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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.}}
 
'''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.
See [[Breedsmic temperaments #Tertiaseptal]] for more information.
Line 988: Line 990:
<sup>a</sup> in 11-limit POTE tuning
<sup>a</sup> in 11-limit POTE tuning


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


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


=== Hemitert ===
=== Hemitert ===
Gencom: [2 45/44; 2401/2400 3025/3024 65625/65536]


{| class="wikitable"
Gencom mapping: [{{val|1 3 2 3 6}}, {{val|0 -44 10 -6 -79}}]
 
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Septimal <br>whole tone
! generator<br>(¢)
! Major third
! comments
! Perfect fifth
|-
|-
| 8/7
| 8/7
| 231.1741
| 38.5290
| 385.2902
|  
| 704.7233
|-
|-
| 16/15
| 16/15
| 231.4820
| 38.5803
| 385.8033
|  
| 702.4654
|-
|-
| 12/11
| 12/11
| 231.5378
| 38.5896
| 385.8963
|  
| 702.0563
|-
|-
| 11/8
| 11/8
| 231.5455
| 38.5909
| 385.9091
|  
| 701.9999
|-
|-
| 15/14
| 15/14
| 231.5480
| 38.5913
| 385.9133
|  
| 701.9816
|-
|-
| 4/3
| 4/3
| 231.5516
| 38.5919
| 385.9193
|  
| 701.9550
|-
|-
| 7/5 <br>(7, 9, 11-limit<br>minimax)
| 7/5
| 231.5579
| 38.5930
| 385.9299
| 7, 9 and 11-odd-limit minimax
| 701.9085
|-
|-
| 11/10
| 11/10
| 231.5727
| 38.5955
| 385.9546
|  
| 701.7998
|-
|-
| 10/9
| 10/9
| 231.5757
| 38.59596
| 385.9596
|  
| 701.7779
|-
|-
| 14/11
| 14/11
| 231.5760
| 38.59600
| 385.9600
|  
| 701.7760
|-
|-
| 9/7
| 9/7
| 231.5792
| 38.5965
| 385.9654
|  
| 701.7524
|-
|-
| 15/11
| 15/11
| 231.5934
| 38.5989
| 385.9891
|  
| 701.6481
|-
|-
| 6/5 <br>(5-limit minimax)
| 6/5
| 231.5954
| 38.5992
| 385.9924
| 5-odd-limit minimax
| 701.6336
|-
|-
| 11/9
| 11/9
| 231.6053
| 38.6009
| 386.0088
|  
| 701.5612
|-
|-
| 7/6
| 7/6
| 231.6112
| 38.6019
| 386.0187
|  
| 701.5179
|-
|-
| 5/4
| 5/4
| 231.7882
| 38.6314
| 386.3137
|  
| 700.2197
|}
|}


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