Tertiaseptal: Difference between revisions

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Created page with "'''Tertiaseptal''' is a temperament for the 7, 11, 13, and 17 limit. EDOs that support tertiaseptal include 31edo, 140edo, and 171edo. See..."
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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]].
#redirect [[Breedsmic temperaments #Tertiaseptal]]


See [[Breedsmic_temperaments#Tertiaseptal|Breedsmic temperaments]] for more information.
[[Category:Tertiaseptal| ]] <!-- main article -->
 
[[Category:Rank-2 temperaments]]
==Interval chain==
[[Category:Microtemperaments]]
<font style="font-size:1.3em;font-weight:bold;">Tertiaseptal and tertia</font>
[[Category:Breedsmic temperaments]]
{| class="wikitable"
[[Category:Horwell temperaments]]
|-
[[Category:Metric microtemperaments]]
! rowspan="2"| generator
! rowspan="2"| cents value <sup>a</sup><br>(octave-reduced)
! colspan="2"| 17-limit ratio<br>(octave-reduced)
|-
! | tertiaseptal <br>(31&amp;171)
! | tertia <br>(31&amp;140)
|-
| | 1
| | 77.2
| | 117/112, 256/245, 68/65
| | 117/112, 256/245, 68/65, [[22/21]]
|-
| | 2
| | 154.4
| | 130/119, [[35/32]]
| | '''[[12/11]]''', 130/119, 35/32
|-
| | 3
| | 231.6
| colspan="2"| '''[[8/7]]'''
|-
| | 4
| | 308.8
| colspan="2"| 117/98, 140/117
|-
| | 5
| | 386.0
| colspan="2"| '''[[5/4]]'''
|-
| | 6
| | 463.1
| colspan="2"| '''[[17/13]]'''
|-
| | 7
| | 540.3
| | 175/128
| | '''[[15/11]]''', 175/128
|-
| | 8
| | 617.5
| colspan="2"| '''[[10/7]]'''
|-
| | 9
| | 694.7
| colspan="2"| 112/75
|-
| | 10
| | 771.9
| colspan="2"| [[25/16]]
|-
| | 11
| | 849.1
| | 44/27, 80/49, 49/30, 85/52, '''[[18/11]]'''
| | 80/49, 49/30, 85/52
|-
| | 12
| | 926.3
| colspan="2"| 128/75
|-
| | 13
| | 1003.5
| colspan="2"| [[25/14]]
|-
| | 14
| | 1080.7
| colspan="2"| '''[[28/15]]'''
|-
| | 15
| | 1157.9
| | 39/20
| | 39/20, 88/45
|-
| | 16
| | 35.1
| | 55/54, 52/51, 51/50, [[50/49]], [[49/48]], [[45/44]]
| | 56/55, 52/51, 51/50, 50/49, 49/48
|-
| | 17
| | 112.3
| colspan="2"| '''[[16/15]]'''
|-
| | 18
| | 189.4
| colspan="2"| 39/35
|-
| | 19
| | 266.6
| colspan="2"| '''[[7/6]]'''
|-
| | 20
| | 343.8
| | 39/32
| | 39/32, '''[[11/9]]'''
|-
| | 21
| | 421.0
| | [[51/40]]
| | '''[[14/11]]''', 51/40
|-
| | 22
| | 498.2
| colspan="2"| '''[[4/3]]'''
|-
| | 23
| | 575.4
| colspan="2"| 39/28
|-
| | 24
| | 652.6
| | [[35/24]]
| | '''[[16/11]]''', 35/24
|-
| | 25
| | 729.8
| colspan="2"| [[32/21]]
|-
| | 26
| | 807.0
| | 51/32
| | 35/22, 51/32
|-
| | 27
| | 884.2
| colspan="2"| '''[[5/3]]'''
|-
| | 28
| | 961.4
| colspan="2"| 68/39
|-
| | 29
| | 1038.6
| | 51/28
| | '''[[20/11]]''', 51/28
|-
| | 30
| | 1115.7
| | [[40/21]], [[21/11]]
| | 40/21
|-
| | 31
| | 1192.9
| colspan="2"|
|-
| | 32
| | 70.1
| colspan="2"| [[26/25]], [[25/24]]
|-
| | 33
| | 147.3
| | 49/45, '''12/11'''
| | 49/45
|-
| | 34
| | 224.5
| | 91/80
| | [[25/22]], 91/80
|-
| | 35
| | 301.7
| colspan="2"| [[25/21]]
|-
| | 36
| | 378.9
| | 56/45, 96/77
| | 56/45
|-
| | 37
| | 456.1
| colspan="2"| '''[[13/10]]'''
|-
| | 38
| | 533.3
| | 34/25, '''15/11'''
| | 34/25
|-
| | 39
| | 610.5
| colspan="2"| [[64/45]]
|-
| | 40
| | 687.7
| colspan="2"| 52/35
|-
| | 41
| | 764.8
| colspan="2"| '''[[14/9]]'''
|-
| | 42
| | 842.0
| colspan="2"| '''[[13/8]]'''
|-
| | 43
| | 919.2
| colspan="2"| '''[[17/10]]'''
|-
| | 44
| | 996.4
| colspan="2"| '''[[16/9]]'''
|-
| | 45
| | 1073.6
| colspan="2"| '''[[13/7]]'''
|-
| | 46
| | 1150.8
| | 68/35, [[35/18]]
| | 64/33, 68/35, 35/18
|-
| | 47
| | 28.0
| | [[65/64]], [[64/63]], [[56/55]]
| | 78/77, 65/64, 64/63, 55/54
|-
| | 48
| | 105.2
| colspan="2"| '''[[17/16]]'''
|-
| | 49
| | 182.4
| colspan="2"| '''[[10/9]]'''
|-
| | 50
| | 259.6
| | 65/56, [[64/55]]
| | 65/56
|-
| | 51
| | 336.8
| colspan="2"| '''[[17/14]]'''
|-
| | 52
| | 414.0
| | 80/63, '''14/11'''
| | 80/63
|-
| | 53
| | 491.1
| colspan="2"| 65/49
|-
| | 54
| | 568.3
| colspan="2"| [[25/18]]
|-
| | 55
| | 645.5
| | '''16/11'''
| |
|-
| | 56
| | 722.7
| | 85/56
| | 50/33, 85/56
|-
| | 57
| | 799.9
| | 100/63, 35/22
| | 100/63
|-
| | 58
| | 877.1
| | 128/77
| |
|-
| | 59
| | 954.3
| colspan="2"| '''[[26/15]]'''
|-
| | 60
| | 1031.5
| | 136/75, '''20/11'''
| | 136/75
|-
| | 61
| | 1108.7
| colspan="2"| 91/48, 256/135
|-
| | 62
| | 1185.9
| | 208/105
| | 196/99, 208/105
|-
| | 63
| | 63.1
| colspan="2"| [[28/27]]
|-
| | 64
| | 140.3
| colspan="2"| '''[[13/12]]'''
|-
| | 65
| | 217.4
| | '''[[17/15]]''', 25/22
| | '''17/15'''
|-
| | 66
| | 294.6
| | [[32/27]]
| | '''[[13/11]]''', 32/27
|-
| | 67
| | 371.8
| colspan="2"| [[26/21]]
|-
| | 68
| | 449.0
| colspan="2"| [[35/27]]
|-
| | 69
| | 526.2
| colspan="2"| 65/48
|-
| | 70
| | 603.4
| colspan="2"| '''[[17/12]]'''
|-
| | 71
| | 680.6
| colspan="2"| [[40/27]]
|-
| | 72
| | 757.8
| | 65/42
| | '''[[17/11]]''', 65/42
|-
| | 73
| | 835.0
| colspan="2"| [[34/21]]
|-
| | 74
| | 912.2
| | 56/33
| |
|-
| | 75
| | 989.4
| | 39/22
| | 136/77, 85/48
|-
| | 76
| | 1066.6
| colspan="2"| 50/27
|-
| | 77
| | 1143.7
| | 64/33
| | 85/44
|-
| | 78
| | 20.9
| | 91/90, 85/84, 78/77
| | [[100/99]], 91/90, 85/84
|-
| | 79
| | 98.1
| | 35/33
| |
|-
| | 80
| | 175.3
| | 195/176
| |
|-
| | 81
| | 252.5
| colspan="2"| 52/45
|-
| | 82
| | 329.7
| | 40/33
| |
|-
| | 83
| | 406.9
| colspan="2"| 91/72
|-
| | 84
| | 484.1
| colspan="2"| 119/90
|-
| | 85
| | 561.3
| colspan="2"| 112/81
|-
| | 86
| | 638.5
| colspan="2"| '''[[13/9]]'''
|-
| | 87
| | 715.7
| | 68/45, 50/33
| | 68/45
|-
| | 88
| | 792.8
| | 128/81
| | 52/33, 128/81
|-
| | 89
| | 870.0
| colspan="2"| 119/72
|-
| | 90
| | 947.2
| colspan="2"| 140/81
|-
| | 91
| | 1024.4
| colspan="2"| 65/36
|-
| | 92
| | 1101.6
| colspan="2"| '''[[17/9]]'''
|-
| | 93
| | 1178.8
| | [[160/81]], 196/99, 240/121
| | 65/33, 160/81
|-
| | 94
| | 56.0
| | 91/88
| | 34/33
|-
| | 95
| | 133.2
| colspan="2"| 68/63
|-
| | 96
| | 210.4
| | 112/99
| |
|-
| | 97
| | 287.6
| | '''13/11'''
| |
|-
| | 98
| | 364.8
| | 68/55
| |
|-
| | 99
| | 442.0
| | 128/99
| |
|-
| | 100
| | 519.1
| | 104/77
| |
|-
| | 101
| | 596.3
| |
| |
|-
| | 102
| | 673.5
| |
| |
|-
| | 103
| | 750.7
| | '''17/11'''
| |
|-
| | 104
| | 827.9
| | 160/99
| |
|-
| | 105
| | 905.1
| |
| |
|-
| | 106
| | 982.3
| | 136/77
| |
|-
| | 107
| | 1059.5
| |
| |
|-
| | 108
| | 1136.7
| | 52/27, 85/44
| | 52/27
|-
| | 109
| | 13.9
| | 100/99
| |
|-
| | 110
| | 91.1
| | 128/121, [[256/243]]
| | 104/99, 256/243
|-
| | 111
| | 168.3
| |
| |
|-
| | 112
| | 245.4
| |
| |
|-
| | 113
| | 322.6
| |
| |
|-
| | 114
| | 399.8
| colspan="2"| 34/27
|-
| | 115
| | 477.0
| |
| |
|-
| | 116
| | 554.2
| |
| |
|-
| | 117
| | 631.4
| |
| |
|-
| | 118
| | 708.6
| |
| |
|-
| | 119
| | 785.8
| | 52/33
| |
|-
| | 120
| | 863.0
| |
| |
|-
| | 121
| | 940.2
| |
| |
|-
| | 122
| | 1017.4
| |
| |
|-
| | 123
| | 1094.5
| |
| |
|-
| | 124
| | 1171.7
| | 65/33
| |
|-
| | 125
| | 48.9
| | 34/33
| |
|}
<sup>a</sup> in 7-limit POTE tuning
 
<font style="font-size:1.3em;font-weight:bold;">Hemitert</font>
 
==Tuning spectrum by Eigenmonzos==
<font style="font-size:1.3em;font-weight:bold;">Tertiaseptal</font>
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Septimal <br>whole tone
! | Major third
! | Perfect fifth
|-
| | 4/3
| | 231.5516
| | 385.9193
| | 701.9550
|-
| | 5/4
| | 231.7882
| | 386.3137
| | 700.2197
|-
| | 6/5
| | 231.5954
| | 385.9924
| | 701.6336
|-
| | 7/5
| | 231.5579
| | 385.9299
| | 701.9085
|-
| | 7/6
| | 231.6112
| | 386.0187
| | 701.5179
|-
| | 8/7
| | 231.1741
| | 385.2902
| | 704.7233
|-
| | 9/7
| | 231.5792
| | 385.9654
| | 701.7524
|-
| | 10/9
| | 231.5757
| | 385.9596
| | 701.7779
|-
| | 11/8
| | 231.7463
| | 386.2438
| | 700.5272
|-
| | 11/9
| | 232.5251
| | 387.5418
| | 694.8159
|-
| | 11/10
| | 231.7498
| | 386.2496
| | 700.5016
|-
| | 12/11
| | 231.8761
| | 386.4602
| | 699.5753
|-
| | 14/11
| | 231.7793
| | 386.2988
| | 700.2851
|-
| | 13/10
| | 231.4228
| | 385.7046
| | 702.8998
|-
| | 13/11
| | 231.6250
| | 386.0417
| | 701.4164
|-
| | 13/12
| | 231.4956
| | 385.8260
| | 702.3656
|-
| | 14/13
| | 231.4468
| | 385.7446
| | 702.7236
|-
| | 16/13
| | 231.4663
| | 385.7771
| | 702.5807
|-
| | 18/13
| | 231.5099
| | 385.8499
| | 702.2606
|-
| | 15/11
| | 231.8645
| | 386.4409
| | 699.6601
|-
| | 15/13
| | 231.4708
| | 385.7847
| | 702.5475
|-
| | 15/14
| | 231.5480
| | 385.9133
| | 701.9816
|-
| | 16/15
| | 231.4820
| | 385.8033
| | 702.4654
|-
| | 17/13
| | 232.2139
| | 387.0231
| | 697.0983
|-
| | 17/14
| | 231.5370
| | 385.8950
| | 702.0618
|-
| | 17/15
| | 231.5394
| | 385.8990
| | 702.0445
|-
| | 17/16
| | 231.5597
| | 385.9329
| | 701.8954
|-
| | 18/17
| | 231.5558
| | 385.9264
| | 701.9239
|-
| | 20/17
| | 231.5331
| | 385.8886
| | 702.0903
|-
| | 22/17
| | 231.6593
| | 386.0989
| | 701.1648
|-
| | 24/17
| | 231.5572
| | 385.9286
| | 701.9142
|}
 
<font style="font-size:1.3em;font-weight:bold;">Tertia</font>
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Septimal <br>whole tone
! | Major third
! | Perfect fifth
|-
| | 4/3
| | 231.5516
| | 385.9193
| | 701.9550
|-
| | 5/4
| | 231.7882
| | 386.3137
| | 700.2197
|-
| | 6/5
| | 231.5954
| | 385.9924
| | 701.6336
|-
| | 7/5
| | 231.5579
| | 385.9299
| | 701.9085
|-
| | 7/6
| | 231.6112
| | 386.0187
| | 701.5179
|-
| | 8/7
| | 231.1741
| | 385.2902
| | 704.7233
|-
| | 9/7
| | 231.5792
| | 385.9654
| | 701.7524
|-
| | 10/9
| | 231.5757
| | 385.9596
| | 701.7779
|-
| | 11/8
| | 231.0853
| | 385.1421
| | 705.3748
|-
| | 11/9
| | 232.1112
| | 386.8520
| | 697.8513
|-
| | 11/10
| | 231.2065
| | 385.3441
| | 704.4860
|-
| | 12/11
| | 225.9556
| | 376.5926
| | 742.9924
|-
| | 14/11
| | 231.0726
| | 385.1209
| | 705.4678
|-
| | 13/10
| | 231.4228
| | 385.7046
| | 702.8998
|-
| | 13/11
| | 231.3277
| | 385.5462
| | 703.5968
|-
| | 13/12
| | 231.4956
| | 385.8260
| | 702.3656
|-
| | 14/13
| | 231.4468
| | 385.7446
| | 702.7236
|-
| | 16/13
| | 231.4663
| | 385.7771
| | 702.5807
|-
| | 18/13
| | 231.5099
| | 385.8499
| | 702.2606
|-
| | 15/11
| | 230.1218
| | 383.5363
| | 712.4404
|-
| | 15/13
| | 231.4708
| | 385.7847
| | 702.5475
|-
| | 15/14
| | 231.5480
| | 385.9133
| | 701.9816
|-
| | 16/15
| | 231.4820
| | 385.8033
| | 702.4654
|-
| | 17/13
| | 232.2139
| | 387.0231
| | 697.0983
|-
| | 17/14
| | 231.5370
| | 385.8950
| | 702.0618
|-
| | 17/15
| | 231.5394
| | 385.8990
| | 702.0445
|-
| | 17/16
| | 231.5597
| | 385.9329
| | 701.8954
|-
| | 18/17
| | 231.5558
| | 385.9264
| | 701.9239
|-
| | 20/17
| | 231.5331
| | 385.8886
| | 702.0903
|-
| | 22/17
| | 231.4016
| | 385.6693
| | 703.0552
|-
| | 24/17
| | 231.5572
| | 385.9286
| | 701.9142
|}
 
<font style="font-size:1.3em;font-weight:bold;">Hemitert</font>
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Septimal <br>whole tone
! | Major third
! | Perfect fifth
|-
| | 4/3
| | 231.5516
| | 385.9193
| | 701.9550
|-
| | 5/4
| | 231.7882
| | 386.3137
| | 700.2197
|-
| | 6/5
| | 231.5954
| | 385.9924
| | 701.6336
|-
| | 7/5
| | 231.5579
| | 385.9299
| | 701.9085
|-
| | 7/6
| | 231.6112
| | 386.0187
| | 701.5179
|-
| | 8/7
| | 231.1741
| | 385.2902
| | 704.7233
|-
| | 9/7
| | 231.5792
| | 385.9654
| | 701.7524
|-
| | 10/9
| | 231.5757
| | 385.9596
| | 701.7779
|-
| | 11/8
| | 231.5455
| | 385.9091
| | 701.9999
|-
| | 11/9
| | 231.6053
| | 386.0088
| | 701.5612
|-
| | 11/10
| | 231.5727
| | 385.9546
| | 701.7998
|-
| | 12/11
| | 231.5378
| | 385.8963
| | 702.0563
|-
| | 14/11
| | 231.5760
| | 385.9600
| | 701.7760
|-
| | 15/11
| | 231.5934
| | 385.9891
| | 701.6481
|-
| | 15/14
| | 231.5480
| | 385.9133
| | 701.9816
|-
| | 16/15
| | 231.4820
| | 385.8033
| | 702.4654
|}
 
[[Category:breed]]
[[Category:temperament]]

Latest revision as of 10:26, 30 October 2026

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