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== Intervals ==
== Intervals ==
All intervals shown are within the 85-[[odd limit#Nonoctave equaves|throdd limit]] and are consistently represented.
All intervals shown are within the 119-[[odd limit#Nonoctave equaves|throdd limit]] and are consistently represented.


{| class="wikitable center-all right-2 right-3"
{| class="wikitable center-all right-2 right-3"
Line 7: Line 7:
! [[Cent]]s
! [[Cent]]s
! [[Hekt]]s
! [[Hekt]]s
! [[4L 5s (3/1-equivalent)|Enneatonic]] degree
! Corresponding<br />3.5.7.11.17 subgroup<br />intervals
! Corresponding<br />no-twos 19-limit<br />intervals
! Corresponding<br />intervals of 13 and 19
! Dubhe  
! Dubhe  
(LLLLLLLLs, <br>
(LLLLLLLLs, <br>
Line 17: Line 17:
| 0
| 0
| 0
| 0
| P1
| [[1/1]]
| [[1/1]]
|
| J
| J
| E
| E
Line 25: Line 25:
| 0
| 0
| 0
| 0
| P1
|  
| [[1/1]]
|  
| J
| ^J
| E
| ^E
|-
|-
| 2
| 2
| 48.8
| 48.8
| 33.3
| 33.3
| SP1
| [[77/75]] (+3.2c)
| [[77/75]] (+3.2c); [[65/63]] (-5.3c)
| [[65/63]] (-5.3c)
| ^J
| vJ#
| ^E, vF
| ^^E, vvF
|-
|-
| 3
| 3
| 73.2
| 73.2
| 50
| 50
| Sa1/sd2
| [[51/49]] (+3.9c); [[85/81]] (-10.3c)
| [[51/49]] (+3.9c); [[85/81]] (-10.3c)
|
| J#
| J#
| ^E, vF
| vF
|-
|-
| 4
| 4
| 97.5
| 97.5
| 66.7
| 66.7
| sA1/sm2
| [[35/33]] (-4.3c); [[81/77]] (+9.9c)
| [[35/33]] (-4.3c); [[81/77]] (+9.9c)
| vK
|  
| ^J#
| F
| F
|-
|-
Line 57: Line 57:
| 97.5
| 97.5
| 66.7
| 66.7
| sA1/sm2
|  
| [[35/33]] (-4.3c); [[81/77]] (+9.9c)
|  
| vK
| vKb
| F
| ^F
|-
|-
| 6
| 6
| 146.3
| 146.3
| 100
| 100
| A1/m2
| [[49/45]] (-1.1c)
| [[49/45]] (-1.1c); [[27/25]] (+13.1c)
| [[99/91]] (+0.4c)
| K
| Kb
| ^F, vGb, Dx
| ^^F, vvGb, Dx
|-
|-
| 7
| 7
| 146.3
| 146.3
| 100
| 100
| A1/m2
|  
| [[49/45]] (-1.1c); [[27/25]] (+13.1c)
|  
| K
| ^Kb
| ^F, vGb, Dx
| vGb
|-
|-
| 8
| 8
| 195.1
| 195.1
| 133.3
| 133.3
| SA1/Sm2
| [[55/49]] (-4.9c)
| [[55/49]] (-4.9c); [[39/35]] (+7.7c)
| [[91/81]] (-6.5c); [[39/35]] (+7.7c)
| ^K
| vK
| Gb, vE#
| Gb, vvE#
|-
|-
| 9
| 9
| 219.5
| 219.5
| 150
| 150
| N2
| [[135/119]] (+1.1c); [[17/15]] (+2.8c)
| [[17/15]] (+2.8c)
|
| K
| K
| ^F, vF#, vGb
| ^Gb, vE#
|-
|-
| 10
| 10
| 243.8
| 243.8
| 166.7
| 166.7
| sM2/sd3
| [[63/55]] (+8.7c)
| [[15/13]] (-3.9c); [[63/55]] (+8.7c)
| [[15/13]] (-3.9c)
| vK#, vLb
| ^K
| ^Gb, E#
| ^^Gb, E#
|-
|-
| 11
| 11
| 243.8
| 243.8
| 166.7
| 166.7
| sM2/sd3
|  
| [[15/13]] (-3.9c); [[63/55]] (+8.7c)
|  
| vK#, vLb
| vK#
| ^Gb, E#
| ^^^Gb, vvvF#, ^E#
|-
|-
| 12
| 12
| 292.6
| 292.6
| 200
| 200
| M2/d3
| [[25/21]] (-9.2c)
| [[77/65]] (-0.7c); [[13/11]] (+3.4c); [[25/21]] (-9.2c)
| [[77/65]] (-0.7c); [[13/11]] (+3.4c)
| K#, Lb
| K#
| vF#, ^E#
| vvF#, ^^E#
|-
|-
| 13
| 13
| 292.6
| 292.6
| 200
| 200
| M2/d3
|  
| [[77/65]] (-0.7c); [[13/11]] (+3.4c); [[25/21]] (-9.2c)
|  
| K#, Lb
| ^K#
| vF#, ^E#
| vF#
|-
|-
| 14
| 14
| 341.4
| 341.4
| 233.3
| 233.3
| SM2/Sd3
| [[11/9]] (-6.0c)
| [[11/9]] (-6.0c)
| ^K#, ^Lb
| [[91/75]] (+6.6c)
| vLb
| F#
| F#
|-
|-
Line 137: Line 137:
| 365.8
| 365.8
| 250
| 250
| Sa2/sd3
| [[21/17]] (-0.06c)
| [[21/17]] (-0.06c)
|
| Lb
| Lb
| vG, ^F#, ^Gb
| ^F#
|-
|-
| 16
| 16
| 390.1
| 390.1
| 266.7
| 266.7
| sA2/sP3/sd4
|  
| [[49/39]] (-5.0c); [[81/65]] (+9.2c)
| [[49/39]] (-5.0c); [[81/65]] (+9.2c)
| vL
| ^Lb
| vG, ^F#
| vvG, ^^F#
|-
|-
| 17
| 17
| 390.1
| 390.1
| 266.7
| 266.7
| sA2/sP3/sd4
|  
| [[49/39]] (-5.0c); [[81/65]] (+9.2c)
|  
| vL
| vL
| vG, ^F#
| vG
|-
|-
| 18
| 18
| 438.9
| 438.9
| 300
| 300
| A2/P3/d4
| [[9/7]] (+3.8c); [[35/27]] (-10.3c)
| [[9/7]] (+3.8c); [[35/27]] (-10.3c)
|
| L
| L
| G
| G
Line 169: Line 169:
| 438.9
| 438.9
| 300
| 300
| A2/P3/d4
|  
| [[9/7]] (+3.8c); [[35/27]] (-10.3c)
|  
| L
| ^L
| G
| ^G
|-
|-
| 20
| 20
| 487.7
| 487.7
| 333.3
| 333.3
| SA2/SP3/Sd4
| [[33/25]] (+7.0c)
| [[65/49]] (-1.5c); [[33/25]] (+7.0c)
| [[65/49]] (-1.5c)
| ^L
| vL#
| ^G, vAb
| ^^G, vvAb
|-
|-
| 21
| 21
| 512.1
| 512.1
| 350
| 350
| Sa3/sd4
| [[85/63]] (-6.5c)
| [[85/63]] (-6.5c)
|
| L#
| L#
| ^G, vH
| vAb
|-
|-
| 22
| 22
| 536.4
| 536.4
| 366.7
| 366.7
| sA3/sm4/sd5
| [[15/11]] (-0.5c)
| [[15/11]] (-0.5c)
| vM
|  
| ^L#
| Ab
| Ab
|-
|-
Line 201: Line 201:
| 536.4
| 536.4
| 366.7
| 366.7
| sA3/sm4/sd5
|  
| [[15/11]] (-0.5c)
|  
| vM
| vMb
| Ab
| ^Ab
|-
|-
| 24
| 24
| 585.2
| 585.2
| 400
| 400
| A3/m4/d5
| [[7/5]] (+2.7c)
| [[7/5]] (+2.7c)
| M
|  
| ^Ab, Fx
| Mb
| ^^Ab, Fx
|-
|-
| 25
| 25
| 585.2
| 585.2
| 400
| 400
| A3/m4/d5
|  
| [[7/5]] (+2.7c)
|  
| M
| ^Mb
| ^Ab, Fx
| ^^^Ab, vvvG#, vFx
|-
|-
| 26
| 26
| 634.0
| 634.0
| 433.3
| 433.3
| SA3/Sm4/Sd5
|  
| [[13/9]] (-2.6c)
| [[13/9]] (-2.6c)
| ^M
| vM
| vG#
| vvG#
|-
|-
| 27
| 27
| 658.4
| 658.4
| 450
| 450
| N4/sd5
| [[51/35]] (+6.6c); [[119/81]] (-7.6c); [[25/17]] (-9.3c)
| [[51/35]] (+6.6c); [[25/17]] (-9.3c)
|
| M
| M
| ^H, vH#, vJb
| vG#
|-
|-
| 28
| 28
| 682.7
| 682.7
| 466.7
| 466.7
| sM4/sm5
| [[49/33]] (-1.6c); [[81/55]] (+12.6c)
| [[49/33]] (-1.6c); [[81/55]] (+12.6c)
| vM#, vNb
| [[135/91]] (+0.07c)
| ^M
| G#
| G#
|-
|-
Line 249: Line 249:
| 682.7
| 682.7
| 466.7
| 466.7
| sM4/sm5
|  
| [[49/33]] (-1.6c); [[81/55]] (+12.6c)
|  
| vM#, vNb
| vM#
| G#
| ^G#
|-
|-
| 30
| 30
| 731.5
| 731.5
| 500
| 500
| M4/m5
| [[75/49]] (-5.4c)
| [[75/49]] (-5.4c); [[117/77]] (+7.2c)
| [[117/77]] (+7.2c)
| M#, Nb
| M#
| vA, ^G#
| vvA, ^^G#
|-
|-
| 31
| 31
| 731.5
| 731.5
| 500
| 500
| M4/m5
|  
| [[75/49]] (-5.4c); [[117/77]] (+7.2c)
|  
| M#, Nb
| ^M#
| vA, ^G#
| vA
|-
|-
| 32
| 32
| 780.3
| 780.3
| 533.3
| 533.3
| SM4/Sm5
| [[11/7]] (-2.2c)
| [[11/7]] (-2.2c); [[39/25]] (+10.4c)
| [[39/25]] (+10.4c)
| ^M#, ^Nb
| vNb
| A
| A
|-
|-
Line 281: Line 281:
| 804.7
| 804.7
| 550
| 550
| Sa4/N5
| [[27/17]] (+3.8c); [[119/75]] (+5.5c)
| [[27/17]] (+3.8c)
|
| Nb
| Nb
| vJ, ^H#, ^Jb
| ^A
|-
|-
| 34
| 34
| 829.0
| 829.0
| 566.7
| 566.7
| sA4/sM5
|  
| [[21/13]] (-1.2c)
| [[21/13]] (-1.2c)
| vN
| ^Nb
| ^A, vBb
| ^^A, vvBb
|-
|-
| 35
| 35
| 829.0
| 829.0
| 566.7
| 566.7
| sA4/sM5
|  
| [[21/13]] (-1.2c)
|  
| vN
| vN
| ^A, vBb
| vBb
|-
|-
| 36
| 36
| 877.8
| 877.8
| 600
| 600
| A4/M5
| [[5/3]] (-6.5c); [[81/49]] (+7.7c)
| [[5/3]] (-6.5c); [[81/49]] (+7.7c)
| [[91/55]] (+6.1c)
| N
| N
| Bb
| Bb
Line 313: Line 313:
| 877.8
| 877.8
| 600
| 600
| A4/M5
|  
| [[5/3]] (-6.5c); [[81/49]] (+7.7c)
|  
| N
| ^N
| Bb
| ^Bb
|-
|-
| 38
| 38
| 926.6
| 926.6
| 633.3
| 633.3
| SA4/SM5
| [[77/45]] (-3.3c)
| [[77/45]] (-3.3c)
| ^N
|  
| ^Bb, vCb, Gx
| vN#
| ^^Bb, vvCb, Gx
|-
|-
| 39
| 39
| 951.0
| 951.0
| 650
| 650
| Sa5/sd6
| [[85/49]] (-2.6c), [[147/85]] (+2.6c)
| [[85/49]] (-2.6c), [[147/85]] (+2.6c)
|
| N#
| N#
| ^J, vA
| ^^^Bb, vvvA#, ^Cb, vGx
|-
|-
| 40
| 40
| 975.3
| 975.3
| 666.7
| 666.7
| sA5/sm6/sd7
| [[135/77]] (+3.3c)
| [[135/77]] (+3.3c)
| vO
|  
| vA#, Cb
| ^N#
| vvA#, Cb
|-
|-
| 41
| 41
| 975.3
| 975.3
| 666.7
| 666.7
| sA5/sm6/sd7
|  
| [[135/77]] (+3.3c)
|  
| vO
| vOb
| vA#, Cb
| vA#, ^Cb
|-
|-
| 42
| 42
| 1024.1
| 1024.1
| 700
| 700
| A5/m6/d7
| [[9/5]] (+6.5c); [[49/27]] (-7.7c)
| [[9/5]] (+6.5c); [[49/27]] (-7.7c)
| O
| [[165/91]] (-6.1c)
| A#, ^Cb
| Ob
| A#, ^^Cb
|-
|-
| 43
| 43
| 1024.1
| 1024.1
| 700
| 700
| A5/m6/d7
|  
| [[9/5]] (+6.5c); [[49/27]] (-7.7c)
|  
| O
| ^Ob
| A#, ^Cb
| ^A#
|-
|-
| 44
| 44
| 1072.9
| 1072.9
| 733.3
| 733.3
| SA5/Sm6/Sd7
|  
| [[13/7]] (+1.2c)
| [[13/7]] (+1.2c)
| ^O
| vO
| vB, ^A#
| vvB, ^^A#
|-
|-
| 45
| 45
| 1097.3
| 1097.3
| 750
| 750
| N6/sd7
| [[17/9]] (-3.8c); [[225/119]] (-5.5c)
| [[17/9]] (-3.8c)
|
| O
| O
| ^A, vA#, vBb
| vB
|-
|-
| 46
| 46
| 1121.6
| 1121.6
| 766.7
| 766.7
| sM6/sm7
| [[21/11]] (+2.2c)
| [[21/11]] (+2.2c); [[25/13]] (-10.4c)
| [[25/13]] (-10.4c)
| vO#, vPb
| ^O
| B
| B
|-
|-
Line 393: Line 393:
| 1121.6
| 1121.6
| 766.7
| 766.7
| sM6/sm7
|  
| [[21/11]] (+2.2c); [[25/13]] (-10.4c)
|  
| vO#, vPb
| vO#
| B
| ^B
|-
|-
| 48
| 48
| 1170.4
| 1170.4
| 800
| 800
| M6/m7
| [[49/25]] (+5.4c)
| [[49/25]] (+5.4c); [[77/39]] (-7.2c)
| [[77/39]] (-7.2c)
| O#, Pb
| O#
| ^B, vC
| ^^B, vvC
|-
|-
| 49
| 49
| 1170.4
| 1170.4
| 800
| 800
| M6/m7
|  
| [[49/25]] (+5.4c); [[77/39]] (-7.2c)
|  
| O#, Pb
| ^O#
| ^B, vC
| vC
|-
|-
| 50
| 50
| 1219.2
| 1219.2
| 833.3
| 833.3
| SM6/Sm7
| [[99/49]] (+1.6c); [[55/27]] (-12.6c)
| [[99/49]] (+1.6c); [[55/27]] (-12.6c)
| ^O#, ^Pb
| [[91/45]] (+0.07c)
| vPb
| C
| C
|-
|-
Line 425: Line 425:
| 1243.6
| 1243.6
| 850
| 850
| Sa6/N7
| [[35/17]] (-6.6c); [[243/119]] (+7.6c); [[51/25]] (+9.3c)
| [[35/17]] (-6.6c); [[51/25]] (+9.3c)
|
| Pb
| Pb
| vB, ^A#, ^Bb
| ^C
|-
|-
| 52
| 52
| 1267.9
| 1267.9
| 866.7
| 866.7
| sA6/sM7/sd8
|  
| [[27/13]] (+2.6c)
| [[27/13]] (+2.6c)
| vP
| ^Pb
| ^C, vDb
| ^^C, vvDb
|-
|-
| 53
| 53
| 1267.9
| 1267.9
| 866.7
| 866.7
| sA6/sM7/sd8
|  
| [[27/13]] (+2.6c)
|  
| vP
| vP
| ^C, vDb
| vDb
|-
|-
| 54
| 54
| 1316.7
| 1316.7
| 900
| 900
| A6/M7/d8
| [[15/7]] (-2.7c)
| [[15/7]] (-2.7c)
|
| P
| P
| Db, vB#
| Db, vvB#
|-
|-
| 55
| 55
| 1316.7
| 1316.7
| 900
| 900
| A6/M7/d8
|  
| [[15/7]] (-2.7c)
|  
| P
| ^P
| Db, vB#
| ^Db, vB#
|-
|-
| 56
| 56
| 1365.5
| 1365.5
| 933.3
| 933.3
| SA6/SM7/Sd8
| [[11/5]] (+0.5c)
| [[11/5]] (+0.5c)
| ^P
|  
| ^Db, B#
| vP#
| ^^Db, B#
|-
|-
| 57
| 57
| 1389.9
| 1389.9
| 950
| 950
| Sa7/sd8
| [[189/85]] (+6.5c)
| [[189/85]] (+6.5c)
|
| P#
| P#
| ^B, vC
| ^^^Db, vvvC#, ^B#
|-
|-
| 58
| 58
| 1414.2
| 1414.2
| 966.7
| 966.7
| sP8/sd9
| [[25/11]] (-7.0c)
| [[147/65]] (+1.5c); [[25/11]] (-7.0c)
| [[147/65]] (+1.5c)
| vQ
| ^P#
| vC#, ^B#
| vvC#, ^^B#
|-
|-
| 59
| 59
| 1414.2
| 1414.2
| 966.7
| 966.7
| sP8/sd9
|  
| [[147/65]] (+1.5c); [[25/11]] (-7.0c)
|  
| vQ
| vQb
| vC#, ^B#
| vC#
|-
|-
| 60
| 60
| 1463.0
| 1463.0
| 1000
| 1000
| P8/d9
| [[7/3]] (-3.8c); [[81/35]] (+10.3c)
| [[7/3]] (-3.8c); [[81/35]] (+10.3c)
| Q
|  
| Qb
| C#
| C#
|-
|-
Line 505: Line 505:
| 1463.0
| 1463.0
| 1000
| 1000
| P8/d9
|  
| [[7/3]] (-3.8c); [[81/35]] (+10.3c)
|  
| Q
| ^Qb
| C#
| ^C#
|-
|-
| 62
| 62
| 1511.8
| 1511.8
| 1033.3
| 1033.3
| SP8/Sd9
|  
| [[117/49]] (+5.0c); [[65/27]] (-9.2c)
| [[117/49]] (+5.0c); [[65/27]] (-9.2c)
| ^Q
| vQ
| vD, ^C#
| vvD, ^^C#
|-
|-
| 63
| 63
| 1536.2
| 1536.2
| 1050
| 1050
| Sa8/sd9
| [[17/7]] (+0.06c)
| [[17/7]] (+0.06c)
|
| Q
| Q
| ^C, vC#, vDb
| vD
|-
|-
| 64
| 64
| 1560.5
| 1560.5
| 1066.7
| 1066.7
| sA8/sm9
| [[27/11]] (+6.0c)
| [[27/11]] (+6.0c)
| vQ#, vRb
| [[225/91]] (+6.6c)
| ^Q
| D
| D
|-
|-
Line 537: Line 537:
| 1560.5
| 1560.5
| 1066.7
| 1066.7
| sA8/sm9
|  
| [[27/11]] (+6.0c)
|  
| vQ#, vRb
| vQ#
| D
| ^D
|-
|-
| 66
| 66
| 1609.3
| 1609.3
| 1100
| 1100
| A8/m9
| [[63/25]] (+9.2c)
| [[195/77]] (-0.7c); [[33/13]] (-3.4c); [[63/25]] (+9.2c)
| [[195/77]] (-0.7c); [[33/13]] (-3.4c)
| Q#, Rb
| Q#
| ^D, vEb
| ^^D, vvEb
|-
|-
| 67
| 67
| 1609.3
| 1609.3
| 1100
| 1100
| A8/m9
|  
| [[195/77]] (-0.7c); [[33/13]] (-3.4c); [[63/25]] (+9.2c)
|  
| Q#, Rb
| ^Q#
| ^D, vEb
| vEb
|-
|-
| 68
| 68
| 1658.1
| 1658.1
| 1133.3
| 1133.3
| SA8/Sm9
| [[55/21]] (-8.7c)
| [[13/5]] (+3.9c); [[55/21]] (-8.7c)
| [[13/5]] (+3.9c)
| ^Q#, ^Rb
| vRb
| Eb
| Eb
|-
|-
Line 569: Line 569:
| 1682.5
| 1682.5
| 1150
| 1150
| N9
| [[119/45]] (-1.1c); [[45/17]] (-2.8c)
| [[45/17]] (-2.8c)
|
| Rb
| Rb
| vD, ^C#, ^Db
| ^Eb
|-
|-
| 70
| 70
| 1706.9
| 1706.9
| 1166.7
| 1166.7
| sM9/sd10
| [[147/55]] (+4.9c)
| [[147/55]] (+4.9c); [[35/13]] (-7.7c)
| [[243/91]] (+6.5c); [[35/13]] (-7.7c)
| vR
| ^Rb
| ^Eb, vFb, Cx
| ^^Eb, vvFb, Cx
|-
|-
| 71
| 71
| 1706.9
| 1706.9
| 1166.7
| 1166.7
| sM9/sd10
|  
| [[147/55]] (+4.9c); [[35/13]] (-7.7c)
|  
| vR
| vR
| ^Eb, vFb, Cx
| ^^^Eb, vvvD#, vFb, ^Cx
|-
|-
| 72
| 72
| 1755.7
| 1755.7
| 1200
| 1200
| M9/d10
| [[135/49]] (+1.1c)
| [[135/49]] (+1.1c); [[25/9]] (-13.1c)
| [[91/33]] (+0.4c)
| R
| R
| vD#, Fb
| vvD#, Fb
|-
|-
| 73
| 73
| 1755.7
| 1755.7
| 1200
| 1200
| M9/d10
|  
| [[135/49]] (+1.1c); [[25/9]] (-13.1c)
|  
| R
| ^R
| vD#, Fb
| vD#, ^Fb
|-
|-
| 74
| 74
| 1804.5
| 1804.5
| 1233.3
| 1233.3
| SM9/Sd10
| [[99/35]] (+4.3c); [[77/27]] (-9.9c)
| [[99/35]] (+4.3c); [[77/27]] (-9.9c)
| ^R
|  
| D#, ^Fb
| vR#, vJb
| D#, ^^Fb
|-
|-
| 75
| 75
| 1828.8
| 1828.8
| 1250
| 1250
| Sa9/sd10
| [[49/17]] (-3.9c); [[243/85]] (+10.3c)
| [[49/17]] (-3.9c); [[243/85]] (+10.3c)
|
| R#, Jb
| R#, Jb
| ^D, vE
| ^D#
|-
|-
| 76
| 76
| 1853.2
| 1853.2
| 1266.7
| 1266.7
| sA9/sP10
| [[225/77]] (-3.2c)
| [[225/77]] (-3.2c); [[189/65]] (+5.3c)
| [[189/65]] (+5.3c)
| vJ
| ^R#, ^Jb
| vE, ^D#
| vvE, ^^D#
|-
|-
| 77
| 77
| 1853.2
| 1853.2
| 1266.7
| 1266.7
| sA9/sP10
|  
| [[225/77]] (-3.2c); [[189/65]] (+5.3c)
|  
| vJ
| vJ
| vE, ^D#
| vE
|-
|-
| 78
| 78
| 1902.0
| 1902.0
| 1300
| 1300
| A9/P10
| [[3/1]]
| [[3/1]]
|
| J
| J
| E
| E
|}
|}
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