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Analytical visions: Searching for hidden inter-raga relations via swara-set spreadsheeting – my formal comparison table of 300+ Hindustani ragas, analysing melodic geometries, symmetries, murchanas, 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 Hindustani music’s melodic complexity, we must ‘upgrade the mind’, using formalised methods to really see the hidden inter-swara connections. And, while I could have chosen more advanced software than Google Sheets, I wanted a free-access, 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 •

Divisions & manipulations (n.b. ‘m’=shuddha, ‘M’=tivra)

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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’]

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

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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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• Intervallic Geometries •

Analysing via ‘semitonal spacings’ to uncover new dimensions…

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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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• Congruents: Which other ragas have an identical swara set? [Search pitch class column for current raga’s sequence, print result count -1, e.g. Jhinjhoti‘s appears 7 times, thus it has 6 congruents]

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

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

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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‘]

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

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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‘]

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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 exact original sequence, excluding root positions]

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• Murchanas & More •

More fields to clarify, compare, check, etc…

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• Murchana: Possibles: 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‘ (…no raga can truly omit its own Sa!): also calculate other summary stats for the original swara set: e.g. degrees of freedom, unique rotation possibilities]

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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 murchana groupings, and some truly surprising inter-raga connections! See my Murchanas page for more.]

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

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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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• Flags: Various fields used to classify ragas according to the Full Tag List, often for visual or formatting clarity [e.g. Splitting into ‘audav/shadav/sampurna‘ via generic swara count, filtering ragas by varjit and double swaras, searching sequences for ‘diminished squares‘ (3-3-3-3) and ‘augmented triangles‘ (4-4-4), etc]

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(More soon: including separate aroha/avroh analysis)

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