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'''Tertiaseptal''' is a [[regular temperament|temperament]] for the 7, 11, 13, and 17 limit. EDOs that support tertiaseptal include [[31edo]], [[140edo]], and [[171edo]].
{{Todo|inline=1|improve synopsis|improve readability|comment= Add infobox. Cut huge tables to reasonable sizes.}}


See [[Breedsmic_temperaments#Tertiaseptal|Breedsmic temperaments]] for more information.
'''Tertiaseptal''' is a [[regular temperament|temperament]] for the 7, 11, 13, and 17 limit. EDOs that support tertiaseptal include [[31edo]], [[140edo]], [[171edo]] and [[311edo]].
 
See [[Breedsmic temperaments #Tertiaseptal]] for more information.
 
== Interval chain ==
=== Tertiaseptal and tertia ===


==Interval chain==
<font style="font-size:1.3em;font-weight:bold;">Tertiaseptal and tertia</font>
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 11: Line 14:
! colspan="2"| 17-limit ratio<br>(octave-reduced)
! colspan="2"| 17-limit ratio<br>(octave-reduced)
|-
|-
! | tertiaseptal <br>(31&amp;171)
! tertiaseptal <br>(31&amp;171)
! | tertia <br>(31&amp;140)
! tertia <br>(31&amp;140)
|-
|-
| | 1
| 1
| | 77.2
| 77.2
| | 117/112, 256/245, 68/65
| 117/112, 256/245, 68/65
| | 117/112, 256/245, 68/65, [[22/21]]
| 117/112, 256/245, 68/65, [[22/21]]
|-
|-
| | 2
| 2
| | 154.4
| 154.4
| | 130/119, [[35/32]]
| 130/119, [[35/32]]
| | '''[[12/11]]''', 130/119, 35/32
| '''[[12/11]]''', 130/119, 35/32
|-
|-
| | 3
| 3
| | 231.6
| 231.6
| colspan="2"| '''[[8/7]]'''
| colspan="2"| '''[[8/7]]'''
|-
|-
| | 4
| 4
| | 308.8
| 308.8
| colspan="2"| 117/98, 140/117
| colspan="2"| 117/98, 140/117
|-
|-
| | 5
| 5
| | 386.0
| 386.0
| colspan="2"| '''[[5/4]]'''
| colspan="2"| '''[[5/4]]'''
|-
|-
| | 6
| 6
| | 463.1
| 463.1
| colspan="2"| '''[[17/13]]'''
| colspan="2"| '''[[17/13]]'''
|-
|-
| | 7
| 7
| | 540.3
| 540.3
| | 175/128
| 175/128
| | '''[[15/11]]''', 175/128
| '''[[15/11]]''', 175/128
|-
|-
| | 8
| 8
| | 617.5
| 617.5
| colspan="2"| '''[[10/7]]'''
| colspan="2"| '''[[10/7]]'''
|-
|-
| | 9
| 9
| | 694.7
| 694.7
| colspan="2"| 112/75
| colspan="2"| 112/75
|-
|-
| | 10
| 10
| | 771.9
| 771.9
| colspan="2"| [[25/16]]
| colspan="2"| [[25/16]]
|-
|-
| | 11
| 11
| | 849.1
| 849.1
| | 44/27, 80/49, 49/30, 85/52, '''[[18/11]]'''
| 44/27, 80/49, 49/30, 85/52, '''[[18/11]]'''
| | 80/49, 49/30, 85/52
| 80/49, 49/30, 85/52
|-
|-
| | 12
| 12
| | 926.3
| 926.3
| colspan="2"| 128/75
| colspan="2"| 128/75
|-
|-
| | 13
| 13
| | 1003.5
| 1003.5
| colspan="2"| [[25/14]]
| colspan="2"| [[25/14]]
|-
|-
| | 14
| 14
| | 1080.7
| 1080.7
| colspan="2"| '''[[28/15]]'''
| colspan="2"| '''[[28/15]]'''
|-
|-
| | 15
| 15
| | 1157.9
| 1157.9
| | 39/20
| 39/20
| | 39/20, 88/45
| 39/20, 88/45
|-
|-
| | 16
| 16
| | 35.1
| 35.1
| | 55/54, 52/51, 51/50, [[50/49]], [[49/48]], [[45/44]]
| 55/54, 52/51, 51/50, [[50/49]], [[49/48]], [[45/44]]
| | 56/55, 52/51, 51/50, 50/49, 49/48
| 56/55, 52/51, 51/50, 50/49, 49/48
|-
|-
| | 17
| 17
| | 112.3
| 112.3
| colspan="2"| '''[[16/15]]'''
| colspan="2"| '''[[16/15]]'''
|-
|-
| | 18
| 18
| | 189.4
| 189.4
| colspan="2"| 39/35
| colspan="2"| 39/35
|-
|-
| | 19
| 19
| | 266.6
| 266.6
| colspan="2"| '''[[7/6]]'''
| colspan="2"| '''[[7/6]]'''
|-
|-
| | 20
| 20
| | 343.8
| 343.8
| | 39/32
| 39/32
| | 39/32, '''[[11/9]]'''
| 39/32, '''[[11/9]]'''
|-
|-
| | 21
| 21
| | 421.0
| 421.0
| | [[51/40]]
| [[51/40]]
| | '''[[14/11]]''', 51/40
| '''[[14/11]]''', 51/40
|-
|-
| | 22
| 22
| | 498.2
| 498.2
| colspan="2"| '''[[4/3]]'''
| colspan="2"| '''[[4/3]]'''
|-
|-
| | 23
| 23
| | 575.4
| 575.4
| colspan="2"| 39/28
| colspan="2"| 39/28
|-
|-
| | 24
| 24
| | 652.6
| 652.6
| | [[35/24]]
| [[35/24]]
| | '''[[16/11]]''', 35/24
| '''[[16/11]]''', 35/24
|-
|-
| | 25
| 25
| | 729.8
| 729.8
| colspan="2"| [[32/21]]
| colspan="2"| [[32/21]]
|-
|-
| | 26
| 26
| | 807.0
| 807.0
| | 51/32
| 51/32
| | 35/22, 51/32
| 35/22, 51/32
|-
|-
| | 27
| 27
| | 884.2
| 884.2
| colspan="2"| '''[[5/3]]'''
| colspan="2"| '''[[5/3]]'''
|-
|-
| | 28
| 28
| | 961.4
| 961.4
| colspan="2"| 68/39
| colspan="2"| 68/39
|-
|-
| | 29
| 29
| | 1038.6
| 1038.6
| | 51/28
| 51/28
| | '''[[20/11]]''', 51/28
| '''[[20/11]]''', 51/28
|-
|-
| | 30
| 30
| | 1115.7
| 1115.7
| | [[40/21]], [[21/11]]
| [[40/21]], [[21/11]]
| | 40/21
| 40/21
|-
|-
| | 31
| 31
| | 1192.9
| 1192.9
| colspan="2"|  
| colspan="2"|  
|-
|-
| | 32
| 32
| | 70.1
| 70.1
| colspan="2"| [[26/25]], [[25/24]]
| colspan="2"| [[26/25]], [[25/24]]
|-
|-
| | 33
| 33
| | 147.3
| 147.3
| | 49/45, '''12/11'''
| 49/45, '''12/11'''
| | 49/45
| 49/45
|-
|-
| | 34
| 34
| | 224.5
| 224.5
| | 91/80
| 91/80
| | [[25/22]], 91/80
| [[25/22]], 91/80
|-
|-
| | 35
| 35
| | 301.7
| 301.7
| colspan="2"| [[25/21]]
| colspan="2"| [[25/21]]
|-
|-
| | 36
| 36
| | 378.9
| 378.9
| | 56/45, 96/77
| 56/45, 96/77
| | 56/45
| 56/45
|-
|-
| | 37
| 37
| | 456.1
| 456.1
| colspan="2"| '''[[13/10]]'''
| colspan="2"| '''[[13/10]]'''
|-
|-
| | 38
| 38
| | 533.3
| 533.3
| | 34/25, '''15/11'''
| 34/25, '''15/11'''
| | 34/25
| 34/25
|-
|-
| | 39
| 39
| | 610.5
| 610.5
| colspan="2"| [[64/45]]
| colspan="2"| [[64/45]]
|-
|-
| | 40
| 40
| | 687.7
| 687.7
| colspan="2"| 52/35
| colspan="2"| 52/35
|-
|-
| | 41
| 41
| | 764.8
| 764.8
| colspan="2"| '''[[14/9]]'''
| colspan="2"| '''[[14/9]]'''
|-
|-
| | 42
| 42
| | 842.0
| 842.0
| colspan="2"| '''[[13/8]]'''
| colspan="2"| '''[[13/8]]'''
|-
|-
| | 43
| 43
| | 919.2
| 919.2
| colspan="2"| '''[[17/10]]'''
| colspan="2"| '''[[17/10]]'''
|-
|-
| | 44
| 44
| | 996.4
| 996.4
| colspan="2"| '''[[16/9]]'''
| colspan="2"| '''[[16/9]]'''
|-
|-
| | 45
| 45
| | 1073.6
| 1073.6
| colspan="2"| '''[[13/7]]'''
| colspan="2"| '''[[13/7]]'''
|-
|-
| | 46
| 46
| | 1150.8
| 1150.8
| | 68/35, [[35/18]]
| 68/35, [[35/18]]
| | 64/33, 68/35, 35/18
| 64/33, 68/35, 35/18
|-
|-
| | 47
| 47
| | 28.0
| 28.0
| | [[65/64]], [[64/63]], [[56/55]]
| [[65/64]], [[64/63]], [[56/55]]
| | 78/77, 65/64, 64/63, 55/54
| 78/77, 65/64, 64/63, 55/54
|-
|-
| | 48
| 48
| | 105.2
| 105.2
| colspan="2"| '''[[17/16]]'''
| colspan="2"| '''[[17/16]]'''
|-
|-
| | 49
| 49
| | 182.4
| 182.4
| colspan="2"| '''[[10/9]]'''
| colspan="2"| '''[[10/9]]'''
|-
|-
| | 50
| 50
| | 259.6
| 259.6
| | 65/56, [[64/55]]
| 65/56, [[64/55]]
| | 65/56
| 65/56
|-
|-
| | 51
| 51
| | 336.8
| 336.8
| colspan="2"| '''[[17/14]]'''
| colspan="2"| '''[[17/14]]'''
|-
|-
| | 52
| 52
| | 414.0
| 414.0
| | 80/63, '''14/11'''
| 80/63, '''14/11'''
| | 80/63
| 80/63
|-
|-
| | 53
| 53
| | 491.1
| 491.1
| colspan="2"| 65/49
| colspan="2"| 65/49
|-
|-
| | 54
| 54
| | 568.3
| 568.3
| colspan="2"| [[25/18]]
| colspan="2"| [[25/18]]
|-
|-
| | 55
| 55
| | 645.5
| 645.5
| | '''16/11'''
| '''16/11'''
| |  
|  
|-
|-
| | 56
| 56
| | 722.7
| 722.7
| | 85/56
| 85/56
| | 50/33, 85/56
| 50/33, 85/56
|-
|-
| | 57
| 57
| | 799.9
| 799.9
| | 100/63, 35/22
| 100/63, 35/22
| | 100/63
| 100/63
|-
|-
| | 58
| 58
| | 877.1
| 877.1
| | 128/77
| 128/77
| |  
|  
|-
|-
| | 59
| 59
| | 954.3
| 954.3
| colspan="2"| '''[[26/15]]'''
| colspan="2"| '''[[26/15]]'''
|-
|-
| | 60
| 60
| | 1031.5
| 1031.5
| | 136/75, '''20/11'''
| 136/75, '''20/11'''
| | 136/75
| 136/75
|-
|-
| | 61
| 61
| | 1108.7
| 1108.7
| colspan="2"| 91/48, 256/135
| colspan="2"| 91/48, 256/135
|-
|-
| | 62
| 62
| | 1185.9
| 1185.9
| | 208/105
| 208/105
| | 196/99, 208/105
| 196/99, 208/105
|-
|-
| | 63
| 63
| | 63.1
| 63.1
| colspan="2"| [[28/27]]
| colspan="2"| [[28/27]]
|-
|-
| | 64
| 64
| | 140.3
| 140.3
| colspan="2"| '''[[13/12]]'''
| colspan="2"| '''[[13/12]]'''
|-
|-
| | 65
| 65
| | 217.4
| 217.4
| | '''[[17/15]]''', 25/22
| '''[[17/15]]''', 25/22
| | '''17/15'''
| '''17/15'''
|-
|-
| | 66
| 66
| | 294.6
| 294.6
| | [[32/27]]
| [[32/27]]
| | '''[[13/11]]''', 32/27
| '''[[13/11]]''', 32/27
|-
|-
| | 67
| 67
| | 371.8
| 371.8
| colspan="2"| [[26/21]]
| colspan="2"| [[26/21]]
|-
|-
| | 68
| 68
| | 449.0
| 449.0
| colspan="2"| [[35/27]]
| colspan="2"| [[35/27]]
|-
|-
| | 69
| 69
| | 526.2
| 526.2
| colspan="2"| 65/48
| colspan="2"| 65/48
|-
|-
| | 70
| 70
| | 603.4
| 603.4
| colspan="2"| '''[[17/12]]'''
| colspan="2"| '''[[17/12]]'''
|-
|-
| | 71
| 71
| | 680.6
| 680.6
| colspan="2"| [[40/27]]
| colspan="2"| [[40/27]]
|-
|-
| | 72
| 72
| | 757.8
| 757.8
| | 65/42
| 65/42
| | '''[[17/11]]''', 65/42
| '''[[17/11]]''', 65/42
|-
|-
| | 73
| 73
| | 835.0
| 835.0
| colspan="2"| [[34/21]]
| colspan="2"| [[34/21]]
|-
|-
| | 74
| 74
| | 912.2
| 912.2
| | 56/33
| 56/33
| |  
|  
|-
|-
| | 75
| 75
| | 989.4
| 989.4
| | 39/22
| 39/22
| | 136/77, 85/48
| 136/77, 85/48
|-
|-
| | 76
| 76
| | 1066.6
| 1066.6
| colspan="2"| 50/27
| colspan="2"| 50/27
|-
|-
| | 77
| 77
| | 1143.7
| 1143.7
| | 64/33
| 64/33
| | 85/44
| 85/44
|-
|-
| | 78
| 78
| | 20.9
| 20.9
| | 91/90, 85/84, 78/77
| 91/90, 85/84, 78/77
| | [[100/99]], 91/90, 85/84
| [[100/99]], 91/90, 85/84
|-
|-
| | 79
| 79
| | 98.1
| 98.1
| | 35/33
| 35/33
| |  
|  
|-
|-
| | 80
| 80
| | 175.3
| 175.3
| | 195/176
| 195/176
| |  
|  
|-
|-
| | 81
| 81
| | 252.5
| 252.5
| colspan="2"| 52/45
| colspan="2"| 52/45
|-
|-
| | 82
| 82
| | 329.7
| 329.7
| | 40/33
| 40/33
| |  
|  
|-
|-
| | 83
| 83
| | 406.9
| 406.9
| colspan="2"| 91/72
| colspan="2"| 91/72
|-
|-
| | 84
| 84
| | 484.1
| 484.1
| colspan="2"| 119/90
| colspan="2"| 119/90
|-
|-
| | 85
| 85
| | 561.3
| 561.3
| colspan="2"| 112/81
| colspan="2"| 112/81
|-
|-
| | 86
| 86
| | 638.5
| 638.5
| colspan="2"| '''[[13/9]]'''
| colspan="2"| '''[[13/9]]'''
|-
|-
| | 87
| 87
| | 715.7
| 715.7
| | 68/45, 50/33
| 68/45, 50/33
| | 68/45
| 68/45
|-
|-
| | 88
| 88
| | 792.8
| 792.8
| | 128/81
| 128/81
| | 52/33, 128/81
| 52/33, 128/81
|-
|-
| | 89
| 89
| | 870.0
| 870.0
| colspan="2"| 119/72
| colspan="2"| 119/72
|-
|-
| | 90
| 90
| | 947.2
| 947.2
| colspan="2"| 140/81
| colspan="2"| 140/81
|-
|-
| | 91
| 91
| | 1024.4
| 1024.4
| colspan="2"| 65/36
| colspan="2"| 65/36
|-
|-
| | 92
| 92
| | 1101.6
| 1101.6
| colspan="2"| '''[[17/9]]'''
| colspan="2"| '''[[17/9]]'''
|-
|-
| | 93
| 93
| | 1178.8
| 1178.8
| | [[160/81]], 196/99, 240/121
| [[160/81]], 196/99, 240/121
| | 65/33, 160/81
| 65/33, 160/81
|-
|-
| | 94
| 94
| | 56.0
| 56.0
| | 91/88
| 91/88
| | 34/33
| 34/33
|-
|-
| | 95
| 95
| | 133.2
| 133.2
| colspan="2"| 68/63
| colspan="2"| 68/63
|-
|-
| | 96
| 96
| | 210.4
| 210.4
| | 112/99
| 112/99
| |  
|  
|-
|-
| | 97
| 97
| | 287.6
| 287.6
| | '''13/11'''
| '''13/11'''
| |  
|  
|-
|-
| | 98
| 98
| | 364.8
| 364.8
| | 68/55
| 68/55
| |  
|  
|-
|-
| | 99
| 99
| | 442.0
| 442.0
| | 128/99
| 128/99
| |  
|  
|-
|-
| | 100
| 100
| | 519.1
| 519.1
| | 104/77
| 104/77
| |  
|  
|-
|-
| | 101
| 101
| | 596.3
| 596.3
| |  
|  
| |  
|  
|-
|-
| | 102
| 102
| | 673.5
| 673.5
| |  
|  
| |  
|  
|-
|-
| | 103
| 103
| | 750.7
| 750.7
| | '''17/11'''
| '''17/11'''
| |  
|  
|-
|-
| | 104
| 104
| | 827.9
| 827.9
| | 160/99
| 160/99
| |  
|  
|-
|-
| | 105
| 105
| | 905.1
| 905.1
| |  
|  
| |  
|  
|-
|-
| | 106
| 106
| | 982.3
| 982.3
| | 136/77
| 136/77
| |  
|  
|-
|-
| | 107
| 107
| | 1059.5
| 1059.5
| |  
|  
| |  
|  
|-
|-
| | 108
| 108
| | 1136.7
| 1136.7
| | 52/27, 85/44
| 52/27, 85/44
| | 52/27
| 52/27
|-
|-
| | 109
| 109
| | 13.9
| 13.9
| | 100/99
| 100/99
| |  
|  
|-
|-
| | 110
| 110
| | 91.1
| 91.1
| | 128/121, [[256/243]]
| 128/121, [[256/243]]
| | 104/99, 256/243
| 104/99, 256/243
|-
|-
| | 111
| 111
| | 168.3
| 168.3
| |  
|  
| |  
|  
|-
|-
| | 112
| 112
| | 245.4
| 245.4
| |  
|  
| |  
|  
|-
|-
| | 113
| 113
| | 322.6
| 322.6
| |  
|  
| |  
|  
|-
|-
| | 114
| 114
| | 399.8
| 399.8
| colspan="2"| 34/27
| colspan="2"| 34/27
|-
|-
| | 115
| 115
| | 477.0
| 477.0
| |  
|  
| |  
|  
|-
|-
| | 116
| 116
| | 554.2
| 554.2
| |  
|  
| |  
|  
|-
|-
| | 117
| 117
| | 631.4
| 631.4
| |  
|  
| |  
|  
|-
|-
| | 118
| 118
| | 708.6
| 708.6
| |  
|  
| |  
|  
|-
|-
| | 119
| 119
| | 785.8
| 785.8
| | 52/33
| 52/33
| |  
|  
|-
|-
| | 120
| 120
| | 863.0
| 863.0
| |  
|  
| |  
|  
|-
|-
| | 121
| 121
| | 940.2
| 940.2
| |  
|  
| |  
|  
|-
|-
| | 122
| 122
| | 1017.4
| 1017.4
| |  
|  
| |  
|  
|-
|-
| | 123
| 123
| | 1094.5
| 1094.5
| |  
|  
| |  
|  
|-
|-
| | 124
| 124
| | 1171.7
| 1171.7
| | 65/33
| 65/33
| |  
|  
|-
|-
| | 125
| 125
| | 48.9
| 48.9
| | 34/33
| 34/33
| |  
|  
|}
|}
<sup>a</sup> in 7-limit POTE tuning
<sup>a</sup> in 7-limit POTE tuning


<font style="font-size:1.3em;font-weight:bold;">Hemitert</font>
=== Hemitert ===
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | generator
! generator
! | cents value <sup>a</sup><br>(octave-reduced)
! cents value <sup>a</sup><br>(octave-reduced)
! | 11-limit ratio<br>(octave-reduced)
! 11-limit ratio<br>(octave-reduced)
|-
|-
| | 1
| 1
| | 38.6
| 38.6
| | 45/44
| [[45/44]]
|-
|-
| | 2
| 2
| | 77.2
| 77.2
| | 256/245
| 256/245
|-
|-
| | 3
| 3
| | 115.8
| 115.8
| |  
|  
|-
|-
| | 4
| 4
| | 154.4
| 154.4
| | 35/32
| [[35/32]]
|-
|-
| | 5
| 5
| | 193.0
| 193.0
| |  
|  
|-
|-
| | 6
| 6
| | 231.6
| 231.6
| | '''8/7'''
| '''[[8/7]]'''
|-
|-
| | 7
| 7
| | 270.2
| 270.2
| |  
|  
|-
|-
| | 8
| 8
| | 308.8
| 308.8
| |  
|  
|-
|-
| | 9
| 9
| | 347.4
| 347.4
| | '''11/9'''
| '''[[11/9]]'''
|-
|-
| | 10
| 10
| | 386.0
| 386.0
| | '''5/4'''
| '''[[5/4]]'''
|-
|-
| | 11
| 11
| | 424.6
| 424.6
| |  
|  
|-
|-
| | 12
| 12
| | 463.1
| 463.1
| |
| 64/49
|-
|-
| | 13
| 13
| | 501.7
| 501.7
| |  
|  
|-
|-
| | 14
| 14
| | 540.3
| 540.3
| |  
|  
|-
|-
| | 15
| 15
| | 578.9
| 578.9
| |  
|  
|-
|-
| | 16
| 16
| | 617.5
| 617.5
| | '''10/7'''
| '''[[10/7]]'''
|-
|-
| | 17
| 17
| | 656.1
| 656.1
| |  
|  
|-
|-
| | 18
| 18
| | 694.7
| 694.7
| |  
|  
|-
|-
| | 19
| 19
| | 733.3
| 733.3
| |  
|  
|-
|-
| | 20
| 20
| | 771.9
| 771.9
| |
| [[25/16]]
|-
|-
| | 21
| 21
| | 810.5
| 810.5
| |  
|  
|-
|-
| | 22
| 22
| | 849.1
| 849.1
| |  
|  
|-
|-
| | 23
| 23
| | 887.7
| 887.7
| |  
|  
|-
|-
| | 24
| 24
| | 926.3
| 926.3
| |  
|  
|-
|-
| | 25
| 25
| | 964.9
| 964.9
| |  
|  
|-
|-
| | 26
| 26
| | 1003.5
| 1003.5
| |
| [[25/14]]
|-
|-
| | 27
| 27
| | 1042.1
| 1042.1
| |  
|  
|-
|-
| | 28
| 28
| | 1080.7
| 1080.7
| | '''28/15'''
| '''[[28/15]]'''
|-
|-
| | 29
| 29
| | 1119.3
| 1119.3
| |
| [[21/11]]
|-
|-
| | 30
| 30
| | 1157.9
| 1157.9
| |  
|  
|-
|-
| | 31
| 31
| | 1196.5
| 1196.5
| |  
|  
|-
|-
| | 32
| 32
| | 35.1
| 35.1
| |
| [[50/49]], [[49/48]]
|-
|-
| | 33
| 33
| | 73.7
| 73.7
| |  
|  
|-
|-
| | 34
| 34
| | 112.2
| 112.2
| | '''16/15'''
| '''[[16/15]]'''
|-
|-
| | 35
| 35
| | 150.8
| 150.8
| | '''12/11'''
| '''[[12/11]]'''
|-
|-
| | 36
| 36
| | 189.4
| 189.4
| |  
|  
|-
|-
| | 37
| 37
| | 228.0
| 228.0
| |  
|  
|-
|-
| | 38
| 38
| | 266.6
| 266.6
| | '''7/6'''
| '''[[7/6]]'''
|-
|-
| | 39
| 39
| | 305.2
| 305.2
| |  
|  
|-
|-
| | 40
| 40
| | 343.8
| 343.8
| |  
|  
|-
|-
| | 41
| 41
| | 382.4
| 382.4
| |  
|  
|-
|-
| | 42
| 42
| | 421.0
| 421.0
| |  
|  
|-
|-
| | 43
| 43
| | 459.6
| 459.6
| |  
|  
|-
|-
| | 44
| 44
| | 498.2
| 498.2
| | '''4/3'''
| '''[[4/3]]'''
|-
|-
| | 45
| 45
| | 536.8
| 536.8
| | '''15/11'''
| '''[[15/11]]'''
|-
|-
| | 46
| 46
| | 575.4
| 575.4
| |  
|  
|-
|-
| | 47
| 47
| | 614.0
| 614.0
| |  
|  
|-
|-
| | 48
| 48
| | 652.6
| 652.6
| |  
|  
|-
|-
| | 49
| 49
| | 691.2
| 691.2
| |  
|  
|-
|-
| | 50
| 50
| | 729.8
| 729.8
| |
| 32/21
|-
|-
| | 51
| 51
| | 768.4
| 768.4
| |  
|  
|-
|-
| | 52
| 52
| | 807.0
| 807.0
| |  
|  
|-
|-
| | 53
| 53
| | 845.6
| 845.6
| |  
|  
|-
|-
| | 54
| 54
| | 884.2
| 884.2
| | '''5/3'''
| '''[[5/3]]'''
|-
|-
| | 55
| 55
| | 922.8
| 922.8
| |  
|  
|-
|-
| | 56
| 56
| | 961.4
| 961.4
| |  
|  
|-
|-
| | 57
| 57
| | 999.9
| 999.9
| |  
|  
|-
|-
| | 58
| 58
| | 1038.5
| 1038.5
| |  
|  
|-
|-
| | 59
| 59
| | 1077.1
| 1077.1
| |  
|  
|-
|-
| | 60
| 60
| | 1115.7
| 1115.7
| |
| 40/21
|-
|-
| | 61
| 61
| | 1154.3
| 1154.3
| |  
|  
|-
|-
| | 62
| 62
| | 1192.9
| 1192.9
| |  
|  
|-
|-
| | 63
| 63
| | 31.5
| 31.5
| |  
|  
|-
|-
| | 64
| 64
| | 70.1
| 70.1
| |
| [[25/24]]
|-
|-
| | 65
| 65
| | 108.7
| 108.7
| |  
|  
|-
|-
| | 66
| 66
| | 147.3
| 147.3
| |  
|  
|-
|-
| | 67
| 67
| | 185.9
| 185.9
| |  
|  
|-
|-
| | 68
| 68
| | 224.5
| 224.5
| |  
|  
|-
|-
| | 69
| 69
| | 263.1
| 263.1
| |  
|  
|-
|-
| | 70
| 70
| | 301.7
| 301.7
| |  
|  
|-
|-
| | 71
| 71
| | 340.3
| 340.3
| |  
|  
|-
|-
| | 72
| 72
| | 378.9
| 378.9
| |  
|  
|-
|-
| | 73
| 73
| | 417.5
| 417.5
| | '''14/11'''
| '''[[14/11]]'''
|-
|-
| | 74
| 74
| | 456.1
| 456.1
| |  
|  
|-
|-
| | 75
| 75
| | 494.7
| 494.7
| |  
|  
|-
|-
| | 76
| 76
| | 533.3
| 533.3
| |  
|  
|-
|-
| | 77
| 77
| | 571.9
| 571.9
| |  
|  
|-
|-
| | 78
| 78
| | 610.5
| 610.5
| |  
|  
|-
|-
| | 79
| 79
| | 649.1
| 649.1
| | '''16/11'''
| '''[[16/11]]'''
|-
|-
| | 80
| 80
| | 687.6
| 687.6
| |  
|  
|-
|-
| | 81
| 81
| | 726.2
| 726.2
| |  
|  
|-
|-
| | 82
| 82
| | 764.8
| 764.8
| | '''14/9'''
| '''[[14/9]]'''
|-
|-
| | 83
| 83
| | 803.4
| 803.4
| |  
|  
|-
|-
| | 84
| 84
| | 842.0
| 842.0
| |  
|  
|-
|-
| | 85
| 85
| | 880.6
| 880.6
| |  
|  
|-
|-
| | 86
| 86
| | 919.2
| 919.2
| |  
|  
|-
|-
| | 87
| 87
| | 957.8
| 957.8
| |  
|  
|-
|-
| | 88
| 88
| | 996.4
| 996.4
| | '''16/9'''
| '''[[16/9]]'''
|-
|-
| | 89
| 89
| | 1035.0
| 1035.0
| | '''20/11'''
| '''[[20/11]]'''
|-
|-
| | 90
| 90
| | 1073.6
| 1073.6
| |  
|  
|-
|-
| | 91
| 91
| | 1112.2
| 1112.2
| |  
|  
|-
|-
| | 92
| 92
| | 1150.8
| 1150.8
| |  
|  
|-
|-
| | 93
| 93
| | 1189.4
| 1189.4
| |  
|  
|-
|-
| | 94
| 94
| | 28.0
| 28.0
| |
| [[64/63]]
|-
|-
| | 95
| 95
| | 66.6
| 66.6
| |  
|  
|-
|-
| | 96
| 96
| | 105.2
| 105.2
| |  
|  
|-
|-
| | 97
| 97
| | 143.8
| 143.8
| |  
|  
|-
|-
| | 98
| 98
| | 182.4
| 182.4
| | '''10/9'''
| '''[[10/9]]'''
|}
|}
<sup>a</sup> in 11-limit POTE tuning
<sup>a</sup> in 11-limit POTE tuning


==Tuning spectrum by Eigenmonzos==
== Tuning spectra ==
<font style="font-size:1.3em;font-weight:bold;">Tertiaseptal</font>
=== Tertiaseptal ===
Gencom: [2 68/65; 243/242 375/374 441/440 625/624 3584/3575]


{| class="wikitable"
Gencom mapping: [{{val|1 3 2 3 7 1 1}}, {{val|0 -22 5 -3 -55 42 48}}]
 
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! | Septimal <br>whole tone
! generator<br>(¢)
! | Major third
! comments
! | Perfect fifth
|-
|-
| | 4/3
| 8/7
| | 231.5516
| 77.0580
| | 385.9193
|  
| | 701.9550
|-
|-
| | 5/4
| 13/10
| | 231.7882
| 77.1409
| | 386.3137
|  
| | 700.2197
|-
|-
| | 6/5
| 14/13
| | 231.5954
| 77.1489
| | 385.9924
|  
| | 701.6336
|-
|-
| | 7/5
| 16/13
| | 231.5579
| 77.1554
| | 385.9299
|  
| | 701.9085
|-
|-
| | 7/6
| 15/13
| | 231.6112
| 77.1569
| | 386.0187
|  
| | 701.5179
|-
|-
| | 8/7
| 16/15
| | 231.1741
| 77.1607
| | 385.2902
|  
| | 704.7233
|-
|-
| | 9/7
| 13/12
| | 231.5792
| 77.1652
| | 385.9654
|  
| | 701.7524
|-
|-
| | 10/9
| 18/13
| | 231.5757
| 77.1700
| | 385.9596
|  
| | 701.7779
|-
|-
| | 11/8
| 20/17
| | 231.7463
| 77.1777
| | 386.2438
|  
| | 700.5272
|-
|-
| | 11/9
| 17/14
| | 232.5251
| 77.1790
| | 387.5418
|  
| | 694.8159
|-
|-
| | 11/10
| 17/15
| | 231.7498
| 77.1798
| | 386.2496
|  
| | 700.5016
|-
|-
| | 12/11
| 15/14
| | 231.8761
| 77.1827
| | 386.4602
|  
| | 699.5753
|-
|-
| | 14/11
| 4/3
| | 231.7793
| 77.1839
| | 386.2988
|  
| | 700.2851
|-
|-
| | 13/10
| 18/17
| | 231.4228
| 77.1853
| | 385.7046
|  
| | 702.8998
|-
|-
| | 13/11
| 24/17
| | 231.6250
| 77.1857
| | 386.0417
|  
| | 701.4164
|-
|-
| | 13/12
| 7/5
| | 231.4956
| 77.1860
| | 385.8260
| 7 and 9-odd-limit minimax
| | 702.3656
|-
|-
| | 14/13
| 17/16
| | 231.4468
| 77.1866
| | 385.7446
|  
| | 702.7236
|-
|-
| | 16/13
| 10/9
| | 231.4663
| 77.1919
| | 385.7771
|  
| | 702.5807
|-
|-
| | 18/13
| 9/7
| | 231.5099
| 77.1931
| | 385.8499
|  
| | 702.2606
|-
|-
| | 15/11
| 6/5
| | 231.8645
| 77.1985
| | 386.4409
| 5-odd-limit minimax
| | 699.6601
|-
|-
| | 15/13
| 7/6
| | 231.4708
| 77.2037
| | 385.7847
|  
| | 702.5475
|-
|-
| | 15/14
| 13/11
| | 231.5480
| 77.2083
| | 385.9133
| 13, 15 and 17-odd-limit minimax
| | 701.9816
|-
|-
| | 16/15
| 22/17
| | 231.4820
| 77.2198
| | 385.8033
|  
| | 702.4654
|-
|-
| | 17/13
| 11/8
| | 232.2139
| 77.2488
| | 387.0231
|  
| | 697.0983
|-
|-
| | 17/14
| 11/10
| | 231.5370
| 77.2499
| | 385.8950
| 11-odd-limit minimax
| | 702.0618
|-
|-
| | 17/15
| 14/11
| | 231.5394
| 77.2598
| | 385.8990
|  
| | 702.0445
|-
|-
| | 17/16
| 5/4
| | 231.5597
| 77.2627
| | 385.9329
|  
| | 701.8954
|-
|-
| | 18/17
| 15/11
| | 231.5558
| 77.2882
| | 385.9264
|  
| | 701.9239
|-
|-
| | 20/17
| 12/11
| | 231.5331
| 77.2920
| | 385.8886
|  
| | 702.0903
|-
|-
| | 22/17
| 17/13
| | 231.6593
| 77.4046
| | 386.0989
|  
| | 701.1648
|-
|-
| | 24/17
| 11/9
| | 231.5572
| 77.5084
| | 385.9286
|  
| | 701.9142
|}
|}


<font style="font-size:1.3em;font-weight:bold;">Tertia</font>
=== Tertia ===
Gencom: [2 22/21; 352/351 385/384 561/560 625/624 715/714]


{| class="wikitable"
Gencom mapping: [{{val|1 3 2 3 5 1 1}}, {{val|0 -22 5 -3 -24 42 48}}]
 
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! | Septimal <br>whole tone
! generator<br>(¢)
! | Major third
! comments
! | Perfect fifth
|-
|-
| | 4/3
| 12/11
| | 231.5516
| 75.3185
| | 385.9193
|  
| | 701.9550
|-
|-
| | 5/4
| 15/11
| | 231.7882
| 76.7073
| | 386.3137
|  
| | 700.2197
|-
|-
| | 6/5
| 14/11
| | 231.5954
| 77.0242
| | 385.9924
|  
| | 701.6336
|-
|-
| | 7/5
| 11/8
| | 231.5579
| 77.0284
| | 385.9299
|  
| | 701.9085
|-
|-
| | 7/6
| 8/7
| | 231.6112
| 77.0580
| | 386.0187
|  
| | 701.5179
|-
|-
| | 8/7
| 11/10
| | 231.1741
| 77.0688
| | 385.2902
|  
| | 704.7233
|-
|-
| | 9/7
| 13/11
| | 231.5792
| 77.1092
| | 385.9654
|  
| | 701.7524
|-
|-
| | 10/9
| 22/17
| | 231.5757
| 77.1339
| | 385.9596
|  
| | 701.7779
|-
|-
| | 11/8
| 13/10
| | 231.0853
| 77.1409
| | 385.1421
|  
| | 705.3748
|-
|-
| | 11/9
| 14/13
| | 232.1112
| 77.1489
| | 386.8520
|  
| | 697.8513
|-
|-
| | 11/10
| 16/13
| | 231.2065
| 77.1554
| | 385.3441
|  
| | 704.4860
|-
|-
| | 12/11
| 15/13
| | 225.9556
| 77.1569
| | 376.5926
|  
| | 742.9924
|-
|-
| | 14/11
| 16/15
| | 231.0726
| 77.1607
| | 385.1209
|  
| | 705.4678
|-
|-
| | 13/10
| 13/12
| | 231.4228
| 77.1652
| | 385.7046
|  
| | 702.8998
|-
|-
| | 13/11
| 18/13
| | 231.3277
| 77.1700
| | 385.5462
| 13, 15 and 17-odd-limit minimax
| | 703.5968
|-
|-
| | 13/12
| 20/17
| | 231.4956
| 77.1777
| | 385.8260
|  
| | 702.3656
|-
|-
| | 14/13
| 17/14
| | 231.4468
| 77.1790
| | 385.7446
|  
| | 702.7236
|-
|-
| | 16/13
| 17/15
| | 231.4663
| 77.1798
| | 385.7771
|  
| | 702.5807
|-
|-
| | 18/13
| 15/14
| | 231.5099
| 77.1827
| | 385.8499
|  
| | 702.2606
|-
|-
| | 15/11
| 4/3
| | 230.1218
| 77.1839
| | 383.5363
| 11-odd-limit minimax
| | 712.4404
|-
|-
| | 15/13
| 18/17
| | 231.4708
| 77.1853
| | 385.7847
|  
| | 702.5475
|-
|-
| | 15/14
| 24/17
| | 231.5480
| 77.1857
| | 385.9133
|  
| | 701.9816
|-
|-
| | 16/15
| 7/5
| | 231.4820
| 77.1860
| | 385.8033
| 7 and 9-odd-limit minimax
| | 702.4654
|-
|-
| | 17/13
| 17/16
| | 232.2139
| 77.1866
| | 387.0231
|  
| | 697.0983
|-
|-
| | 17/14
| 10/9
| | 231.5370
| 77.1919
| | 385.8950
|  
| | 702.0618
|-
|-
| | 17/15
| 9/7
| | 231.5394
| 77.1931
| | 385.8990
|  
| | 702.0445
|-
|-
| | 17/16
| 6/5
| | 231.5597
| 77.1985
| | 385.9329
| 5-odd-limit minimax
| | 701.8954
|-
|-
| | 18/17
| 7/6
| | 231.5558
| 77.2037
| | 385.9264
|  
| | 701.9239
|-
|-
| | 20/17
| 5/4
| | 231.5331
| 77.2627
| | 385.8886
|  
| | 702.0903
|-
|-
| | 22/17
| 11/9
| | 231.4016
| 77.3704
| | 385.6693
|  
| | 703.0552
|-
|-
| | 24/17
| 17/13
| | 231.5572
| 77.4046
| | 385.9286
|  
| | 701.9142
|}
|}


<font style="font-size:1.3em;font-weight:bold;">Hemitert</font>
=== Hemitert ===
Gencom: [2 45/44; 2401/2400 3025/3024 65625/65536]
 
Gencom mapping: [{{val|1 3 2 3 6}}, {{val|0 -44 10 -6 -79}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! | Septimal <br>whole tone
! generator<br>(¢)
! | Major third
! comments
! | Perfect fifth
|-
|-
| | 4/3
| 8/7
| | 231.5516
| 38.5290
| | 385.9193
|  
| | 701.9550
|-
|-
| | 5/4
| 16/15
| | 231.7882
| 38.5803
| | 386.3137
|  
| | 700.2197
|-
|-
| | 6/5
| 12/11
| | 231.5954
| 38.5896
| | 385.9924
|  
| | 701.6336
|-
|-
| | 7/5
| 11/8
| | 231.5579
| 38.5909
| | 385.9299
|  
| | 701.9085
|-
|-
| | 7/6
| 15/14
| | 231.6112
| 38.5913
| | 386.0187
|  
| | 701.5179
|-
|-
| | 8/7
| 4/3
| | 231.1741
| 38.5919
| | 385.2902
|  
| | 704.7233
|-
|-
| | 9/7
| 7/5
| | 231.5792
| 38.5930
| | 385.9654
| 7, 9 and 11-odd-limit minimax
| | 701.7524
|-
|-
| | 10/9
| 11/10
| | 231.5757
| 38.5955
| | 385.9596
|  
| | 701.7779
|-
|-
| | 11/8
| 10/9
| | 231.5455
| 38.59596
| | 385.9091
|  
| | 701.9999
|-
|-
| | 11/9
| 14/11
| | 231.6053
| 38.59600
| | 386.0088
|  
| | 701.5612
|-
|-
| | 11/10
| 9/7
| | 231.5727
| 38.5965
| | 385.9546
|  
| | 701.7998
|-
|-
| | 12/11
| 15/11
| | 231.5378
| 38.5989
| | 385.8963
|  
| | 702.0563
|-
|-
| | 14/11
| 6/5
| | 231.5760
| 38.5992
| | 385.9600
| 5-odd-limit minimax
| | 701.7760
|-
|-
| | 15/11
| 11/9
| | 231.5934
| 38.6009
| | 385.9891
|  
| | 701.6481
|-
|-
| | 15/14
| 7/6
| | 231.5480
| 38.6019
| | 385.9133
|  
| | 701.9816
|-
|-
| | 16/15
| 5/4
| | 231.4820
| 38.6314
| | 385.8033
|  
| | 702.4654
|}
|}


[[Category:breed]]
[[Category:Tertiaseptal| ]] <!-- main article -->
[[Category:temperament]]
[[Category:Rank-2 temperaments]]
[[Category:Microtemperaments]]
[[Category:Breedsmic temperaments]]
[[Category:Horwell temperaments]]
[[Category:Metric microtemperaments]]
Retrieved from "https://en.xen.wiki/w/Tertiaseptal"