Table of 99edo intervals: Difference between revisions

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VisualWikitext
Overhaul to accommodate higher limit extensions and the variable mappings for 11 and 13
+marks on diatonic intervals to improve readability
Line 1: Line 1:
This table of [[99edo]] intervals assumes the 99ef val {{val| 99 157 230 278 '''343 367''' 405 421 448 481 }} as tending sharp and 99 patent val {{val| 99 157 230 278 '''342 366''' 405 421 448 481 }} as tending flat. Prime harmonics and subharmonics are labeled in '''bold'''.  
This table of [[99edo]] intervals assumes the 99ef val {{val| 99 157 230 278 '''343 367''' 405 421 448 481 }} as tending sharp and 99 patent val {{val| 99 157 230 278 '''342 366''' 405 421 448 481 }} as tending flat. Prime harmonics and subharmonics are labeled in '''bold'''.  


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! #
! #
! Cents
! Cents
! Marks
! 5-limit
! 5-limit
! 7-limit
! 7-limit
Line 13: Line 14:
| 0
| 0
| 0.00
| 0.00
| P1
| colspan="5" | '''1/1'''
| colspan="5" | '''1/1'''
|-
|-
| 1
| 1
| 12.{{overline|12}}
| 12.{{overline|12}}
|
| 2048/2025
| 2048/2025
| 126/125
| 126/125
Line 25: Line 28:
| 2
| 2
| 24.{{overline|24}}
| 24.{{overline|24}}
|
| 81/80
| 81/80
| 64/63
| 64/63
Line 33: Line 37:
| 3
| 3
| 36.{{overline|36}}
| 36.{{overline|36}}
|
| 128/125
| 128/125
| 49/48, 50/49
| 49/48, 50/49
Line 41: Line 46:
| 4
| 4
| 48.{{overline|48}}
| 48.{{overline|48}}
|
| 250/243
| 250/243
| 36/35
| 36/35
Line 49: Line 55:
| 5
| 5
| 60.{{overline|60}}
| 60.{{overline|60}}
|
| 648/625
| 648/625
| 28/27
| 28/27
Line 57: Line 64:
| 6
| 6
| 72.{{overline|72}}
| 72.{{overline|72}}
|
| 25/24
| 25/24
| 26/25
| 26/25
Line 65: Line 73:
| 7
| 7
| 84.{{overline|84}}
| 84.{{overline|84}}
| m2
| 256/243
| 256/243
| 21/20
| 21/20
Line 73: Line 82:
| 8
| 8
| 96.{{overline|96}}
| 96.{{overline|96}}
|
| 135/128
| 135/128
| "
| "
Line 81: Line 91:
| 9
| 9
| 109.{{overline|09}}
| 109.{{overline|09}}
|
| 16/15
| 16/15
| "
| "
Line 89: Line 100:
| 10
| 10
| 121.{{overline|21}}
| 121.{{overline|21}}
|
| 2187/2048
| 2187/2048
| 15/14
| 15/14
Line 97: Line 109:
| 11
| 11
| 133.{{overline|33}}
| 133.{{overline|33}}
|
| 27/25
| 27/25
| "
| "
Line 105: Line 118:
| 12
| 12
| 145.{{overline|45}}
| 145.{{overline|45}}
|
| 625/576
| 625/576
| 49/45
| 49/45
Line 113: Line 127:
| 13
| 13
| 157.{{overline|57}}
| 157.{{overline|57}}
|
| 800/729
| 800/729
| 35/32
| 35/32
Line 121: Line 136:
| 14
| 14
| 169.{{overline|69}}
| 169.{{overline|69}}
|
| 1125/1024
| 1125/1024
| 54/49
| 54/49
Line 129: Line 145:
| 15
| 15
| 181.{{overline|81}}
| 181.{{overline|81}}
|
| 10/9
| 10/9
| "
| "
Line 137: Line 154:
| 16
| 16
| 193.{{overline|93}}
| 193.{{overline|93}}
|
| 4096/3645
| 4096/3645
| 28/25
| 28/25
Line 145: Line 163:
| 17
| 17
| 206.{{overline|06}}
| 206.{{overline|06}}
| M2
| 9/8
| 9/8
| "
| "
Line 153: Line 172:
| 18
| 18
| 218.{{overline|18}}
| 218.{{overline|18}}
|
| 256/225
| 256/225
| 245/216
| 245/216
Line 161: Line 181:
| 19
| 19
| 230.{{overline|30}}
| 230.{{overline|30}}
|
| 729/640
| 729/640
| '''8/7'''
| '''8/7'''
Line 169: Line 190:
| 20
| 20
| 242.{{overline|42}}
| 242.{{overline|42}}
|
| 144/125
| 144/125
| "
| "
Line 177: Line 199:
| 21
| 21
| 254.{{overline|54}}
| 254.{{overline|54}}
|
| 125/108
| 125/108
| 81/70
| 81/70
Line 185: Line 208:
| 22
| 22
| 266.{{overline|66}}
| 266.{{overline|66}}
|
| 729/625
| 729/625
| 7/6
| 7/6
Line 193: Line 217:
| 23
| 23
| 278.{{overline|78}}
| 278.{{overline|78}}
|
| 75/64
| 75/64
| "
| "
Line 201: Line 226:
| 24
| 24
| 290.{{overline|90}}
| 290.{{overline|90}}
| m3
| 32/27
| 32/27
| "
| "
Line 209: Line 235:
| 25
| 25
| 303.{{overline|03}}
| 303.{{overline|03}}
|
| 1215/1024
| 1215/1024
| 25/21
| 25/21
Line 217: Line 244:
| 26
| 26
| 315.{{overline|15}}
| 315.{{overline|15}}
|
| 6/5
| 6/5
| "
| "
Line 225: Line 253:
| 27
| 27
| 327.{{overline|27}}
| 327.{{overline|27}}
|
| 3125/2592
| 3125/2592
| 98/81
| 98/81
Line 233: Line 262:
| 28
| 28
| 339.{{overline|39}}
| 339.{{overline|39}}
|
| 243/200
| 243/200
| 128/105
| 128/105
Line 241: Line 271:
| 29
| 29
| 351.{{overline|51}}
| 351.{{overline|51}}
|
| 625/512
| 625/512
| 49/40, 60/49
| 49/40, 60/49
Line 249: Line 280:
| 30
| 30
| 363.{{overline|63}}
| 363.{{overline|63}}
|
| 100/81
| 100/81
| "
| "
Line 257: Line 289:
| 31
| 31
| 375.{{overline|75}}
| 375.{{overline|75}}
|
| 3888/3125
| 3888/3125
| 56/45
| 56/45
Line 265: Line 298:
| 32
| 32
| 387.{{overline|87}}
| 387.{{overline|87}}
|
| '''5/4'''
| '''5/4'''
| "
| "
Line 273: Line 307:
| 33
| 33
| 400.00
| 400.00
|
| 512/405
| 512/405
| 63/50
| 63/50
Line 281: Line 316:
| 34
| 34
| 412.{{overline|12}}
| 412.{{overline|12}}
| M3
| 81/64
| 81/64
| 80/63
| 80/63
Line 289: Line 325:
| 35
| 35
| 424.{{overline|24}}
| 424.{{overline|24}}
|
| 32/25
| 32/25
| "
| "
Line 297: Line 334:
| 36
| 36
| 436.{{overline|36}}
| 436.{{overline|36}}
|
| 625/486
| 625/486
| 9/7
| 9/7
Line 305: Line 343:
| 37
| 37
| 448.{{overline|48}}
| 448.{{overline|48}}
|
| 162/125
| 162/125
| 35/27
| 35/27
Line 313: Line 352:
| 38
| 38
| 460.{{overline|60}}
| 460.{{overline|60}}
|
| 125/96
| 125/96
| 64/49
| 64/49
Line 321: Line 361:
| 39
| 39
| 472.{{overline|72}}
| 472.{{overline|72}}
|
| 320/243
| 320/243
| 21/16
| 21/16
Line 329: Line 370:
| 40
| 40
| 484.{{overline|84}}
| 484.{{overline|84}}
|
| 675/512
| 675/512
| 250/189
| 250/189
Line 337: Line 379:
| 41
| 41
| 496.{{overline|96}}
| 496.{{overline|96}}
| P4
| '''4/3'''
| '''4/3'''
| "
| "
Line 345: Line 388:
| 42
| 42
| 509.{{overline|09}}
| 509.{{overline|09}}
|
| 8192/6075
| 8192/6075
| 75/56
| 75/56
Line 353: Line 397:
| 43
| 43
| 521.{{overline|21}}
| 521.{{overline|21}}
|
| 27/20
| 27/20
| "
| "
Line 361: Line 406:
| 44
| 44
| 533.{{overline|33}}
| 533.{{overline|33}}
|
| 512/375
| 512/375
| 49/36
| 49/36
Line 369: Line 415:
| 45
| 45
| 545.{{overline|45}}
| 545.{{overline|45}}
|
| 1000/729
| 1000/729
| 48/35
| 48/35
Line 377: Line 424:
| 46
| 46
| 557.{{overline|57}}
| 557.{{overline|57}}
|
| 864/625
| 864/625
| 112/81
| 112/81
Line 385: Line 433:
| 47
| 47
| 569.{{overline|69}}
| 569.{{overline|69}}
|
| 25/18
| 25/18
| "
| "
Line 393: Line 442:
| 48
| 48
| 581.{{overline|81}}
| 581.{{overline|81}}
| d5
| 1024/729
| 1024/729
| 7/5
| 7/5
Line 401: Line 451:
| 49
| 49
| 593.{{overline|93}}
| 593.{{overline|93}}
|
| 45/32
| 45/32
| "
| "
Line 409: Line 460:
| 50
| 50
| 606.{{overline|06}}
| 606.{{overline|06}}
|
| 64/45
| 64/45
| "
| "
Line 417: Line 469:
| 51
| 51
| 618.{{overline|18}}
| 618.{{overline|18}}
| A4
| 729/512
| 729/512
| 10/7
| 10/7
Line 425: Line 478:
| 52
| 52
| 630.{{overline|30}}
| 630.{{overline|30}}
|
| 36/25
| 36/25
| "
| "
Line 433: Line 487:
| 53
| 53
| 642.{{overline|42}}
| 642.{{overline|42}}
|
| 625/432
| 625/432
| 81/56
| 81/56
Line 441: Line 496:
| 54
| 54
| 654.{{overline|54}}
| 654.{{overline|54}}
|
| 729/500
| 729/500
| 35/24
| 35/24
Line 449: Line 505:
| 55
| 55
| 666.{{overline|66}}
| 666.{{overline|66}}
|
| 375/256
| 375/256
| 72/49
| 72/49
Line 457: Line 514:
| 56
| 56
| 678.{{overline|78}}
| 678.{{overline|78}}
|
| 40/27
| 40/27
| "
| "
Line 465: Line 523:
| 57
| 57
| 690.{{overline|90}}
| 690.{{overline|90}}
|
| 6075/4096
| 6075/4096
| 112/75
| 112/75
Line 473: Line 532:
| 58
| 58
| 703.{{overline|03}}
| 703.{{overline|03}}
| P5
| '''3/2'''
| '''3/2'''
| "
| "
Line 481: Line 541:
| 59
| 59
| 715.{{overline|15}}
| 715.{{overline|15}}
|
| 1024/675
| 1024/675
| 189/125
| 189/125
Line 489: Line 550:
| 60
| 60
| 727.{{overline|27}}
| 727.{{overline|27}}
|
| 243/160
| 243/160
| 32/21
| 32/21
Line 497: Line 559:
| 61
| 61
| 739.{{overline|39}}
| 739.{{overline|39}}
|
| 192/125
| 192/125
| 49/32
| 49/32
Line 505: Line 568:
| 62
| 62
| 751.{{overline|51}}
| 751.{{overline|51}}
|
| 125/81
| 125/81
| 54/35
| 54/35
Line 513: Line 577:
| 63
| 63
| 763.{{overline|63}}
| 763.{{overline|63}}
|
| 972/625
| 972/625
| 14/9
| 14/9
Line 521: Line 586:
| 64
| 64
| 775.{{overline|75}}
| 775.{{overline|75}}
|
| 25/16
| 25/16
| "
| "
Line 529: Line 595:
| 65
| 65
| 787.{{overline|87}}
| 787.{{overline|87}}
| m6
| 128/81
| 128/81
| 63/40
| 63/40
Line 537: Line 604:
| 66
| 66
| 800.00
| 800.00
|
| 405/256
| 405/256
| 100/63
| 100/63
Line 545: Line 613:
| 67
| 67
| 812.{{overline|12}}
| 812.{{overline|12}}
|
| '''8/5'''
| '''8/5'''
| "
| "
Line 553: Line 622:
| 68
| 68
| 824.{{overline|24}}
| 824.{{overline|24}}
|
| 3125/1944
| 3125/1944
| 45/28
| 45/28
Line 561: Line 631:
| 69
| 69
| 836.{{overline|36}}
| 836.{{overline|36}}
|
| 81/50
| 81/50
| "
| "
Line 569: Line 640:
| 70
| 70
| 848.{{overline|48}}
| 848.{{overline|48}}
|
| 625/384
| 625/384
| 49/30, 80/49
| 49/30, 80/49
Line 577: Line 649:
| 71
| 71
| 860.{{overline|60}}
| 860.{{overline|60}}
|
| 400/243
| 400/243
| 105/64
| 105/64
Line 585: Line 658:
| 72
| 72
| 872.{{overline|72}}
| 872.{{overline|72}}
|
| 3375/2048
| 3375/2048
| 81/49
| 81/49
Line 593: Line 667:
| 73
| 73
| 884.{{overline|84}}
| 884.{{overline|84}}
|
| 5/3
| 5/3
| "
| "
Line 601: Line 676:
| 74
| 74
| 896.{{overline|96}}
| 896.{{overline|96}}
|
| 2048/1215
| 2048/1215
| 42/25
| 42/25
Line 609: Line 685:
| 75
| 75
| 909.{{overline|09}}
| 909.{{overline|09}}
| M6
| 27/16
| 27/16
| "
| "
Line 617: Line 694:
| 76
| 76
| 921.{{overline|21}}
| 921.{{overline|21}}
|
| 128/75
| 128/75
| "
| "
Line 625: Line 703:
| 77
| 77
| 933.{{overline|33}}
| 933.{{overline|33}}
|
| 1250/729
| 1250/729
| 12/7
| 12/7
Line 633: Line 712:
| 78
| 78
| 945.{{overline|45}}
| 945.{{overline|45}}
|
| 216/125
| 216/125
| 140/81
| 140/81
Line 641: Line 721:
| 79
| 79
| 957.{{overline|57}}
| 957.{{overline|57}}
|
| 125/72
| 125/72
| 26/15
| 26/15
Line 649: Line 730:
| 80
| 80
| 969.{{overline|69}}
| 969.{{overline|69}}
|
| 1280/729
| 1280/729
| '''7/4'''
| '''7/4'''
Line 657: Line 739:
| 81
| 81
| 981.{{overline|81}}
| 981.{{overline|81}}
|
| 225/128
| 225/128
| "
| "
Line 665: Line 748:
| 82
| 82
| 993.{{overline|93}}
| 993.{{overline|93}}
| m7
| 16/9
| 16/9
| "
| "
Line 673: Line 757:
| 83
| 83
| 1006.{{overline|06}}
| 1006.{{overline|06}}
|
| 3645/2048
| 3645/2048
| 25/14
| 25/14
Line 681: Line 766:
| 84
| 84
| 1018.{{overline|18}}
| 1018.{{overline|18}}
|
| 9/5
| 9/5
| "
| "
Line 689: Line 775:
| 85
| 85
| 1030.{{overline|30}}
| 1030.{{overline|30}}
|
| 2048/1125
| 2048/1125
| 49/27
| 49/27
Line 697: Line 784:
| 86
| 86
| 1042.{{overline|42}}
| 1042.{{overline|42}}
|
| 729/400
| 729/400
| 64/35
| 64/35
Line 705: Line 793:
| 87
| 87
| 1054.{{overline|54}}
| 1054.{{overline|54}}
|
| 1152/625
| 1152/625
| 90/49
| 90/49
Line 713: Line 802:
| 88
| 88
| 1066.{{overline|66}}
| 1066.{{overline|66}}
|
| 50/27
| 50/27
| "
| "
Line 721: Line 811:
| 89
| 89
| 1078.{{overline|78}}
| 1078.{{overline|78}}
|
| 4096/2187
| 4096/2187
| 28/15
| 28/15
Line 729: Line 820:
| 90
| 90
| 1090.{{overline|90}}
| 1090.{{overline|90}}
|
| 15/8
| 15/8
| "
| "
Line 737: Line 829:
| 91
| 91
| 1103.{{overline|03}}
| 1103.{{overline|03}}
|
| 256/135
| 256/135
| 189/100
| 189/100
Line 745: Line 838:
| 92
| 92
| 1115.{{overline|15}}
| 1115.{{overline|15}}
| M7
| 243/128
| 243/128
| 40/21
| 40/21
Line 753: Line 847:
| 93
| 93
| 1127.{{overline|27}}
| 1127.{{overline|27}}
|
| 48/25
| 48/25
| "
| "
Line 761: Line 856:
| 94
| 94
| 1139.{{overline|39}}
| 1139.{{overline|39}}
|
| 625/324
| 625/324
| 27/14
| 27/14
Line 769: Line 865:
| 95
| 95
| 1151.{{overline|51}}
| 1151.{{overline|51}}
|
| 243/125
| 243/125
| 35/18
| 35/18
Line 777: Line 874:
| 96
| 96
| 1163.{{overline|63}}
| 1163.{{overline|63}}
|
| 125/64
| 125/64
| 49/25, 96/49
| 49/25, 96/49
Line 785: Line 883:
| 97
| 97
| 1175.{{overline|75}}
| 1175.{{overline|75}}
|
| 160/81
| 160/81
| 63/32
| 63/32
Line 793: Line 892:
| 98
| 98
| 1187.{{overline|87}}
| 1187.{{overline|87}}
|
| 2025/1024
| 2025/1024
| 125/63
| 125/63
Line 801: Line 901:
| 99
| 99
| 1200.00
| 1200.00
| P8
| colspan="5" | '''2/1'''
| colspan="5" | '''2/1'''
|}
|}

Revision as of 08:35, 2 August 2021

This table of 99edo intervals assumes the 99ef val ⟨99 157 230 278 343 367 405 421 448 481] as tending sharp and 99 patent val ⟨99 157 230 278 342 366 405 421 448 481] as tending flat. Prime harmonics and subharmonics are labeled in bold.

# Cents Marks 5-limit 7-limit 13-limit Extension
(Tending Sharp) 		13-limit Extension
(Tending Flat) 		Higher Limit Extension
0 0.00 P1 1/1
1 12.12 2048/2025 126/125
2 24.24 81/80 64/63 56/55, 66/65, 78/77 55/54, 66/65, 78/77 58/57, 69/68, 70/69, 76/75
3 36.36 128/125 49/48, 50/49 40/39, 45/44, 55/54 56/55 46/45, 51/50, 57/56
4 48.48 250/243 36/35 33/32, 40/39, 45/44 35/34
5 60.60 648/625 28/27 27/26, 33/32 26/25 29/28, 30/29
6 72.72 25/24 26/25 22/21, 27/26 24/23
7 84.84 m2 256/243 21/20 22/21 20/19
8 96.96 135/128 " 18/17, 19/18
9 109.09 16/15 " 17/16
10 121.21 2187/2048 15/14 14/13 29/27
11 133.33 27/25 " 13/12, 14/13
12 145.45 625/576 49/45 12/11, 13/12
13 157.57 800/729 35/32 11/10, 12/11 23/21
14 169.69 1125/1024 54/49 11/10 21/19, 32/29
15 181.81 10/9 "
16 193.93 4096/3645 28/25 19/17
17 206.06 M2 9/8 "
18 218.18 256/225 245/216 25/22 17/15
19 230.30 729/640 8/7 25/22
20 242.42 144/125 " 15/13 23/20
21 254.54 125/108 81/70 15/13
22 266.66 729/625 7/6
23 278.78 75/64 " 33/28 20/17, 27/23, 34/29
24 290.90 m3 32/27 " 13/11, 33/28 13/11
25 303.03 1215/1024 25/21 19/16
26 315.15 6/5 "
27 327.27 3125/2592 98/81 40/33 23/19, 29/24
28 339.39 243/200 128/105 11/9, 39/32, 40/33 17/14, 28/23
29 351.51 625/512 49/40, 60/49 11/9, 16/13, 27/22, 39/32
30 363.63 100/81 " 16/13, 26/21, 27/22 21/17
31 375.75 3888/3125 56/45 26/21 36/29
32 387.87 5/4 "
33 400.00 512/405 63/50 24/19, 29/23
34 412.12 M3 81/64 80/63 14/11, 33/26 33/26 19/15
35 424.24 32/25 " 14/11 23/18
36 436.36 625/486 9/7
37 448.48 162/125 35/27 13/10
38 460.60 125/96 64/49 13/10 30/23
39 472.72 320/243 21/16 33/25 38/29
40 484.84 675/512 250/189 33/25
41 496.96 P4 4/3 "
42 509.09 8192/6075 75/56 51/38
43 521.21 27/20 " 23/17
44 533.33 512/375 49/36 15/11
45 545.45 1000/729 48/35 11/8, 15/11
46 557.57 864/625 112/81 11/8, 18/13 29/21, 40/29
47 569.69 25/18 " 18/13 32/23
48 581.81 d5 1024/729 7/5
49 593.93 45/32 " 24/17, 38/27
50 606.06 64/45 " 17/12, 27/19
51 618.18 A4 729/512 10/7
52 630.30 36/25 " 13/9 23/16
53 642.42 625/432 81/56 16/11 29/20, 42/29
54 654.54 729/500 35/24 16/11, 22/15
55 666.66 375/256 72/49 22/15
56 678.78 40/27 " 34/23
57 690.90 6075/4096 112/75 76/51
58 703.03 P5 3/2 "
59 715.15 1024/675 189/125 50/33
60 727.27 243/160 32/21 50/33 29/19
61 739.39 192/125 49/32 20/13 23/15
62 751.51 125/81 54/35 20/13
63 763.63 972/625 14/9
64 775.75 25/16 " 11/7 36/23
65 787.87 m6 128/81 63/40 11/7, 52/33 52/33
66 800.00 405/256 100/63 27/17, 46/29
67 812.12 8/5 "
68 824.24 3125/1944 45/28 21/13 29/18
69 836.36 81/50 " 13/8, 21/13, 44/27 34/21
70 848.48 625/384 49/30, 80/49 13/8, 18/11, 44/27, 64/39
71 860.60 400/243 105/64 18/11, 33/20, 64/39 28/17, 23/14
72 872.72 3375/2048 81/49 33/20 38/23, 48/29
73 884.84 5/3 "
74 896.96 2048/1215 42/25 32/19
75 909.09 M6 27/16 " 22/13, 56/33 22/13
76 921.21 128/75 " 56/33 17/10, 29/17, 46/27
77 933.33 1250/729 12/7
78 945.45 216/125 140/81 26/15
79 957.57 125/72 26/15 40/23
80 969.69 1280/729 7/4 44/25
81 981.81 225/128 " 44/25 30/17
82 993.93 m7 16/9 "
83 1006.06 3645/2048 25/14 34/19
84 1018.18 9/5 "
85 1030.30 2048/1125 49/27 20/11 29/16
86 1042.42 729/400 64/35 11/6, 20/11 42/23
87 1054.54 1152/625 90/49 11/6, 24/13
88 1066.66 50/27 " 13/7, 24/13
89 1078.78 4096/2187 28/15 13/7 54/29
90 1090.90 15/8 " 32/17
91 1103.03 256/135 189/100 17/9, 36/19
92 1115.15 M7 243/128 40/21 19/10
93 1127.27 48/25 " 25/13 52/27 23/12
94 1139.39 625/324 27/14 52/27, 64/33 25/13 29/15, 56/29
95 1151.51 243/125 35/18 39/20, 64/33, 88/45
96 1163.63 125/64 49/25, 96/49 39/20, 88/45, 108/55 55/28 45/23, 100/51, 112/57
97 1175.75 160/81 63/32 55/28, 65/33, 77/39 65/33, 77/39, 108/55 57/29, 69/35, 75/38, 136/69
98 1187.87 2025/1024 125/63
99 1200.00 P8 2/1
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