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]: 19*
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]: 19*
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"
|-
|-
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|}
|}


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 &lt; g &lt; 1</span>
| |g = 45\46
| |''g = 23\24, 24\25, 25\26''
| |22g-21+1-g = 21g-20
|-
| |2L21s
| |11\23 &lt; g &lt; 1\2
| |g = 45\92
| |g = ''12\25, 13\27'', 14\29
| |21g-10+1-2g = 19g-9
|-
| |3L20s
| |15\23 &lt; g &lt; 2\3
| |g = 91\138
| |g = ''17\26'', 19\29, 21\32
| |20g-13+1-3g = 17g-12
|-
| |4L19s
| |17\23 &lt; g &lt; 3\4
| |g = 137\184
| |g = ''20\27'', 23\31, 26\35
| |19g-14+3-4g = 15g-11
|-
| |5L18s
| |9\23 &lt; g &lt; 2\5
| |g = 91\230
| |g = ''11\28'', 13\33, 15\38
| |18g-7+2-5g = 13g-5
|-
| |6L17s
| |19\23 &lt; g &lt; 5\6
| |g = 229\276
| |g = 24\29, 29\35, 34\41
| |17g-15+1-6g = 11g-14
|-
| |7L16s
| |13\23 &lt; g &lt; 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 &lt; g &lt; 7\8
| |g = 321\368
| |g = 27\31, 34\39, 41\47
| |15g-13+7-8g = 7g-6
|-
| |9L14s
| |5\23 &lt; g &lt; 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 &lt; g &lt; 7\10
| |g = 321\460
| |g = 23\33, 30\43, 37\53
| |13g-9+7-10g = 3g-2
|-
| |11L12s
| |2\23 &lt; g &lt; 1\11
| |g = 45\506
| |g = 3\34, 4\45, 5\56
| |12g-1+1-11g = g
|-
| |12L11s
| |21\23 &lt; g &lt; 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 &lt; g &lt; 4\13
| |g = 183\598
| |g = 11\36, 15\49, 19\62
| |10g-3+4-13g =1-3g
|-
| |14L9s
| |18\23 &lt; g &lt; 11\14
| |g = 505\644
| |g = 29\37, 40\51, 51\65
| |9g-7+11-14g = 4-5g
|-
| |15L8s
| |3\23 &lt; g &lt; 2\15
| |g = 91\690
| |g = 5\38, 7\53, 9\68
| |8g-1+2-15g = 1-7g
|-
| |16L7s
| |10\23 &lt; g &lt; 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 &lt; g &lt; 3\17
| |g = 137\782
| |g = 7\40, 10\57, 13\74
| |6g-1+3-17g = 2-11g
|-
| |18L5s
| |14\23 &lt; g &lt; 11\18
| |g = 505\828
| |g = 25\41, 36\59, 47\77
| |5g-4+11-18g = 7-13g
|-
| |19L4s
| |6\23 &lt; g &lt; 5\19
| |g = 229\874
| |g = 11\42, 16\61, 21\80
| |4g-1+5-19g = 4-15g
|-
| |20L3s
| |8\23 &lt; g &lt; 7\20
| |g = 321\920
| |g = 15\43, 22\63, 29\83
| |3g-1+13-20g = 12-17g
|-
| |21L2s
| |12\23 &lt; g &lt; 11\21
| |g = 505\966
| |g = 23\44, 34\65, 45\86
| |2g-1+11-21g = 10-19g
|-
| |22L1s
| |1\23 &lt; g &lt; 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"
|-
|-
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| | 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 &lt; g &lt; 1
| |g = 51\52
| |''g = 26\27, 27\28, 28\29''
| |25g-24+1-g = 24g-23
|-
| |2L24s
| |12\26 &lt; g &lt; 1\2
| |g = 25\52
| |''g = 13\28, 14\30, 15\32''
| |12g-11\2+1\2-g = 11g-5
|-
| |3L23s
| |17\26 &lt; g &lt; 2\3
| |g = 103\156
| |g = ''19\29'', ''21\32'', 23\35
| |23g-15+2-3g = 20g-13
|-
| |4L22s
| |6\26 &lt; g &lt; 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 &lt; g &lt; 1\5
| |g = 51\260
| |g = ''6\31'', 7\36, 8\41
| |21g-4+1-5g = 16g-3
|-
| |6L20s
| |4\26 &lt; g &lt; 1\6
| |g = 25\156
| |g = ''5\32'', 6\38, 7\44
| |10g-3\2+1\2-3g = 7g-1
|-
| |7L19s
| |11\26 &lt; g &lt; 3\7
| |g = 155\364
| |g = 14\33, 17\40, 20\47
| |19g-8+3-7g = 12g-5
|-
| |8L18s
| |3\26 &lt; g &lt; 1\8
| |g = 25\208
| |g = 4\34, 5\42, 6\50
| |9g-1+1\2-4g = 5g-1\2
|-
| |9L17s
| |23\26 &lt; g &lt; 8\9
| |g = 415\468
| |g = 31\35, 39\44, 47\53
| |17g-15+8-9g = 8g-7
|-
| |10L16s
| |5\26 &lt; g &lt; 2\10
| |g = 51\260
| |g = 7\36, 9\46, 11\56
| |8g-3\2+1-5g = 3g-1\2
|-
| |11L15s
| |7\26 &lt; g &lt; 3\11
| |g = 155\572
| |g = 10\37, 13\48, 16\59
| |15g-4+3-11g = 4g-1
|-
| |12L14s
| |2\26 &lt; g &lt; 1\12
| |g = 25\312
| |g = 3\38, 4\50, 5\62
| |7g-1\2+1\2-6g = g
|-
| |13L13s
| |1\26 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 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 &lt; g &lt; 1\24
| |g = 25\312
| |g = 2\50, 3\74, 4\98
| |g+1\2-12g = 1\2-11g
|-
| |25L1s
| |1\26 &lt; g &lt; 1\25
| |g = 51\1300
| |g = 2\51, 3\76, 4\101
| |g+1-25g = 1-24g
|}
|}