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Analytical visions: Searching for hidden inter-raga relations via swara-set spreadsheeting – my formal comparison table of 320+ Hindustani ragas, analysing melodic geometries, symmetries, quirks, etc

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• Home | Megalist | Tags •

Swara Classifications | Intervallic Geometries | Murchanas & More

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Why turn to the spreadsheets? While ragas are never reducible to mere scale forms, my own state of knowledge will never expand to encompass the true fullness of the ragascape either. Given the melodic complexity of Hindustani music, we must ‘upgrade the mind’, using formalised methods to really find the hidden inter-swara connections. And, while I could have chosen more advanced software than just Google Sheets, I wanted a free-access and fully ‘visible’ format: you don’t need complex tools to carry out useful inquiry!

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—FULL RAGATABLE HERE—

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(Also see my ‘Megatable‘ of guitar tunings)

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• Swara Classifications •

Tonal divisions & manipulations…

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• Swara string: The main manual input required for each raga [the specific swaras in the raga’s ‘core form‘, entered in ‘Sa-to-Sa’ ascending order with ‘–‘ separators: e.g. Jog: ‘S-gG-m-P-n-S‘]

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• Specific swaras (#): How many specific swaras are in the raga’s core form? [Calculated as ‘string length without ‘-‘ characters -1’]

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• Generic swaras (#): How many generic swaras are in the raga’s core form? [Calculated as ‘count of ‘-‘ characters in string’]

(Sa–Re–Ga–Ma–Pa–Dha–Ni)

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• Chal: Which of the 10 ‘moveable swaras‘ are present in the raga’s core form? i.e. All specific positions other than the ‘achal‘ Sa and Pa [Print specific swara string with ‘S‘ and ‘P‘ characters removed, e.g. Jog: ‘SgGmPnS‘ > ‘gGmn‘)]

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• Poorvang-uttarang: Which swaras appear in the lower and upper portions of the saptak? [Reprint string as chromatic pitch classes (‘SrRgGmMPdDnNS‘), divide specific swaras into ‘poorvang | uttarang‘ (Jog: ‘SgGm‘ | ‘PnS‘), and group results by generic swaras (‘Sa-Ga-Ma‘ | ‘Pa-Ni-Sa‘)]

(Poorvang—Uttarang)

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• Intervallic Geometries •

Analysing via ‘semitonal spacings’

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• Pitch Classes: Which ‘pitch class positions’ does the raga occupy? [Reprint 13 specific swara cells as ‘0-12’ digits, then reappend: e.g. Jhinjhoti: ‘S-R-Gm-P-Dn-S‘ > ‘0-2-4-5-7-9-10-12‘]

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• ‘Imperfect’ swaras: Which swaras are ‘imperfect‘: i.e. with no available swara 7 semitones above (=perfect 5th sangati)? – e.g. Gangeshwari‘s shuddha Ga has no shuddha Ni above [Query relevant ‘+7 semitones’ columns to see which are unoccupied]

(‘imperfect’ shuddha Ga, e.g. Gangeshwari)

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• ‘Detached’ swaras: Which swaras are ‘detached‘: i.e. with no available swara 7 semitones above or below them (=perfect 5th up/down)? – e.g. Ahir Bhairav‘s komal re has no komal dha above or tivra Ma below [Query relevant ‘+7 and -7’ columns to see which are unoccupied]

(‘detached’ komal re, e.g. Ahir Bhairav)

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• Fragmented: Are at least half the swaras ‘detached’? (n.b. It is geometrically impossible for scales with 8 or more swaras to possess this property (and the only possible ‘fragmented’ 7-swara interval shape is the ‘unfilled’ thaat #11/22) [Query detached swara total to see if it is ≥50% of specific swara total]

(e.g. Rajeshwari [3/5] & Imratkauns [3/6])

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• Atritonal: Does the raga permit tritones (i.e. are any swara-pairs are separated by exactly 6 semitones [Query relevant ‘+6 semitones’ columns: if all are unoccupied, mark as ‘atritonal‘]

(e.g. Madhumad Sarang & Shankara)

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• Congruents: Which other ragas have an identical swara set (‘prakriti‘)? [Search pitch class column for current raga’s sequence, print result count -1, e.g. Ahiri‘s appears 3 times, thus it has 2 congruents: Jaiwanti Todi & Prabhateshwari]

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• Western: Restating the swaras as jazz-style ‘accidentalled’ scale steps (‘1,b2,2,b3,3,4,#4,5,b6,6,b7,7,8‘) and classical ‘C-rooted‘ notes (‘C,Db,D,Eb,E,F,F#,G,Ab,A,Bb,B,C‘) [Reprint specific swaras via direct character substitutions, e.g. Vachaspati: ‘1-2-3-#4-5-6-b7-1‘ & ‘C-D-E-F#-G-A-Bb-C‘]

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• Pattern: What is the raga’s ‘languageless’ dot-by-dot pattern? [Used for visual representations: Reprint pitch classes as binaries using ‘o‘ or ‘•‘, e.g. Vachaspati: ‘o • o • o • o o • o o • o’]

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• Sequences: What is the raga’s ‘noughts & crosses’ pattern? [Used for index-friendly searchability: Reprint pitch binaries as ‘x‘ or ‘o‘, as, e.g. Vachaspati: ‘xoxoxoxxoxxox‘]

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• Manipulations: How can the swara sequence ‘recombine’ with itself? [Reprint pattern in reverse (Jhinjhoti: ‘xoxoxxoxoxxox‘ > ‘xoxxoxoxxoxox‘), and ‘doubled’ (‘xoxoxxoxoxxoxoxoxxoxoxxox‘) in order to make a ‘complete loop’ from all chromatic positions, plus other related rearrangements: with the ‘octave-position Sa‘ (pitch class 12) swapped in and out as required]

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• Clusters: How many adjacent swara positions does the raga contain? [Search sequence for occurences of ‘xx‘ (=’hemitonic‘), ‘xxx‘ (=’cohemitonic‘), ‘xxxx‘ (=’co-cohemitonic‘), and ‘xxxxx‘ (=’co-co-cohemitonic‘) – or, if ‘xx’ does not appear, label as ‘anhemitonic‘]

(e.g. Malkauns, Chandrakauns, Jog, Miyan ki Malhar, Poorvi)

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• Symmetry: reflectional: Does the raga possess at least one reflection axis (‘mirror symmetry‘) [Search the raga’s ‘doubled sequence’ for complete occurrences of ‘reversed sequence’]

(all possible ‘mirror lines‘)

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• Symmetry: palindromic: Does the raga’s interval sequence read the same ‘forwards and backwards from Sa‘? [Just a ‘special class’ of mirror symmetry, where the axis runs ‘Sa–Ma‘]

(‘palindromicity‘)

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• Symmetry: rotational: Does the raga possess ‘rotational symmetry‘ (i.e. does its specific swara set produce at least one murchana identical to itself)? [Search ‘doubled sequence’ for recurrences of the original sequence, excluding the root position]

(‘rotational symmetry‘)

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• Murchanas & More •

Clarifying, comparing, checking, etc…

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• Murchana: options: Which scales are produced by ‘rotating the raga‘? [Print all 12 murchana possibilities via sequentially selecting the ‘next 13 characters’ from chromatic positions 0-12 in the ‘doubled sequence’ above, then exclude all results which start with ‘o‘, as no raga can omit its own Sa: also calculate other summary stats for the original swara set: e.g. unique rotation possibilities]

(Bhupali‘s ‘Re-murchana’ = Megh)

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• Murchana: matches: Which other ragas are exact ‘rotation matches’? [Query full ‘doubled sequence’ column for exact occurrences of the raga’s sequence, count results, then manually examine the most populous sets to identify and name them (e.g. Bilawal, Bihag, & Bhupali). This ended up as a somewhat convoluted ‘step-by-step’ manual process, adding the sequence of each new set to the search formula as it was identified: but yielded dozens of new groupings, and some truly surprising inter-raga connections! See my Murchanas page for more.]

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• Bhatkhande’s 10 thaat: Comparing the raga to Bhatkhande’s 10 thaat scales [If the raga has exactly 7 specific swaras, iteratively query for exact matches with each thaat sequence (e.g. Khamaj: ‘SRGmPDnS‘): and if it has less than 7 specific swaras, query each thaat for whether it ‘encloses‘ all the swaras (which may produce multiple results: e.g. Malkauns (SgmdnS) fits into both Bhairavi and Asavari thaat: SrgmPdnS & SRgmPdnS) – with remaining ragas marked as ‘inexact‘]

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• Expanded 32 thaat: Comparing the raga to the list of all 32 sampurna thaat – i.e. all scales with exactly 7 generic and 7 specific swaras [As above: minus the ‘enclosure’ step]

(Expanded ‘Dartboard‘ of 32 thaat)

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• More Fields: Various other fields used to classify ragas as per the Full Tag List, and also for general clarity  [e.g. Splitting into ‘audav–shadav–sampurna‘, filtering by varjit and double swaras, finding ‘diminished squares‘ (3-3-3-3) and ‘augmented triangles‘ (4-4-4), cross-checking all transcriptions against swara sets to identify mismatches, defining fields relevant to geometric quirks such as ‘centredness‘, ‘maximality‘, ‘komal Pa‘, etc…]

• All Tags & Classifiers •

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(More soon: including separate aroha/avroh analysis)

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