OTC JI 22 sruti scale: Difference between revisions
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This page examines the [[ | {{stub}} | ||
This page examines the [[omnitetrachordality]] of the 22-tone Indian 'sruti' scale, a 5-limit [[Just_intonation|JI]] scale with three step sizes -- one of many possible theoretical tunings for Indian classical music. (This scale may be found in the [[Scala|Scala]] archive as <tt> indian.scl </tt>.) | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 142: | Line 143: | ||
| style="text-align:center;" | '''step size''' | | style="text-align:center;" | '''step size''' | ||
|- | |- | ||
| style="text-align:center;" | 1-2 | | style="text-align:center;" | 0-1-2-3-4 | ||
| style="text-align:center;" | 256/243 | | style="text-align:center;" | 256/243-81/80-25/24-81/80 | ||
| style="text-align:center;" | A-b-c-b | |||
| style="text-align:center;" | | |||
|- | |- | ||
| style="text-align:center;" | 5-6 | | style="text-align:center;" |4-5-6-7-8 | ||
| style="text-align:center;" | 256/243 | | style="text-align:center;" | 256/243-81/80-25/24-81/80 | ||
| style="text-align:center;" | A | | style="text-align:center;" | A-b-c-b | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | 8-9-10-11-12 | ||
| style="text-align:center;" | 256/243-81/80-25/24-81/80 | |||
| style="text-align:center;" | A-b-c-b | |||
| style="text-align:center;" | | |||
| style="text-align:center;" | A | |||
|- | |- | ||
| style="text-align:center;" | 12-13 | | style="text-align:center;" | 12-13 | ||
| style="text-align:center;" | 256/243 | | style="text-align:center;" | 256/243 | ||
| style="text-align:center;" | A | | style="text-align:center;" | A | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | 13-14-15-16-17 | ||
| style="text-align:center;" | 81/80 | | style="text-align:center;" | 256/243-81/80-25/24-81/80 | ||
| style="text-align:center;" | b | | style="text-align:center;" | A-b-c-b | ||
|- | |- | ||
| style="text-align:center;" | 20-21 | | style="text-align:center;" | 17-18-19-20-21 | ||
| style="text-align:center;" | 25/24 | | style="text-align:center;" | 256/243-81/80-25/24-81/80 | ||
| style="text-align:center;" | c | | style="text-align:center;" | A-b-c-b | ||
|- | |- | ||
| style="text-align:center;" | 21-22 | | style="text-align:center;" | 21-22 | ||
| style="text-align:center;" | 256/243 | | style="text-align:center;" | 256/243 | ||
| style="text-align:center;" | A | | style="text-align:center;" | A | ||
| Line 237: | Line 178: | ||
| | <tt> Abcb AbcbAbcbA AbcbAbcbA </tt> | | | <tt> Abcb AbcbAbcbA AbcbAbcbA </tt> | ||
| | <tt> AbcbAbcbA bcbA AbcbAbcbA </tt> | | | <tt> AbcbAbcbA bcbA AbcbAbcbA </tt> | ||
| | | | | <tt> AbcbAbcbA AbcbAbcbA Abcb </tt> | ||
|- | |- | ||
| | <tt> bcbA bcbAbcbAA bcbAbcbAA </tt> | | | <tt> bcbA bcbAbcbAA bcbAbcbAA </tt> | ||
| | | | | <tt> AbcbAbcbA Abcb AbcbAbcbA </tt> | ||
| | | | | <tt> bcbAbcbAA bcbAbcbAA bcbA </tt> | ||
|- | |- | ||
| | <tt> cbAb cbAbcbAAb cbAbcbAAb </tt> | | | <tt> cbAb cbAbcbAAb cbAbcbAAb </tt> | ||
| | | | | <tt> bcbAbcbAA bcbA bcbAbcbAA </tt> | ||
| | | | | <tt> cbAbcbAAb cbAbcbAAb cbAb </tt> | ||
|- | |- | ||
| | <tt> bAbc bAbcbAAbc bAbcbAAbc </tt> | | | <tt> bAbc bAbcbAAbc bAbcbAAbc </tt> | ||
| | | | | <tt> cbAbcbAAb cbAb cbAbcbAAb </tt> | ||
| | | | | <tt> bAbcbAAbc bAbcbAAbc bAbc </tt> | ||
|- | |- | ||
| | <tt> Abcb AbcbAAbcb AbcbAAbcb </tt> | | | <tt> Abcb AbcbAAbcb AbcbAAbcb </tt> | ||
| | | | | <tt> bAbcbAAbc bAbc bAbcbAAbc </tt> | ||
| | <tt> | | | <tt> AbcbAAbcb AbcbAAbcb Abcb </tt> | ||
|- | |- | ||
| | <tt> bcbA bcbAAbcbA bcbAAbcbA </tt> | | | <tt> bcbA bcbAAbcbA bcbAAbcbA </tt> | ||
| | | | | <tt> AbcbAAbcb Abcb AbcbAAbcb </tt> | ||
| | <tt> | | | <tt> bcbAAbcbA bcbAAbcbA bcbA </tt> | ||
|- | |- | ||
| | <tt> cbAb cbAAbcbAb cbAAbcbAb </tt> | | | <tt> cbAb cbAAbcbAb cbAAbcbAb </tt> | ||
| | | | | <tt> bcbAAbcbA bcbA bcbAAbcbA </tt> | ||
| | <tt> | | | <tt> cbAAbcbAb cbAAbcbAb cbAb </tt> | ||
|- | |- | ||
| | <tt> bAbc bAAbcbAbc bAAbcbAbc </tt> | | | <tt> bAbc bAAbcbAbc bAAbcbAbc </tt> | ||
| | | | | <tt> cbAAbcbAb cbAb cbAAbcbAb </tt> | ||
| | <tt> | | | <tt> bAAbcbAbc bAAbcbAbc bAbc </tt> | ||
|- | |- | ||
| | <tt> Abcb AAbcbAbcb AAbcbAbcb </tt> | | | <tt> Abcb AAbcbAbcb AAbcbAbcb </tt> | ||
| | | | | <tt> bAAbcbAbc bAbc bAAbcbAbc </tt> | ||
| | <tt> | | | <tt> AAbcbAbcb AAbcbAbcb Abcb </tt> | ||
|- | |- | ||
| | <tt> bcbA AbcbAbcbA AbcbAbcbA </tt> | | | <tt> bcbA AbcbAbcbA AbcbAbcbA </tt> | ||
| | <tt> AAbcbAbcb Abcb AAbcbAbcb </tt> | |||
| | <tt> AAbcbAbcb AAbcbAbcb | |||
| | <tt> AbcbAbcbA AbcbAbcbA bcbA </tt> | | | <tt> AbcbAbcbA AbcbAbcbA bcbA </tt> | ||
|} | |} | ||
lattice: | lattice: | ||
<pre> | <pre> | ||
R3 -- D3 -- G3 -- N3 -- m3 | |||
| | | | | | | | | | | | ||
r1 -- d1 -- g1 -- n1 -- Ma -- Sa -- Pa -- R4 -- D4 -- G4 -- N4 -- m4 | r1 -- d1 -- g1 -- n1 -- Ma -- Sa -- Pa -- R4 -- D4 -- G4 -- N4 -- m4 | ||
| Line 344: | Line 238: | ||
16 8 6 9 27 | 16 8 6 9 27 | ||
/ --- / --- / --- / --- / | / --- / --- / --- / --- / | ||
15 5 5 5 20</pre> | 15 5 5 5 20 | ||
</pre> | |||
This scale could be considered a detempering of the following OTC scales with two step sizes: | This scale could be considered a [[Detempering|detempering]] of the following OTC scales with two step sizes: | ||
[[OTC_17L_5s|OTC 17L+5s]] (A=L, b=L, c=s) | [[OTC_17L_5s|OTC 17L+5s]] (A=L, b=L, c=s) | ||
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===References=== | ===References=== | ||
<ul><li>Noted as omnitetrachordal by Paul Erlich; date unknown.</li></ul> | <ul><li>Noted as omnitetrachordal by Paul Erlich; date unknown.</li></ul> | ||
[[Category:22-tone scales]] | |||
[[Category:Indian music]] | |||
[[Category:Omnitetrachordal]] | |||
[[Category:Tables]] | |||
[[Category:5-limit]] | |||
[[Category:Just intonation scales]] | |||
{{Todo| cleanup }} | |||