana of Kafi), but each one will take different dominants (e.g. the Dorian’s ‘Pa‘ vs. the Hypodorian’s ‘dha‘).
Later, three more scales – the Aeolian, Ionian, and Locrian – were added to the set, via a process of expansion completed by Swiss theorist Glareanus in the 16th century. However, in modern times, all seven ‘authentic’ scales above are typically grouped together, primarily to maintain a rotational ‘full house’ (see Bilawal murchana set). Intriguingly, some aspects of raga evolution line up with the European historical sequence: with the Dorian/Kafi as the ‘original’ primary mode, later supplanted in this role by the Ionian/Bilawal in the post-medieval era (hence today’s ‘unaccidentalled‘ Major Scale and ‘all-shuddha‘ Bilawal thaat) – with the awkwardly tritonal Locrian/SrgmMdnS as the last and least-used addition (see Meladalan: Acharya Brahaspati’s ‘thaat-breaking raga’).
- ‘Aeolian‘: S-R-g-m-P-d-n-S (~Asavari)
- ‘Hypoaeolian‘: S-r-g-m-P-d-n-S
- ‘Ionian‘: S-R-G-m-P-D-N-S (~Bilawal)
- ‘Hypoionian‘: S-R-G-m-P-D-n-S
- ‘Locrian‘: S-r-g-mM-d-n-S (~Meladalan)
- ‘Hypolocrian‘: S-R-G-M-P-D-N-S
Naturally, there is further nuance. When approximated using the modern system of ‘12-tone equal temperament’, many of the ‘plagal’ and ‘authentic’ modes appear to be congruent with each other: however, in the tuning frameworks of their own era, this was not the case (principally, the original scales take tones and semitones of differing width, generally prioritising consonant intervals at the expense of coherence and consistency elsewhere: see ‘just intonation’, ‘Pythagorean tuning’, and ‘paucitonality‘). Plainsong composers also applied further quirks: some tones could be flattened under certain conditions, while others became classified into various hierarchical supporting roles.
The rise of polyphonic music (such as by Leonin and Perotin in the 12th century) – and its associated tuning systems – relegated the role of these ‘church modes’ to the history books for several hundred years (in particular, the ‘plagal’ modes were rendered largely obsolete via their newfound congruences). However, in more recent times, the seven ‘authentic’ scales have again risen to prominence, used as a staple in the analysis of jazz, classical, and film music – as well has serving as a concise ‘bridge’ between global traditions (I use them in this project to ‘translate’ swara-sets for my fellow jazzers, e.g. ‘Marwa thaat: Lydian b2‘, or ‘Miyan ki Malhar: Dorian double 7th‘). Here they are on my guitar:
—Modes of the 16th/17th Century—
“Dorian: Majestic, steadfast, constant, severe, moves phlegm… Hypodorian: Pompous, confident, slothful, forbidding, submissive… Phrygian: Exciting, martial, mournful, incites to anger and war… Hypophrygian: Austere, grave, calm, plaintive, appeases anger… Lydian: Funereal, lamenting, sad, harsh, convivial, dignified… Hypolydian: Bacchic, intoxicating, tearful, pleasing but inelegant… Mixolydian: Threnodic, tranquil, exciting, withdrawn… Hypomixolydian: Sublime, incorrupt, sweetness, natural charm… Aeolian: Serious and pleasant… Ionian: Agreeable, sweet, suitable for dancing…” (The Ethos of Modes: compiled by Patricia O’Scannell from Gaffurius 1518 & Glarean 1547 – with listening links courtesy of composer Andrew Downes)
• More global scales •
Naturally, there are countless more ‘scalar frameworks’ in use around the world – which vary wildly in terms of their tones, tunings, geometries, melodic conventions, and basic conceptual groundings. For a few more intriguing dimensions of this zone, consider:
- Maqam: The quarter-tonal framework underlying most Arabic & Middle Eastern classical music, based on combining tetrachordal fragments known as ‘jinn’ into scale-like sequences – read more in my Murchanas article
- Sub-Saharan: Many indigenous traditions in Southern Africa conceptualise their scales as ‘moving downwards as the pitch rises‘ (also see Shivkumar Sharma’s ‘vertical inversion‘ idea, inspired by the shapes of the Himalayas)
- Stave notation: Western classical sheet music displays a ‘C major bias’, with this being the default ‘un-accidentalled’ scale (along with its relative A minor): also visible in the piano’s arrangement of white/black keys
- Overtonal scales: Any scale produced from the overtones of the harmonic series will in some way mirror the ‘hard-wired’ constituents all resonant sound (see Vachaspati: which approximates overtones #8-13)
- Transcultural modes: A few scales – notably including the pentatonic Bhupali shape – seem to turn up in virtually all musical cultures, spanning Scottish and South American folk songs to Palaeolithic bone flutes…
—Power of the Pentatonic—
“I would like to discover a method so that if one of my friends is ill, I’d…play a certain song and he will be cured; when he’d be broke, I’d bring out a different song and immediately he’d receive all the money he needed. But what are these pieces, and what is the road to travel to attain a knowledge of them? That I do not know.” (John Coltrane: from my forthcoming Trane’s Raga Mystery project)
Onward links for swara-sequencing explorers…
- Vishnu Narayan Bhatkhande (1860-1936): In my reckoning, the ‘Chatur-pandit’ may have exerted more influence on actual performance practice than virtually any other global music theorist of the past few 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)—
“[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)
- Historical classification systems: Bhatkhande, when devising his thaat in the early 20th century, took direct inspiration from Venkatamakhin’s Chaturdandi Prakashika (‘Illumination of the Four Dimensions of Music’), a 17th-century precursor to the modern melakarta. Naturally, the lineage does not begin here, with Venkatamakhin in turn drawing from the Swaramela Kalanidhi (‘Wealth of Ragas, Scales, and Arts’): authored circa 1550 by Ramamatya, a composer and architect at King Ramaraja’s court, who, among other classificatory concepts, assigned ragas as ‘superior/middling/inferior’ based on their expressive salience. I’ll publish a full ‘long-scale raga history’ article sometime, but for now, read more about the great lakshanagranthas (scholarly writings) of past eras: notably including Bharata Muni’s 200 C.E. Natyashastra (‘Principles of Dramatic Arts’: an eye-wateringly precise guide to the ‘proper’ performance of music, dance, and drama), and Sarngadeva’s ~13th-century Sangita Ratnakara (‘Ocean of Music and Dance’: an elaboration of 253 ragas via concepts such as swara, sruti, murchana, jati, alankar, sangeet, and nada brahma).
- Header images: My haphazard geometric shatterings of the 32 scales (InDesign/Photoscape X)
- Audio samples: Recorded on my santoor/guitar (tuned to A440 12-tet, Sa=D/A), lightly mastered in Ableton (plus drones)
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• Search: Find your new favourite •
• Tags: Classifying the ragascape •
• Glossary: Raga jargon demystified •
• Murchanas: Swara-set rotations •
• Thaat: Bhatkhande’s base scales •
• Ragatable: Analytical connections •
• Tanpuras: Divine overtonal drones •
• Quotes: Musings from raga artists •
• Talas: Hindustani rhythm cycles •
—Search the Raga Index—
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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