Shruti: Difference between revisions
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'''Secondary functions and "artifact shrutis" introduced by using 19 or 22 (out of n) edo to simulate ragas''' | '''Secondary functions and "artifact shrutis" introduced by using 19 or 22 or 23 or 26 (out of n) edo to simulate ragas''' | ||
komal-ardha re (1): [250/243; 48]: 22 | komal-ardha re (1): [250/243; 48]: 22, 23, 26 | ||
ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~64/59; 138], [625/576; 141]: | ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~64/59; 138], [625/576; 141]: 26 | ||
inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22 | inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22, 26 | ||
inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22 | inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23 | ||
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19 | komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19 | ||
inverse komal re/tivratar Ma [320/243; 476] | inverse komal re/tivratar Ma [320/243; 476]: 23 | ||
inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518] | inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23 | ||
komal ga/komal ga; [36/25; 631]: 19 | komal ga/komal ga; [36/25; 631]: 19 | ||
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inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 22 | inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 22 | ||
ati ati komal re/tivra(tar) Ma [375/256, 661; ~61/41, 682] | ati ati komal re/tivra(tar) Ma [375/256, 661; ~61/41, 682]: 22, 23 | ||
komal re/tivratar Ma [243/160; 724] | komal re/tivratar Ma [243/160; 724]: 22, 23 | ||
komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19 | komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19 | ||
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ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22 | ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22 | ||
ekasruti komal ni, ekasruti Ma/ekasruti Ma: [729/400; 1040]: 22 | ekasruti komal ni, ekasruti Ma/ekasruti Ma: [729/400; 1040]: 22, 23 | ||
inverse ardha komal re (1 3/4), inverse ati ati komal re/ati ati komal re: [50/27; 1067], [~59/32; 1062], [1152/625; 1059]: | inverse ardha komal re (1 3/4), inverse ati ati komal re/ati ati komal re: [50/27; 1067], [~59/32; 1062], [1152/625; 1059]: 26 | ||
inverse komal-ardha re (1): [243/125; 1152]: 22 | inverse komal-ardha re (1): [243/125; 1152]: 22, 23, 26 | ||
==Regular temperaments of the full-status shrutis== | ==Regular temperaments of the full-status shrutis== | ||
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=Underlying= | =Underlying= | ||
Excluding inverses | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 331: | Line 331: | ||
|} | |} | ||
Including inverses | |||
{| class="wikitable" | |||
|- | |||
! |Large-small numbers | |||
! |Generator range | |||
! |<span style="background-color: #ffffff;">Midpoint</span> | |||
! |Boundaries of propriety, maximum expressiveness, diatonicity | |||
! |Large step+Small step | |||
|- | |||
| |1L22s | |||
| |<span style="line-height: 15.6000003814697px;">22\23 < g < 1</span> | |||
| |g = 45\46 | |||
| |''g = 23\24, 24\25, 25\26'' | |||
| |22g-21+1-g = 21g-20 | |||
|- | |||
| |2L21s | |||
| |11\23 < g < 1\2 | |||
| |g = 45\92 | |||
| |g = ''12\25, 13\27'', 14\29 | |||
| |21g-10+1-2g = 19g-9 | |||
|- | |||
| |3L20s | |||
| |15\23 < g < 2\3 | |||
| |g = 91\138 | |||
| |g = ''17\26'', 19\29, 21\32 | |||
| |20g-13+1-3g = 17g-12 | |||
|- | |||
| |4L19s | |||
| |17\23 < g < 3\4 | |||
| |g = 137\184 | |||
| |g = ''20\27'', 23\31, 26\35 | |||
| |19g-14+3-4g = 15g-11 | |||
|- | |||
| |5L18s | |||
| |9\23 < g < 2\5 | |||
| |g = 91\230 | |||
| |g = ''11\28'', 13\33, 15\38 | |||
| |18g-7+2-5g = 13g-5 | |||
|- | |||
| |6L17s | |||
| |19\23 < g < 5\6 | |||
| |g = 229\276 | |||
| |g = 24\29, 29\35, 34\41 | |||
| |17g-15+1-6g = 11g-14 | |||
|- | |||
| |7L16s | |||
| |13\23 < g < 4\7 | |||
| |g = 183\322 | |||
| |g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44 | |||
| |16g-9+4-7g = 9g-5 | |||
|- | |||
| |8L15s | |||
| |20\23 < g < 7\8 | |||
| |g = 321\368 | |||
| |g = 27\31, 34\39, 41\47 | |||
| |15g-13+7-8g = 7g-6 | |||
|- | |||
| |9L14s | |||
| |5\23 < g < 2\9 | |||
| |g = 91\414 | |||
| |g = 7\32, 9\41, 11\50 | |||
| |14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span> | |||
|- | |||
| |10L13s | |||
| |16\23 < g < 7\10 | |||
| |g = 321\460 | |||
| |g = 23\33, 30\43, 37\53 | |||
| |13g-9+7-10g = 3g-2 | |||
|- | |||
| |11L12s | |||
| |2\23 < g < 1\11 | |||
| |g = 45\506 | |||
| |g = 3\34, 4\45, 5\56 | |||
| |12g-1+1-11g = g | |||
|- | |||
| |12L11s | |||
| |21\23 < g < 11\12 | |||
| |g = 505\552 | |||
| |g = 32\35, 43\47, 54\59 | |||
| |<span style="line-height: 15.6000003814697px;">11g-10+11-12g = 1-g</span> | |||
|- | |||
| |13L10s | |||
| |7\23 < g < 4\13 | |||
| |g = 183\598 | |||
| |g = 11\36, 15\49, 19\62 | |||
| |10g-3+4-13g =1-3g | |||
|- | |||
| |14L9s | |||
| |18\23 < g < 11\14 | |||
| |g = 505\644 | |||
| |g = 29\37, 40\51, 51\65 | |||
| |9g-7+11-14g = 4-5g | |||
|- | |||
| |15L8s | |||
| |3\23 < g < 2\15 | |||
| |g = 91\690 | |||
| |g = 5\38, 7\53, 9\68 | |||
| |8g-1+2-15g = 1-7g | |||
|- | |||
| |16L7s | |||
| |10\23 < g < 7\16 | |||
| |g = 321\736 | |||
| |g = 17\39, 24\55, 31\71 | |||
| |7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span> | |||
|- | |||
| |17L6s | |||
| |4\23 < g < 3\17 | |||
| |g = 137\782 | |||
| |g = 7\40, 10\57, 13\74 | |||
| |6g-1+3-17g = 2-11g | |||
|- | |||
| |18L5s | |||
| |14\23 < g < 11\18 | |||
| |g = 505\828 | |||
| |g = 25\41, 36\59, 47\77 | |||
| |5g-4+11-18g = 7-13g | |||
|- | |||
| |19L4s | |||
| |6\23 < g < 5\19 | |||
| |g = 229\874 | |||
| |g = 11\42, 16\61, 21\80 | |||
| |4g-1+5-19g = 4-15g | |||
|- | |||
| |20L3s | |||
| |8\23 < g < 7\20 | |||
| |g = 321\920 | |||
| |g = 15\43, 22\63, 29\83 | |||
| |3g-1+13-20g = 12-17g | |||
|- | |||
| |21L2s | |||
| |12\23 < g < 11\21 | |||
| |g = 505\966 | |||
| |g = 23\44, 34\65, 45\86 | |||
| |2g-1+11-21g = 10-19g | |||
|- | |||
| |22L1s | |||
| |1\23 < g < 1\22 | |||
| |g = 45\1012 | |||
| |g = 2\45, 3\67, 4\89 | |||
| |g+1-22g = 1-221 | |||
|} | |||
=Quoted= | =Quoted= | ||
Excluding inverses | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 488: | Line 629: | ||
| | g = 2\43, 3\64, 4\85 | | | g = 2\43, 3\64, 4\85 | ||
| | g+1-21g = 1-20g | | | g+1-21g = 1-20g | ||
|} | |||
Including inverses | |||
{| class="wikitable" | |||
|- | |||
! |Large-small numbers | |||
! |Generator range | |||
! |<span style="background-color: #ffffff;">Midpoint</span> | |||
! |Boundaries of propriety, maximum expressiveness, diatonicity | |||
! |Large step+Small step | |||
|- | |||
| |1L25s | |||
| |25\26 < g < 1 | |||
| |g = 51\52 | |||
| |''g = 26\27, 27\28, 28\29'' | |||
| |25g-24+1-g = 24g-23 | |||
|- | |||
| |2L24s | |||
| |12\26 < g < 1\2 | |||
| |g = 25\52 | |||
| |''g = 13\28, 14\30, 15\32'' | |||
| |12g-11\2+1\2-g = 11g-5 | |||
|- | |||
| |3L23s | |||
| |17\26 < g < 2\3 | |||
| |g = 103\156 | |||
| |g = ''19\29'', ''21\32'', 23\35 | |||
| |23g-15+2-3g = 20g-13 | |||
|- | |||
| |4L22s | |||
| |6\26 < g < 1\4 | |||
| |g = 25\104 | |||
| |g = ''7\30'', 8\34, 9\38 | |||
| |11g-5\2+<span style="line-height: 15.6000003814697px;">1\2-2g = 9g-2</span> | |||
|- | |||
| |5L21s | |||
| |5\26 < g < 1\5 | |||
| |g = 51\260 | |||
| |g = ''6\31'', 7\36, 8\41 | |||
| |21g-4+1-5g = 16g-3 | |||
|- | |||
| |6L20s | |||
| |4\26 < g < 1\6 | |||
| |g = 25\156 | |||
| |g = ''5\32'', 6\38, 7\44 | |||
| |10g-3\2+1\2-3g = 7g-1 | |||
|- | |||
| |7L19s | |||
| |11\26 < g < 3\7 | |||
| |g = 155\364 | |||
| |g = 14\33, 17\40, 20\47 | |||
| |19g-8+3-7g = 12g-5 | |||
|- | |||
| |8L18s | |||
| |3\26 < g < 1\8 | |||
| |g = 25\208 | |||
| |g = 4\34, 5\42, 6\50 | |||
| |9g-1+1\2-4g = 5g-1\2 | |||
|- | |||
| |9L17s | |||
| |23\26 < g < 8\9 | |||
| |g = 415\468 | |||
| |g = 31\35, 39\44, 47\53 | |||
| |17g-15+8-9g = 8g-7 | |||
|- | |||
| |10L16s | |||
| |5\26 < g < 2\10 | |||
| |g = 51\260 | |||
| |g = 7\36, 9\46, 11\56 | |||
| |8g-3\2+1-5g = 3g-1\2 | |||
|- | |||
| |11L15s | |||
| |7\26 < g < 3\11 | |||
| |g = 155\572 | |||
| |g = 10\37, 13\48, 16\59 | |||
| |15g-4+3-11g = 4g-1 | |||
|- | |||
| |12L14s | |||
| |2\26 < g < 1\12 | |||
| |g = 25\312 | |||
| |g = 3\38, 4\50, 5\62 | |||
| |7g-1\2+1\2-6g = g | |||
|- | |||
| |13L13s | |||
| |1\26 < g < 1\13 | |||
| |g = 3\52 | |||
| |g = 2\39, 3\52, 4\65 | |||
| |g+1\13-g = 1\13 | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">14L12s</span> | |||
| |11\26 < g < 6\14 | |||
| |g = 155\364 | |||
| |g = 17\40, 23\54, 29\68 | |||
| |6g-5\2+3-7g = 1\2-g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">15L11s</span> | |||
| |19\26 < g < 11\15 | |||
| |g = 571\780 | |||
| |g = 30\41, 41\56, 52\71 | |||
| |11g-8+11-15g = 3-4g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">16L10s</span> | |||
| |8\26 < g < 5\16 | |||
| |g = 129\416 | |||
| |g = 13\42, 18\58, 23\74 | |||
| |5g-3\2+5\2-8g = 1-3g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">17L9s</span> | |||
| |3\26 < g < 2\17 | |||
| |g = 103\884 | |||
| |g = 5\43, 7\60, 9\77 | |||
| |9g-1+2-17g = 1-8g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">18L</span>8s | |||
| |10\26 < g < 7\18 | |||
| |g = 181\468 | |||
| |g = 17\44, 24\62, 31\80 | |||
| |4g-7\2+7-9g = 7\2-5g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">19L</span>7s | |||
| |15\26 < g < 11\19 | |||
| |g = 571\988 | |||
| |g = 26\45, 37\64, 48\83 | |||
| |7g-4+11-19g = 7-12g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">20L</span>6s | |||
| |9\26 < g < 7\20 | |||
| |g = 181\520 | |||
| |g = 16\46, 23\66, 30\86 | |||
| |3g-1+7\2-10g = 5\2-7g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">21L</span>5s | |||
| |21\26 < g < 17\21 | |||
| |g = 883\1092 | |||
| |g = 38\47, 55\68, 72\89 | |||
| |5g-4+16-21g = 12-16g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">22L</span>4s | |||
| |7\26 < g < 6\22 | |||
| |g = 155\572 | |||
| |g = 13\48, 19\70, 25\92 | |||
| |2g-1\2+3-11g = 5\2-9g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">23L</span>3s | |||
| |9\26 < g < 8\23 | |||
| |g = 415\1196 | |||
| |g = 17\49, 25\72, 33/95 | |||
| |3g-1+8-23g = 7-20g | |||
|- | |||
| |<span style="line-height: 15.6000003814697px;">24L</span>2s | |||
| |1\26 < g < 1\24 | |||
| |g = 25\312 | |||
| |g = 2\50, 3\74, 4\98 | |||
| |g+1\2-12g = 1\2-11g | |||
|- | |||
| |25L1s | |||
| |1\26 < g < 1\25 | |||
| |g = 51\1300 | |||
| |g = 2\51, 3\76, 4\101 | |||
| |g+1-25g = 1-24g | |||
|} | |} | ||