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Shruti: Difference between revisions

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Line 63: Line 63:
|75/64
|75/64
|274
|274
|
|inverse ekasruti shuddha dha:[~256/219, 273] is the schismatic tuning of this shruti
|-
|-
| rowspan="2" |Ga
| rowspan="2" |Ga
Line 69: Line 69:
|5/4
|5/4
|386
|386
|
|inverse "half"-status shuddha ga/"half"-status shuddha ga [384] is the schismatic tuning of this shruti
|-
|-
|"half"-status shuddha ga
|"half"-status shuddha ga
|81/64
|81/64
|408
|408
|
|inverse "half"-status shuddha ga/shuddha ga [512/405; 406] is the schismatic tuning of this shruti
|-
|-
| colspan="2" |(inverse ati ati komal dha)
| colspan="2" |(inverse ati ati komal dha)
Line 100: Line 100:
|729/512
|729/512
|612
|612
|-
| colspan="2" |(inverse ekasruti Ma)
|40/27
|680
|
|-
|-
| colspan="2" |Pa
| colspan="2" |Pa
|3/2
|3/2
|702
|702
|
|-
| colspan="2" |(inverse ekasruti Ma)
|40/27
|680
|
|
|-
|-
Line 115: Line 115:
|8/5
|8/5
|814
|814
|
|"half"-status shuddha ga/"half"-status shuddha ga [816] is the schismatic tuning of this shruti
|-
|-
|ati komal dha
|ati komal dha
|128/81
|128/81
|792
|792
|
|"half"-status shuddha ga/shuddha ga [405/256; 794] is the schismatic tuning of this shruti
|-
|-
|ati ati komal dha
|ati ati komal dha
Line 139: Line 139:
|128/75
|128/75
|926
|926
|
|ekasruti shuddha dha:[~219/128, 927] is the schismatic tuning of this shruti
|-
|-
| rowspan="2" |komal ni
| rowspan="2" |komal ni
Line 167: Line 167:
|}
|}


'''Secondary functions and "artifact shrutis" introduced by using 19 or 22 or 23 or 26 (out of n) edo to simulate ragas'''
'''Secondary functions and "artifact shrutis" introduced by using 19 or 22 or 23 or 25 or 26 or 29 (out of n) edo to simulate ragas'''
 
komal-ardha re (1): [250/243; 48]: 22, 23. 25, 26, 29
 
ekasruti komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~13/12; 138], [625/576; 141]: 25, 26
 
inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23, 29


komal-ardha re (1): [250/243; 48]: 22, 23, 26  
inverse ati ati komal ga/Pa, komal re/komal re, inverse komal-ardha ni: [256/225; 224], [729/640; 226]: 22, 26


ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~64/59; 138], [625/576; 141]: 26
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19, 25*, 29


inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22, 26
ekasruti komal ga: [243/200; 338]: 25, 29


inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23
inverse inverse ati ati komal dha/inverse ati ati komal dha: [625/512; 344]: 25


komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19
inverse ekasruti komal dha, "half"-status shuddha re/"half"-status shuddha re [100/81; 365]; 23, 26, 29


inverse komal re/tivratar Ma [320/243; 476]: 23
inverse komal-ardha dha [162/125; 449]: 19, 29


inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23
(ati) ati komal re/shuddha ga, inverse komal re/tivratar Ma, inverse ekasruti Pa: [~13/10; 454], [320/243; 476]: 25, 29


komal ga/komal ga; [36/25; 631]: 19
inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23, 25
 
ati ati komal ga/ati ati komal ga: [~56/41; 548]: 22


inverse komal ga/komal ga; [25/18; 569]: 19
inverse komal ga/komal ga; [25/18; 569]: 19


ati ati komal ga/ati ati komal ga: [~563/410; 548]: 22
komal ga/komal ga; [36/25; 631]: 19


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]: 22, 23
ati ati komal re/tivra(tar) Ma [375/256, 661; ~61/41, 682]: 22, 23, 25
 
inverse (ati) ati komal re/shuddha ga, komal re/tivratar Ma, ekasruti Pa: [~20/13; 746], [243/160; 724]: 25, 29
 
komal-ardha dha [125/81; 751]: 19
 
ekasruti komal dha, inverse "half"-status shuddha re/"half"-status shuddha re [81/50; 835]: 23, 26, 29


komal re/tivratar Ma [243/160; 724]: 22, 23
inverse ati ati komal dha/inverse ati ati komal dha: [1024/625; 856]


komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19
inverse ekasruti komal ga: [400/243; 862]: 25, 29


ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22
komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19, 25*, 29
 
ati ati komal ga/Pa, inverse komal re/komal re, komal-ardha ni: [225/128; 976], [1280/729; 974]: 22, 26


ekasruti komal ni, ekasruti Ma/ekasruti Ma: [729/400; 1040]: 22, 23
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]: 26
inverse ekasruti komal re (1 3/4), inverse ati ati komal re/ati ati komal re: [50/27; 1067], [~24/13; 1062], [1152/625; 1059]: 26


inverse komal-ardha re (1): [243/125; 1152]: 22, 23, 26
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==
'''Note: generators in italics will generate a 19 (diatonic)''' '''or 22 tone (superdiatonic) set which is too weakly tonal for serious practice'''
'''Note:'''
* '''generators in (bold) italics will generate a 19/23 (diatonic)''' '''or 22/25/26/29 tone (superdiatonic) set which is too weakly tonal for serious practice'''
* '''all 23, 25 and 29 tone temperaments given in italics due to either not necessarily possessing "real" Ma/Pa or ati atis counting as only "half"''', '''thus messing up what the 25 and 29 tone temperaments should technically be'''


=Underlying=
=Underlying=
Line 331: Line 349:
|}
|}


Including inverses
''Including inverses''
{| class="wikitable"
{| class="wikitable"
|-
|-
! |Large-small numbers
! |''Large-small numbers''
!Status
!''Status''
! |Generator range
! |''Generator range''
! |<span style="background-color: #ffffff;">Midpoint</span>
! |<span style="background-color: #ffffff;">''Midpoint''</span>
! |Boundaries of propriety, maximum expressiveness, diatonicity
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |Large step+Small step
! |''Large step+Small step''
|-
|-
| |1L22s
| |''1L22s''
|"half"
|''"half"''
| |<span style="line-height: 15.6000003814697px;">22\23 &lt; g &lt; 1</span>
| |<span style="line-height: 15.6000003814697px;">''22\23 &lt; g &lt; 1''</span>
| |g = 45\46
| |''g = 45\46''
| |''g = 23\24, 24\25, 25\26''
| |'''''g = 23\24, 24\25, 25\26'''''
| |22g-21+1-g = 21g-20
| |''22g-21+1-g = 21g-20''
|-
|-
| |2L21s
| |''2L21s''
| rowspan="20" |full
| rowspan="20" |''full''
| |11\23 &lt; g &lt; 1\2
| |''11\23 &lt; g &lt; 1\2''
| |g = 45\92
| |''g = 45\92''
| |g = ''12\25, 13\27'', 14\29
| |'''''g = 12\25, 13\27''', 14\29''
| |21g-10+1-2g = 19g-9
| |''21g-10+1-2g = 19g-9''
|-
|-
| |3L20s
| |''3L20s''
| |15\23 &lt; g &lt; 2\3
| |''15\23 &lt; g &lt; 2\3''
| |g = 91\138
| |''g = 91\138''
| |g = ''17\26'', 19\29, 21\32
| |'''''g = 17\26,''''' ''19\29, 21\32''
| |20g-13+1-3g = 17g-12
| |''20g-13+1-3g = 17g-12''
|-
|-
| |4L19s
| |''4L19s''
| |17\23 &lt; g &lt; 3\4
| |''17\23 &lt; g &lt; 3\4''
| |g = 137\184
| |''g = 137\184''
| |g = ''20\27'', 23\31, 26\35
| |'''''g = 20\27,''''' ''23\31, 26\35''
| |19g-14+3-4g = 15g-11
| |''19g-14+3-4g = 15g-11''
|-
|-
| |5L18s
| |''5L18s''
| |9\23 &lt; g &lt; 2\5
| |''9\23 &lt; g &lt; 2\5''
| |g = 91\230
| |''g = 91\230''
| |g = ''11\28'', 13\33, 15\38
| |'''''g = 11\28''', 13\33, 15\38''
| |18g-7+2-5g = 13g-5
| |''18g-7+2-5g = 13g-5''
|-
|-
| |6L17s
| |''6L17s''
| |19\23 &lt; g &lt; 5\6
| |''19\23 &lt; g &lt; 5\6''
| |g = 229\276
| |''g = 229\276''
| |g = 24\29, 29\35, 34\41
| |''g = 24\29, 29\35, 34\41''
| |17g-15+1-6g = 11g-14
| |''17g-15+1-6g = 11g-14''
|-
|-
| |7L16s
| |''7L16s''
| |13\23 &lt; g &lt; 4\7
| |''13\23 &lt; g &lt; 4\7''
| |g = 183\322
| |''g = 183\322''
| |g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44
| |''g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44''
| |16g-9+4-7g = 9g-5
| |''16g-9+4-7g = 9g-5''
|-
|-
| |8L15s
| |''8L15s''
| |20\23 &lt; g &lt; 7\8
| |''20\23 &lt; g &lt; 7\8''
| |g = 321\368
| |''g = 321\368''
| |g = 27\31, 34\39, 41\47
| |''g = 27\31, 34\39, 41\47''
| |15g-13+7-8g = 7g-6
| |''15g-13+7-8g = 7g-6''
|-
|-
| |9L14s
| |''9L14s''
| |5\23 &lt; g &lt; 2\9
| |''5\23 &lt; g &lt; 2\9''
| |g = 91\414
| |''g = 91\414''
| |g = 7\32, 9\41, 11\50
| |''g = 7\32, 9\41, 11\50''
| |14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>
| |''14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>''
|-
|-
| |10L13s
| |''10L13s''
| |16\23 &lt; g &lt; 7\10
| |''16\23 &lt; g &lt; 7\10''
| |g = 321\460
| |''g = 321\460''
| |g = 23\33, 30\43, 37\53
| |''g = 23\33, 30\43, 37\53''
| |13g-9+7-10g = 3g-2
| |''13g-9+7-10g = 3g-2''
|-
|-
| |11L12s
| |''11L12s''
| |2\23 &lt; g &lt; 1\11
| |''2\23 &lt; g &lt; 1\11''
| |g = 45\506
| |''g = 45\506''
| |g = 3\34, 4\45, 5\56
| |''g = 3\34, 4\45, 5\56''
| |12g-1+1-11g = g
| |''12g-1+1-11g = g''
|-
|-
| |12L11s
| |''12L11s''
| |21\23 &lt; g &lt; 11\12
| |''21\23 &lt; g &lt; 11\12''
| |g = 505\552
| |''g = 505\552''
| |g = 32\35, 43\47, 54\59
| |''g = 32\35, 43\47, 54\59''
| |<span style="line-height: 15.6000003814697px;">11g-10+11-12g = 1-g</span>
| |<span style="line-height: 15.6000003814697px;">''11g-10+11-12g = 1-g''</span>
|-
|-
| |13L10s
| |''13L10s''
| |7\23 &lt; g &lt; 4\13
| |''7\23 &lt; g &lt; 4\13''
| |g = 183\598
| |''g = 183\598''
| |g = 11\36, 15\49, 19\62
| |''g = 11\36, 15\49, 19\62''
| |10g-3+4-13g =1-3g
| |''10g-3+4-13g =1-3g''
|-
|-
| |14L9s
| |''14L9s''
| |18\23 &lt; g &lt; 11\14
| |''18\23 &lt; g &lt; 11\14''
| |g = 505\644
| |''g = 505\644''
| |g = 29\37, 40\51, 51\65
| |''g = 29\37, 40\51, 51\65''
| |9g-7+11-14g = 4-5g
| |''9g-7+11-14g = 4-5g''
|-
|-
| |15L8s
| |''15L8s''
| |3\23 &lt; g &lt; 2\15
| |''3\23 &lt; g &lt; 2\15''
| |g = 91\690
| |''g = 91\690''
| |g = 5\38, 7\53, 9\68
| |''g = 5\38, 7\53, 9\68''
| |8g-1+2-15g = 1-7g
| |''8g-1+2-15g = 1-7g''
|-
|-
| |16L7s
| |''16L7s''
| |10\23 &lt; g &lt; 7\16
| |''10\23 &lt; g &lt; 7\16''
| |g = 321\736
| |''g = 321\736''
| |g = 17\39, 24\55, 31\71
| |''g = 17\39, 24\55, 31\71''
| |7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>
| |''7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>''
|-
|-
| |17L6s
| |''17L6s''
| |4\23 &lt; g &lt; 3\17
| |''4\23 &lt; g &lt; 3\17''
| |g = 137\782
| |''g = 137\782''
| |g = 7\40, 10\57, 13\74
| |''g = 7\40, 10\57, 13\74''
| |6g-1+3-17g = 2-11g
| |''6g-1+3-17g = 2-11g''
|-
|-
| |18L5s
| |''18L5s''
| |14\23 &lt; g &lt; 11\18
| |''14\23 &lt; g &lt; 11\18''
| |g = 505\828
| |''g = 505\828''
| |g = 25\41, 36\59, 47\77
| |''g = 25\41, 36\59, 47\77''
| |5g-4+11-18g = 7-13g
| |''5g-4+11-18g = 7-13g''
|-
|-
| |19L4s
| |''19L4s''
| |6\23 &lt; g &lt; 5\19
| |''6\23 &lt; g &lt; 5\19''
| |g = 229\874
| |''g = 229\874''
| |g = 11\42, 16\61, 21\80
| |''g = 11\42, 16\61, 21\80''
| |4g-1+5-19g = 4-15g
| |''4g-1+5-19g = 4-15g''
|-
|-
| |20L3s
| |''20L3s''
| |8\23 &lt; g &lt; 7\20
| |''8\23 &lt; g &lt; 7\20''
| |g = 321\920
| |''g = 321\920''
| |g = 15\43, 22\63, 29\83
| |''g = 15\43, 22\63, 29\83''
| |3g-1+13-20g = 12-17g
| |''3g-1+13-20g = 12-17g''
|-
|-
| |21L2s
| |''21L2s''
| |12\23 &lt; g &lt; 11\21
| |''12\23 &lt; g &lt; 11\21''
| |g = 505\966
| |''g = 505\966''
| |g = 23\44, 34\65, 45\86
| |''g = 23\44, 34\65, 45\86''
| |2g-1+11-21g = 10-19g
| |''2g-1+11-21g = 10-19g''
|-
|-
| |22L1s
| |''22L1s''
|"half"
|''"half"''
| |1\23 &lt; g &lt; 1\22
| |''1\23 &lt; g &lt; 1\22''
| |g = 45\1012
| |''g = 45\1012''
| |g = 2\45, 3\67, 4\89
| |''g = 2\45, 3\67, 4\89''
| |g+1-22g = 1-221
| |''g+1-22g = 1-221''
|}
|}
=Quoted=
=Quoted=
=== Excluding ati atis ===
Excluding inverses
Excluding inverses
{| class="wikitable"
{| class="wikitable"
Line 818: Line 838:
| |g = 2\51, 3\76, 4\101
| |g = 2\51, 3\76, 4\101
| |g+1-25g = 1-24g
| |g+1-25g = 1-24g
|}
=== ''Including ati atis'' ===
''Excluding inverses''
{| class="wikitable"
|-
! |''Large-small numbers''
!''Status''
! |''Generator range''
! |<span style="background-color: #ffffff;">''Midpoint''</span>
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
|-
| |''1L24s''
|''"half"''
| |''24\25 &lt; g &lt; 1''
| |''g = 49\50''
| |'''''g = 25\26, 26\27, 27\28'''''
| |''24g-23+1-g = 23g-22''
|-
| |''2L23s''
| rowspan="3" |''full''
| |''12\25 &lt; g &lt; 1\2''
| |''g = 49\100''
| |'''''g = 13\27, 14\29, 15\31'''''
| |''23g-11+1-2g = 21g-10''
|-
| |''3L22s''
| |''8\25 &lt; g &lt; 1\3''
| |''g = 49\150''
| |'''''g = 9\28, 10\31,''''' ''11\34''
| |''22g-7+1-3g = 19g-6''
|-
| |''4L21s''
| |''6\25 &lt; g &lt; 1\4''
| |''g = 49\200''
| |'''''g = 7\29''', 8\33, 9\37''
| |''21g-5+1-4g = 17g-4''
|-
| |''5L20s''
|''"7/8"''
| |''4\25 &lt; g &lt; 1\5''
| |''g = 9\50''
| |'''''g = 5\30,''' 6\35, 7\40''
| |''4g-3\5+1\5-g = 3g-2\5''
|-
| |''6L19s''
| rowspan="4" |''full''
| |''4\25 &lt; g &lt; 1\6''
| |''g = 49\300''
| |'''''g = 5\31,''''' ''6\37, 7\43''
| |''19g-3+1-6g = 13g-2''
|-
| |''7L18s''
| |''7\25 &lt; g &lt; 2\7''
| |''g = 99\350''
| |''g = 9\32, 11\39, 13\46''
| |''18g-5+2-7g = 11g-3''
|-
| |''8L17s''
| |''3\25 &lt; g &lt; 1\8''
| |''g = 49\400''
| |''g = 4\33, 5\41, 6\47''
| |<span style="line-height: 15.6000003814697px;">''17g-2+1-8g = 9g-1''</span>
|-
| |''9L16s''
| |''11\25 &lt; g &lt; 4\9''
| |''g = 199\450''
| |''g = 15\34, 19\43, 23\52''
| |''16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>''
|-
| |''10L15s''
|''"7/8"''
| |''2\25 &lt; g &lt; 1\10''
| |''g = 9\100''
| |''g = 3\35, 4\45, 5\55''
| |''3g-1\5+1\5-2g = g''
|-
| |''11L14s''
| rowspan="4" |''full''
| |''9\25 &lt; g &lt; 4\11''
| |''g = 199\550''
| |''g = 13\36, 17\47, 21\58''
| |''14g-5+4-11g = 3g-1''
|-
| |''12L13s''
| |''2\25 &lt; g &lt; 1\12''
| |''g = 49\600''
| |''g = 3\37, 4\49, 5\61''
| |''13g-1+1-12g = g''
|-
| |''13L12s''
| |''23\25 &lt; g &lt; 12\13''
| |''g = 599\650''
| |''g = 35\38, 47\51, 59\64''
| |''12g-11+12-13g = 1-g''
|-
| |''14L11s''
| |''16\25 &lt; g &lt; 9\14''
| |''g = 449\700''
| |''g = 25\39, 34\53, 43\67''
| |''11g-7+9-14g = 2-3g''
|-
| |''15L10s''
|''"7/8"''
| |''3\25 &lt; g &lt; 2\15''
| |''g = 19\150''
| |''g = 5\40, 7\55, 9\70''
| |''2g-1\5+2\5-3g = 1\5-g''
|-
| |''16L9s''
| rowspan="4" |''full''
| |''14\25 &lt; g &lt; 9\16''
| |''g = 449\800''
| |''g = 23\41, 32\57, 41\73''
| |''9g-5+9-16g = 4-7g''
|-
| |''17L8s''
| |''22\25 &lt; g &lt; 15\17''
| |''g = 749\850''
| |''g = 37\42, 52\59, 67\76''
| |''8g-7+15-17g = 8-9g''
|-
| |''18L7s''
| |''18\25 &lt; g &lt; 13\18''
| |''g = 649\900''
| |''g = 31\43, 44\61, 57\79''
| |''7g-5+13-18g = 8-11g''
|-
| |''19L6s''
| |''21\25 &lt; g &lt; 16\19''
| |''g = 799\950''
| |''g = 37\44, 53\63, 69\82''
| |''6g-5+16-19g = 11-13g''
|-
| |''20L5s''
|''"7/8"''
| |''1\25 &lt; g &lt; 1\20''
| |''g = 9\200''
| |''g = 2\45, 3\65, 4\85''
| |''g+1\5-4g = 1\5-3g''
|-
| |''21L4s''
| rowspan="3" |''full''
| |''16\21 &lt; g &lt; 19\25''
| |''g = 799\1050''
| |''g = 35\46, 51\67, 71\88''
| |''4g-3+16-21g = 13-17g''
|-
| |''22L3s''
| |''17\25 &lt; g &lt; 15\22''
| |''g = 749\1100''
| |''g = 32\47, 47\69, 62\91''
| |''3g-2+15-22g = 13-19g''
|-
| |''23L2s''
| |''13\25 &lt; g &lt; 12\23''
| |''g = 599\1150''
| |''g = 25\48, 37\71, 49\94''
| |''2g-1+11-23g = 10-21g''
|-
| |''24L1s''
|''"half"''
| |''1\25 &lt; g &lt; 1\24''
| |''g = 49\1200''
| |''g = 2\49, 3\73, 4\97''
| |''g+1-24g = 1-23g''
|}
''Including inverses''
{| class="wikitable"
|-
! |''Large-small numbers''
!''Status''
! |''Generator range''
! |<span style="background-color: #ffffff;">''Midpoint''</span>
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
|-
| |''1L28s''
|''"half"''
| |''28\29 &lt; g &lt; 1''
| |''g = 57\58''
| |'''''g = 29\30, 30\31, 31\32'''''
| |''28g-27+1-g = 27g-26''
|-
| |''2L27s''
| rowspan="26" |''full''
| |''14\29 &lt; g &lt; 1\2''
| |''g = 57\116''
| |'''''g = 15\31, 16\33, 17\35'''''
| |''27g-13+1-2g = 25g-12''
|-
| |''3L26s''
| |''19\29 &lt; g &lt; 2\3''
| |''g = 115\174''
| |'''''g = 21\32, 23\35''', 25\38''
| |''26g-17+2-3g = 23g-15''
|-
| |''4L25s''
| |''7\29 &lt; g &lt; 1\4''
| |''g = 57\232''
| |''g = '''8\33,''' 9\37, 10\41''
| |''25g-6+1-4g = 21g-5''
|-
| |''5L24s''
| |''23\29 &lt; g &lt; 4\5''
| |''g = 231\290''
| |''g = '''27\34''', 31\39, 35\44''
| |''24g-19+4-5g = 19g-15''
|-
| |''6L23s''
| |''24\29 &lt; g &lt; 5\6''
| |''g = 289\348''
| |''g = '''29\35''', 34\41, 39\47''
| |''23g-19+5-6g = 17g-14''
|-
| |''7L22s''
| |''4\29 &lt; g &lt; 1\7''
| |''g = 57\406''
| |''g = '''5\36''', 6\43, 7\50''
| |''22g-3+1-7g = 15g-2''
|-
| |''8L21s''
| |''18\29 &lt; g &lt; 5\8''
| |''g = 289\464''
| |''g = 23\37, 28\45, 33\53''
| |<span style="line-height: 15.6000003814697px;">''21g-13+5-8g = 13g-8''</span>
|-
| |''9L20s''
| |''16\29 &lt; g &lt; 5\9''
| |''g = 289\522''
| |''g = 21\38, 26\47, 31\56''
| |''20g-11+5-9g = 11g-6''
|-
| |''10L19s''
| |''26\29 &lt; g &lt; 9\10''
| |''g = 521\580''
| |''g = 35\39, 44\49, 53\59''
| |''19g-17+9-10g = 9g-8''
|-
| |''11L18s''
| |''21\29 &lt; g &lt; 8\11''
| |''g = 463\638''
| |''g = 29\40, 37\51, 45\62''
| |''18g-13+8-11g = 7g-2''
|-
| |''12L17s''
| |''12\29 &lt; g &lt; 5\12''
| |''g = 289\696''
| |''g = 17\41, 22\53, 27\65''
| |''17g-7+5-12g = 5g-2''
|-
| |''13L16s''
| |''20\29 &lt; g &lt; 9\13''
| |''g = 521\754''
| |''g = 29\42, 38\55, 47\68''
| |''16g+11+9-13g = 3g-2''
|-
| |''14L15s''
| |''2\29 &lt; g &lt; 1\14''
| |''g = 57\812''
| |''g = 3\43, 4\57, 5\71''
| |''15g-1+1-14g = g''
|-
| |''15L14s''
| |''27\29 &lt; g &lt; 14\15''
| |''g = 811\870''
| |''g = 41\44, 55\59, 69\74''
| |''14g-13+14-15g = 1-g''
|-
| |''16L13s''
| |''9\29 &lt; g &lt; 5\16''
| |''g = 289\928''
| |''g = 14\45, 19\61, 24\77''
| |''13g-4+5-16g = 1-3g''
|-
| |''17L12s''
| |''17\29 &lt; g &lt; 10\17''
| |''g = 579\986''
| |''g = 27\46, 37\63, 47\80''
| |''12g-5+7-17g = 2-5g''
|-
| |''18L11s''
| |''8\29 &lt; g &lt; 5\18''
| |''g = 289\1044''
| |''g = 13\47, 18\65, 23\83''
| |''11g-3+5-18g = 2-7g''
|-
| |''19L10s''
| |''3\29 &lt; g &lt; 2\19''
| |''g = 115\1102''
| |''g = 5\48, 7\67, 9\86''
| |''10g-1+2-19g = 1-9g''
|-
| |''20L9s''
| |''13\29 &lt; g &lt; 9\20''
| |''g = 521\1160''
| |''g = 22\49, 31\69, 40\89''
| |''9g-5+9-20g = 4-11g''
|-
| |''21L8s''
| |''11\29 &lt; g &lt; 8\21''
| |''g = 463\1216''
| |''g = 19\50, 27\71, 35\92''
| |''8g-3+8-21g = 5-13g''
|-
| |''22L7s''
| |''25\29 &lt; g &lt; 19\22''
| |''g = 1001\1274''
| |''g = 44\51, 63\73, 82\95''
| |''7g-6+9-22g = 3-16g''
|-
| |''23L6s''
| |''5\29 &lt; g &lt; 4\23''
| |''g = 231\1332''
| |''g = 9\52, 13\75, 17\98''
| |''6g-1+4-23g = 3-17g''
|-
| |''24L5s''
| |''6\29 &lt; g &lt; 5\24''
| |''g = 289\1392''
| |''g = 11\53, 16\77, 21\101''
| |''5g-9+5-24g = 4-19g''
|-
| |''25L4s''
| |''22\29 &lt; g &lt; 19\25''
| |''g = 1001\1450''
| |''g = 41\54, 60\79, 79\104''
| |''4g-3+19-25g = 16-21g''
|-
| |''26L3s''
| |''10\29 &lt; g &lt; 9\26''
| |''g = 521\1508''
| |''g = 19\55, 28\81, 37\107''
| |''3g-1+9-26g = 8-23g''
|-
| |''27L2s''
| |''15\29 &lt; g &lt; 14\27''
| |''g = 811\1564''
| |''g = 29\56, 43\83, 57\110''
| |''2g-1+17-27g = 16-25g''
|-
| |''28L1s''
|''"half"''
| |''1\29 &lt; g &lt; 1\28''
| |''g = 57\1622''
| |''g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113''
| |''g+1-28g = 1-27g''
|}
|}
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