Murchanas: Raga Rotation

 

Spinning the wheels: Exploring the idea of ‘murchana’ in Hindustani music – including my systematic search for previously undiscovered rotational groupings, revealing some surprising geometric connections!

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–Taxonomy of Murchana–
• 5 swaras: Bhupali | Kalavati | Shivranjani • 6 swaras: Shankara | Jog | Hemshri | Kameshwari • 7 swaras: Bilawal | Charukeshi | Bhairav | Nat Bhairav | Basant | Kedar | Kirwani | Todi • 8+ swaras: Bihag | Lachari Kanada | Jaijaiwanti • Murchana Pairs
–More Murchana Musings–
• Jasrangi jugalbandi: simultaneous scales •
• Ravi Shankar’s swara-swirling car-ride •
• Self-murchanas: rotational symmetries •
• Global modalities: Messiaen & more •

What is murchana? ‘Murchana’ refers to ‘melodic rotation’ in Hindustani raga – i.e. ‘relocating the Sa within the same interval pattern’ to form a fresh scale. For example, if you treat Bhupali‘s Re as the ‘new Sa’, Megh is produced: as both are rotations of the same ‘round-the-octave’ sequence:

 

 

Essentially, murchana works along similar lines to the Western ideas of ‘modality’ and ‘relative major/minor’ (i.e. Cmaj and Amin share the notes CDEFGABC: just as Jaunpuri is the ‘Dha murchana’ of Bilawal). The concept can also be represented along a ‘swara-line’, showing how Bhupali and Megh draw from the same ‘recurring interval sequence’ (‘…2-2-3-2-3…’):

 

Next: A rundown of 18 notable murchana sets, unearthed via my Ragatable analysis (plus audio demos on my santoor)…

• Bhupali set (5) •

…2-2-3-2-3…

• Kalavati set (5) •

…4-3-2-1-2…

• Shivranjani set (5) •

…2-1-4-2-3…

• Kameshwari set (6) •

…2-4-1-2-1-2…

• Shankara set (6) •

…2-2-3-2-2-1…

• Jog set (6) •

…3-1-1-2-3-2…

• Hemshri set (6) •

…3-2-2-3-1-1…

• Bilawal set (7) •

…2-2-1-2-2-2-1…

• Charukeshi set (7) •

…2-2-1-2-1-2-2…

• Bhairav set (7) •

…1-3-1-2-1-3-1…

• Nat Bhairav set (7) •

…2-2-1-2-1-3-1…

• Kedar set (7) •

…2-3-1-1-2-2-1…

• Kirwani set (7) •

…2-1-2-2-1-3-1…

• Basant set (7) •

…1-3-2-1-1-3-1…

• Todi set (7) •

…1-2-3-1-1-3-1…

• Bihag set (8) •

…2-2-1-1-1-2-2-1…

• Lachari Kanada set (8) •

…2-1-1-1-2-3-1-1…

• Jaijaiwanti set (9) •

…2-1-1-1-2-2-1-1-1…

• Murchana Pairs •

Some other rotational partners I came across via querying the Ragatable (many of which also have their own prakriti forms: see individual raga pages). Let me know if you find any matches I’ve missed!

5: Devshri [Pa=Sa] Madhuranjani
5: Gunkali [dha=Sa] Kaushik Dhwani
5: Rajeshwari [ma=Sa] Chandramadhu
5: Chandrakauns [ma=Sa] Madhukauns
6: Marwa [re=Sa] Tulsikauns
6: Tilang [Pa=Sa] Jogeshwari
6: Lilavati [ni=Sa] Shivawanti
6: Malavi [Dha=Sa] Milan Gandhar
6: Jansammohini [ni=Sa] Raj Kalyan
6: Miyan ki Malhar [Re=Sa] Suha Todi
8: Virat Bhairav [ni=Sa] Tanseni Madhuvanti
9: Roopkali [Pa=Sa] Basanti Kanada
9: Enayetkhani Kanada [ma=Sa] Rang Malhar
10: Pilu [ma=Sa] Khat

—Chandrakauns [ma=Sa] Madhukauns—
Ranjani & Gayatri (2017)
“We present two ragas at the same time, through a device called murchana…”

—More Murchana Musings—

Further dimensions of this conceptual zone…

• Jasrangi Jugalbandi •

Mewati vocal pioneer Pandit Jasraj used murchana to bring new life to the male-female jugalbandi duet. This zone has long presented great challenge to raga performers – artists are rarely comfortable singing a full octave apart, and Hindustani music provides no explicit ‘harmony’ parts for higher voices. Said to have been inspired by a divine vision, Jasraj sought to overcome this by matching ragas which form near-exact rotations of each other, which could then be sung simultaneously.

 

Roughly translating as ‘Jasraj’s Colour-Duet’, the Jasrangi Jugalbandi is uniquely challenging, and remains rare on the concert stage. However, some superb examples turn up on record – notably including the modern experiments of fellow Mewati singer Sanjeev Abhyankar (e.g. below, seamlessly matching Abhogi & Kalavati with Ashwini Bhide-Deshpande, including double-tuned tabla!). A few further instances:

For me, this fascinating format deserves to be reinvigorated (then again, I may have something of a pro-murchana bias…). Raga practitioners: see where you can take it! Start by working out the most comfortable ‘interval split’ between the two voices, and then search the listings above for raga-pairs which are separated by around that interval – then, see how the pakads and chalans match up (you could even use the concept to create new forms of jod raga). And let me know how it goes!

 

—Kalavati [Pa=Sa] Abhogi—
Sanjeev Abhyankar & Ashwini Bhide-Deshpande (2013)
“My father died suddenly in 1934, and we all had to do our bit to shoulder the burden. I chose the tabla as my means of livelihood: my brother would sing, and I would accompany him. A very senior musician brought my relationship with percussion to an abrupt end, by deriding me for beating a dead animal’s skin – and therefore being utterly unqualified to talk about the finer points of music. I then decided that, henceforth, I would only sing…” (Pandit Jasraj)

• Shankar’s ‘Car ki Seat’ Set •

A pleasing tale of murchana in action…

More on the ‘Kameshwari set‘ above (from my Parameshwari page): Ravi Shankar’s wife Sukanya recounted the origins of Parameshwari in the liner notes to a 1971 release: “The inspiration…goes back to Chengali, a little village near Kolkata. Ravi-ji travelled to Chengali in the morning sometime in March 1968. While riding in the car, he conceived the nucleus of a melodic form that he later developed and called Kameshwari [‘Goddess of Love’]. By using the old murchana…system, he discovered three more ragas at the heart of Kameshwari: and Parameshwari [‘Supreme Lordess’] was one of them. The other two are Gangeshwari [‘Goddess of the Ganges’] and Rangeshwari [‘Goddess of Colours’].”

 

Thus, the Kameshwari set ‘appeared’ via a specific set of theoretical abstractions, rather than being derived from an evolving compositional repertoire. Such a specific origin tale sits in clear contrast to the vague, mythological histories of many ragas. As with Ali Akbar Khan’s Chandranandan (hastily improvised, named during a smoke break, and soon forgotten by its creator), the ease with which we can relate to the human aspects of the situation is almost jarring.

 

It’s hard for us to really imagine the atmospheres of Akbar’s 16th-century durbar – but we’ve all run melodies through our head to idle away long hours stuck in transit. This makes it easier to mull over other questions too: What was Shankar staring at through the window at the moment of Kameshwari’s conception? Would it even exist if he’d taken the train instead? What were his first impressions of its rotations (and why did he discard two of them: SrgGMdS & SRGdDNS)? […read more here!]

 

1 (S-R-M-P-D-n-S): Kameshwari
2 (S-G-m-P-d-n-S): Gangeshwari
4 (S-R-g-m-P-N-S): Rangeshwari
5 (S-r-g-m-D-n-S): Parameshwari
—Kameshwari (‘Goddess of Love’)—
Ravi Shankar (1972)
“My secret ambition was always to provide music for animation films: something with an Indian theme, either a fairytale, or on the Krishna theme. I still have a very deep desire, but these chances don’t always come…” (Ravi Shankar)

• Rotational Symmetries •

Spinning back to the starting swara set…

Some ragas are also ‘self-murchanas’ – i.e. if you rotate them through each available swara position, they form at least one scale identical to the original interval set. This property of ‘rotational symmetry‘ – arguably more abstruse than that of ‘reflective‘ symmetries – is vanishingly rare: with only two ragas in the Index displaying it precisely (n.b. for other rotatable possibilities, see ‘Messiaen’s Modes‘ below):

 

—Gaurimanjari—
  • An intricate ten-toned raga created by Ali Akbar Khan via blending ideas from across the Lalit–Gauri spectrum – which can be rotated 180o (i.e. flipping it along the palindromic S—M axis) to produce the same swara set. Arguably, Gaurimanjari’s rotational symmetry is of relatively subtle consequence, due to the winding complexity of its melodic motions and generally crowded swara-space (also, shades of shuddha Dha do sometimes appear…). Nevertheless, Khan and others (notably his student Brij Bhushan Kabra) have found fruit in exploring its wide-open geometries, which allow for many sub-symmetries and fine-set melodic interconnections.

—Sehera—
  • Among the strangest scales in the whole Hindustani pantheon, Sehera’s six swaras are each spaced in 2-semitone jumps (akin to the Western Whole-Tone scale and the Carnatic Gopriya). This structure produces an ‘equilateral hexagon‘, which is thus rotationally symmetric from all swara positions – summoning a curious, centreless mood (most famous as the ‘dream sequence‘ of countless soundtracks). Here it is on my santoor:
—Ghazal in Sehera—
Mehdi Hassan & Sultan Khan (1977)
“Sarangiya Sultan Khan once described Sehera as “the forbidden scale”, and, after pre-recording it for All India Radio, reportedly requested that his session “should not be aired…it is too sad”. Thankfully, he did cut a haunting ghazal with Mehdi Hassan, manipulating a GMdS refrain over ambiguous harmonium drones (…I mean, what would you even tune a tanpura to?)”

 • Global Modality •

How do other traditions spin their scales?

—The ‘Major Modes’—

A set of seven scales beloved in jazz, folk, film scoring, and far beyond – formed by rotating the Major Scale through each available position (listen below, recorded on my guitar). Essentially the ‘Bilawal set’ above (also equating to the first 6 of Bhatkhande’s thaat scales) – plus the ‘double-Ma, no Pa, ‘unfilled’ 7th position, named ‘Locrian’:

Ionian / Major (SRGmPDNS) = Bilawal thaat
Dorian (SRgmPDnS) = Kafi thaat
Phrygian (SrgmPdnS) = Bhairavi thaat
Lydian (SRGMPDNS) = Kalyan thaat
Mixolydian (SRGmPDnS) = Khamaj thaat
Aeolian (SRgmPdnS) = Asavari thaat
Locrian (SrgmMdnS) = ‘Lalit komal ga/ni‘

—Messiaen’s ‘Modes of Limited Transposition’—

Experimental French composer Olivier Messiaen (1908-1992) sought to identify and define a ‘master set’ of scales with rotational symmetry – titled ‘limited’ as they thus have fewer unique modes than tones (i.e. ‘self-murchanas’: all of which must possess at least two axes of reflectional symmetry). Messiaen identified seven such modes (other than the full chromatic scale), stating: ‘Their series is closed. It is mathematically impossible to find others, at least within our tempered system of 12 semitones” [n.b. more do exist, but only as ‘truncations’ of this set: i.e. formed by removing notes from the scales below]:

Messiaen Mode #1 (SRGMdnS) = Sehera / Whole-Tone Scale
Messiaen Mode #2 (SrgGMPDnS) = ‘Rampriya double Ga‘
Messiaen Mode #3 (SRgGMPdnNS) = ‘Simhendra Madh. dbl. Ga/Ni‘
Messiaen Mode #4 (SrRmMPdNS) = ‘Roopkali no Ga‘
Messiaen Mode #5 (SrmMPNS) = ‘Bihag no Ga/Dha‘
Messiaen Mode #6 (SRGmMdnNS) = ‘Ramkali no Pa komal dha‘
Messiaen Mode #7 (SrRgmMPdDNS): ‘Gaurimanjari se Ni’

—Arabic, Persian, & Turkish Maqam—

‘Maqam’ – the main melodic system of Arabic and Middle Eastern classical music – has significant historical and conceptual overlap with North Indian raga. As per Sami Abu Shumays, every contains “habitual melodic phrases, modulation possibilities, ornamentation techniques, and aesthetic conventions, that together form a rich melodic framework“. The overall concept, combining theoretical abstraction, aesthetic reflection, and cultural association, is something of a ‘distant cousin’ to Hindustani raga – both share elements of common ancestry, including through the diffusion of Islamic ideas in the Mughal period.

 

To oversimplify, each individual maqam (plural: ‘maqamat’) is constructed from two to three ‘building blocks’ known as ‘jins’ (plural: ‘ajnas’): cross-maqam scale-fragments comprising 3/4/5 nearby notes, which are stacked on top of each other to create full scales (usually with 7 notes, although some have more: and a few do not repeat at the octave). As with murchana, many maqamat form rotations of each other (although the numerical complexities of ‘quarterish-tone‘ intervals means that exact scalar overlap is somewhat rarer than in raga). Here are some ‘maqam modulation-pairs’ from Turath (n.b. G=’half–komal‘):

Yakah [‘Pa=Sa‘] Rast (~SRGmPDNS: like taking the ‘mean average’ of Gara‘s generic swaras, i.e. ‘gG>G‘)
Nawa [‘Pa=Sa‘] Bayati (~SRgmPdnS: like a similar ‘averaging’ of Asavari‘s komal and shuddha Re variants)
Busalik [‘Re=Sa‘] Nahawand (~SRgmPdnNS: like ‘Darbari double Ni‘, placing it close to Chandranandan)
Nahawand [‘ma=Sa‘] Farahfaza (~SrgGmPdnS: like ‘Darbari double Ga‘, or ‘Shivmat Bhairav‘s poorvang + Bhairavi‘s uttarang‘)
Shad Araban [‘Pa=Sa‘] Hijazkar (~SrGmPdNS: equatable to Bhairav, and its prakritis Gauri & Kalingada)
—The Arbitrariness of the Scale—
Sami Abu Shumays (2020)
“We can state our objections to the underlying assumptions common in both Western and Arabic music theory in another way: we do not find that there are rules underlying music, but habits. The elements of music must be learned individually: they cannot be derived from other elements of music…therefore the function of music theory from our perspective is not to make rules that ‘explain’ music…So many people falsely assume that you derive scales from mathematical principles, and melodies from rules…” (Sami Abu Shumays/Johnny Farraj)

—Javanese Gamelan—

Gamelan refers to the classical percussion ensembles of Indonesia – in particular, those of Bali and Java. Each ensemble is known as a ‘gamelan’ (from Javanese gamel, ‘to hammer’: distantly related, via Proto-Indo-European, to the English term ‘gavel‘) – a word which also describes the music they play on bronze gongs and chime bars of various shapes, sizes, and tunings. In the words of Suprabanggo, the origins of the music are “ancient and mysterious…gamelan predates the Hindu-Buddhist culture that dominated Indonesia in its earliest records, and instead represents a native art form”.

 

19th-century European composers including Debussy, Ravel, and Messiaen were entranced by gamelan, largely stemming from its showcase at the 1889 Paris World’s Fair (…it seems Debussy just hung out in the music pavilion listening to it for most of the expo). The music draws from a range of xenharmonic tuning systems – principally including the pentatonic Slendro (which approximates 5-tet) and Pelog (an uneven 7-note sequence loosely implying 9-tet). Here’s how they compare to the specific swara semitone positions:

 

(Cent-values of Pelog & Slendro: Objective Harmony)

Gamelan’s microtonally-tuned ‘note-menus’ have common ground with the idea of murchana, with compositions often being drawn from ‘sequential subsets’ of these ‘master scales’. These pseudo-melodic fragments (known as ‘pathet’) often comprise 5 of pelog’s 7 tones, roughly akin to combining the ideas of murchana and thaat scales (by applying the former to ‘limited ranges’ of the latter, which naturally leads to multiple murchana-like overlaps).

 

The famous composition Tabuh Pisan (below) is one such subset of Pelog, using tones 1-2-3-5-6, a grouping known in Javanese gamelan as ‘Pathet Nem’ (or, in another congruent variant, as ‘Pathet Lima’) – while any other pieces are in ‘Pathet Barung’, using tones 2-3-5-6-7. In some ways, this is rather like a ‘re-murchana’ of the original scale – but the concept of a ‘fixed Sa/root‘ is no easy fit with the complex, multi-modal modulations of gamelan (n.b. G=tuned flatter, Ṅ=tuned sharper: see above, although exact pitches vary by region):

Pelog: ~SṙGMPdṄ (closest to ‘Shree with significant sruti–alterations‘: re & Ni go higher, Ga & Ma go lower)
Pathet Nem: ~SṙGPd (somewhat like Bibhas if you ‘sruti-stretched‘ the re-Ga sangati)
Pathet Barung: ~ṙGPdṄ / SgMdN (either ‘Shree no Sa & Ma‘ / or, if taken as Shree’s Re-murchana, ‘Todi no Re & Pa‘)
—Tabuh Pisan (Pelog subset)—
Bangun Anyar (2022)
“According to Javanese mythology, gamelan was created by Sang Hyang Guru, the God who ruled as King of all Java from a palace on the Maendra Volcano. He needed a signal to summon his fellow gods, and thus invented the gong. For more complex messages, he invented two other gongs, forming the original gamelan set. Whatever its history may be, gamelan’s creative ethos stands out amongst South Asian traditions as being relatively untouched by the influences of Subcontinental culture: although Indian interactions are evident in some of the accompanying instruments: e.g. the similarly-named rebab fiddle and siter zither…” (from my Global Instrument Tunings article)

—Bonus: Rhythmic Rotations—

Numerous flamenco rhythm cycles (known as ‘compás’) are based around a particular 12-beat framework, with inter-beat gaps of ‘3–3–2–2–2’. Here’s the basic 12-pattern, which can be neatly displayed around a ‘clock face’ (n.b. the sequence is ‘symmetric’ along its ‘3-to-9 o’clock’ reflection axis: in similar fashion to how some ragas have ‘g—D mirror symmetry’):

 

 

This sequence is treated ‘modally’ – in other words, it can be ‘rotated’ so that the start of the cycle begins on a different beat: essentially, the rhythmic equivalent of ‘murchana‘. Three particular ‘starting points’ (beats 12, 1, and 8) have found enduring popularity, serving as the foundation for further percussive intricacy across a vast range of ‘palos’ (sub-styles), each of which calls for its own expressive subtleties – although the fundamental basis of ‘recycling’ the 3-3-2-2-2 sequence ensures an underlying consistency and cross-stylistic coherency…

(…read more in my Tala Index…)

  • Header image: ‘Nataraja: Shiva as Divine Cosmic Dancer’, bronze figurine of unknown Subcontinental origin (Commons)
  • Audio samples: Recorded on my santoor (tuned to A440 12-tet, Sa=D), lightly mastered in Ableton

 

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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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• Ragatable: Analytical connections •
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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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