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Tertiaseptal: Difference between revisions

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→Tuning spectrum by Eigenmonzos: improve and standardize tuning spectra tables
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<sup>a</sup> in 11-limit POTE tuning
<sup>a</sup> in 11-limit POTE tuning


== Tuning spectrum by Eigenmonzos ==
== Tuning spectra ==
=== Tertiaseptal ===
=== Tertiaseptal ===


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! Septimal <br>whole tone
! septimal <br>whole tone (¢)
! Major third
! major third<br>(¢)
! Perfect fifth
! perfect fifth<br>(¢)
! comments
|-
|-
| 8/7
| 8/7
Line 1,002: Line 1,003:
| 385.2902
| 385.2902
| 704.7233
| 704.7233
|
|-
|-
| 13/10
| 13/10
Line 1,007: Line 1,009:
| 385.7046
| 385.7046
| 702.8998
| 702.8998
|
|-
|-
| 14/13
| 14/13
Line 1,012: Line 1,015:
| 385.7446
| 385.7446
| 702.7236
| 702.7236
|
|-
|-
| 16/13
| 16/13
Line 1,017: Line 1,021:
| 385.7771
| 385.7771
| 702.5807
| 702.5807
|
|-
|-
| 15/13
| 15/13
Line 1,022: Line 1,027:
| 385.7847
| 385.7847
| 702.5475
| 702.5475
|
|-
|-
| 16/15
| 16/15
Line 1,027: Line 1,033:
| 385.8033
| 385.8033
| 702.4654
| 702.4654
|
|-
|-
| 13/12
| 13/12
Line 1,032: Line 1,039:
| 385.8260
| 385.8260
| 702.3656
| 702.3656
|
|-
|-
| 18/13
| 18/13
Line 1,037: Line 1,045:
| 385.8499
| 385.8499
| 702.2606
| 702.2606
|
|-
|-
| 20/17
| 20/17
Line 1,042: Line 1,051:
| 385.8886
| 385.8886
| 702.0903
| 702.0903
|
|-
|-
| 17/14
| 17/14
Line 1,047: Line 1,057:
| 385.8950
| 385.8950
| 702.0618
| 702.0618
|
|-
|-
| 17/15
| 17/15
Line 1,052: Line 1,063:
| 385.8990
| 385.8990
| 702.0445
| 702.0445
|
|-
|-
| 15/14
| 15/14
Line 1,057: Line 1,069:
| 385.9133
| 385.9133
| 701.9816
| 701.9816
|
|-
|-
| 4/3
| 4/3
Line 1,062: Line 1,075:
| 385.9193
| 385.9193
| 701.9550
| 701.9550
|
|-
|-
| 18/17
| 18/17
Line 1,067: Line 1,081:
| 385.9264
| 385.9264
| 701.9239
| 701.9239
|
|-
|-
| 24/17
| 24/17
Line 1,072: Line 1,087:
| 385.9286
| 385.9286
| 701.9142
| 701.9142
|
|-
|-
| 7/5 <br>(7, 9-limit minimax)
| 7/5
| 231.5579
| 231.5579
| 385.9299
| 385.9299
| 701.9085
| 701.9085
| 7, 9-limit minimax
|-
|-
| 17/16
| 17/16
Line 1,082: Line 1,099:
| 385.9329
| 385.9329
| 701.8954
| 701.8954
|
|-
|-
| 10/9
| 10/9
Line 1,087: Line 1,105:
| 385.9596
| 385.9596
| 701.7779
| 701.7779
|
|-
|-
| 9/7
| 9/7
Line 1,092: Line 1,111:
| 385.9654
| 385.9654
| 701.7524
| 701.7524
|
|-
|-
| 6/5 <br>(5-limit minimax)
| 6/5
| 231.5954
| 231.5954
| 385.9924
| 385.9924
| 701.6336
| 701.6336
| 5-limit minimax
|-
|-
| 7/6
| 7/6
Line 1,102: Line 1,123:
| 386.0187
| 386.0187
| 701.5179
| 701.5179
|
|-
|-
| 13/11 <br>(13, 15, 17-limit<br>minimax)
| 13/11
| 231.6250
| 231.6250
| 386.0417
| 386.0417
| 701.4164
| 701.4164
| 13, 15, 17-limit minimax
|-
|-
| 22/17
| 22/17
Line 1,112: Line 1,135:
| 386.0989
| 386.0989
| 701.1648
| 701.1648
|
|-
|-
| 11/8
| 11/8
Line 1,117: Line 1,141:
| 386.2438
| 386.2438
| 700.5272
| 700.5272
|
|-
|-
| 11/10 <br>(11-limit minimax)
| 11/10
| 231.7498
| 231.7498
| 386.2496
| 386.2496
| 700.5016
| 700.5016
| 11-limit minimax
|-
|-
| 14/11
| 14/11
Line 1,127: Line 1,153:
| 386.2988
| 386.2988
| 700.2851
| 700.2851
|
|-
|-
| 5/4
| 5/4
Line 1,132: Line 1,159:
| 386.3137
| 386.3137
| 700.2197
| 700.2197
|
|-
|-
| 15/11
| 15/11
Line 1,137: Line 1,165:
| 386.4409
| 386.4409
| 699.6601
| 699.6601
|
|-
|-
| 12/11
| 12/11
Line 1,142: Line 1,171:
| 386.4602
| 386.4602
| 699.5753
| 699.5753
|
|-
|-
| 17/13
| 17/13
Line 1,147: Line 1,177:
| 387.0231
| 387.0231
| 697.0983
| 697.0983
|
|-
|-
| 11/9
| 11/9
Line 1,152: Line 1,183:
| 387.5418
| 387.5418
| 694.8159
| 694.8159
|
|}
|}


=== Tertia ===
=== Tertia ===


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Septimal <br>whole tone
! septimal <br>whole tone (¢)
! Major third
! major third<br>(¢)
! Perfect fifth
! perfect fifth<br>(¢)
! comments
|-
|-
| 12/11
| 12/11
Line 1,167: Line 1,200:
| 376.5926
| 376.5926
| 742.9924
| 742.9924
|
|-
|-
| 15/11
| 15/11
Line 1,172: Line 1,206:
| 383.5363
| 383.5363
| 712.4404
| 712.4404
|
|-
|-
| 14/11
| 14/11
Line 1,177: Line 1,212:
| 385.1209
| 385.1209
| 705.4678
| 705.4678
|
|-
|-
| 11/8
| 11/8
Line 1,182: Line 1,218:
| 385.1421
| 385.1421
| 705.3748
| 705.3748
|
|-
|-
| 8/7
| 8/7
Line 1,187: Line 1,224:
| 385.2902
| 385.2902
| 704.7233
| 704.7233
|
|-
|-
| 11/10
| 11/10
Line 1,192: Line 1,230:
| 385.3441
| 385.3441
| 704.4860
| 704.4860
|
|-
|-
| 13/11
| 13/11
Line 1,197: Line 1,236:
| 385.5462
| 385.5462
| 703.5968
| 703.5968
|
|-
|-
| 22/17
| 22/17
Line 1,202: Line 1,242:
| 385.6693
| 385.6693
| 703.0552
| 703.0552
|
|-
|-
| 13/10
| 13/10
Line 1,207: Line 1,248:
| 385.7046
| 385.7046
| 702.8998
| 702.8998
|
|-
|-
| 14/13
| 14/13
Line 1,212: Line 1,254:
| 385.7446
| 385.7446
| 702.7236
| 702.7236
|
|-
|-
| 16/13
| 16/13
Line 1,217: Line 1,260:
| 385.7771
| 385.7771
| 702.5807
| 702.5807
|
|-
|-
| 15/13
| 15/13
Line 1,222: Line 1,266:
| 385.7847
| 385.7847
| 702.5475
| 702.5475
|
|-
|-
| 16/15
| 16/15
Line 1,227: Line 1,272:
| 385.8033
| 385.8033
| 702.4654
| 702.4654
|
|-
|-
| 13/12
| 13/12
Line 1,232: Line 1,278:
| 385.8260
| 385.8260
| 702.3656
| 702.3656
|
|-
|-
| 18/13 <br>(13, 15, 17-limit<br>minimax)
| 18/13
| 231.5099
| 231.5099
| 385.8499
| 385.8499
| 702.2606
| 702.2606
| 13, 15, 17-limit minimax
|-
|-
| 20/17
| 20/17
Line 1,242: Line 1,290:
| 385.8886
| 385.8886
| 702.0903
| 702.0903
|
|-
|-
| 17/14
| 17/14
Line 1,247: Line 1,296:
| 385.8950
| 385.8950
| 702.0618
| 702.0618
|
|-
|-
| 17/15
| 17/15
Line 1,252: Line 1,302:
| 385.8990
| 385.8990
| 702.0445
| 702.0445
|
|-
|-
| 15/14
| 15/14
Line 1,257: Line 1,308:
| 385.9133
| 385.9133
| 701.9816
| 701.9816
|
|-
|-
| 4/3 <br>(11-limit minimax)
| 4/3
| 231.5516
| 231.5516
| 385.9193
| 385.9193
| 701.9550
| 701.9550
| 11-limit minimax
|-
|-
| 18/17
| 18/17
Line 1,267: Line 1,320:
| 385.9264
| 385.9264
| 701.9239
| 701.9239
|
|-
|-
| 24/17
| 24/17
Line 1,272: Line 1,326:
| 385.9286
| 385.9286
| 701.9142
| 701.9142
|
|-
|-
| 7/5 <br>(7, 9-limit minimax)
| 7/5
| 231.5579
| 231.5579
| 385.9299
| 385.9299
| 701.9085
| 701.9085
| 7, 9-limit minimax
|-
|-
| 17/16
| 17/16
Line 1,282: Line 1,338:
| 385.9329
| 385.9329
| 701.8954
| 701.8954
|
|-
|-
| 10/9
| 10/9
Line 1,287: Line 1,344:
| 385.9596
| 385.9596
| 701.7779
| 701.7779
|
|-
|-
| 9/7
| 9/7
Line 1,292: Line 1,350:
| 385.9654
| 385.9654
| 701.7524
| 701.7524
|
|-
|-
| 6/5 <br>(5-limit minimax)
| 6/5
| 231.5954
| 231.5954
| 385.9924
| 385.9924
| 701.6336
| 701.6336
| 5-limit minimax
|-
|-
| 7/6
| 7/6
Line 1,302: Line 1,362:
| 386.0187
| 386.0187
| 701.5179
| 701.5179
|
|-
|-
| 5/4
| 5/4
Line 1,307: Line 1,368:
| 386.3137
| 386.3137
| 700.2197
| 700.2197
|
|-
|-
| 11/9
| 11/9
Line 1,312: Line 1,374:
| 386.8520
| 386.8520
| 697.8513
| 697.8513
|
|-
|-
| 17/13
| 17/13
Line 1,317: Line 1,380:
| 387.0231
| 387.0231
| 697.0983
| 697.0983
|
|}
|}


=== Hemitert ===
=== Hemitert ===


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Septimal <br>whole tone
! septimal <br>whole tone (¢)
! Major third
! major third<br>(¢)
! Perfect fifth
! perfect fifth<br>(¢)
! comments
|-
|-
| 8/7
| 8/7
Line 1,332: Line 1,397:
| 385.2902
| 385.2902
| 704.7233
| 704.7233
|
|-
|-
| 16/15
| 16/15
Line 1,337: Line 1,403:
| 385.8033
| 385.8033
| 702.4654
| 702.4654
|
|-
|-
| 12/11
| 12/11
Line 1,342: Line 1,409:
| 385.8963
| 385.8963
| 702.0563
| 702.0563
|
|-
|-
| 11/8
| 11/8
Line 1,347: Line 1,415:
| 385.9091
| 385.9091
| 701.9999
| 701.9999
|
|-
|-
| 15/14
| 15/14
Line 1,352: Line 1,421:
| 385.9133
| 385.9133
| 701.9816
| 701.9816
|
|-
|-
| 4/3
| 4/3
Line 1,357: Line 1,427:
| 385.9193
| 385.9193
| 701.9550
| 701.9550
|
|-
|-
| 7/5 <br>(7, 9, 11-limit<br>minimax)
| 7/5
| 231.5579
| 231.5579
| 385.9299
| 385.9299
| 701.9085
| 701.9085
| 7, 9, 11-limit minimax
|-
|-
| 11/10
| 11/10
Line 1,367: Line 1,439:
| 385.9546
| 385.9546
| 701.7998
| 701.7998
|
|-
|-
| 10/9
| 10/9
Line 1,372: Line 1,445:
| 385.9596
| 385.9596
| 701.7779
| 701.7779
|
|-
|-
| 14/11
| 14/11
Line 1,377: Line 1,451:
| 385.9600
| 385.9600
| 701.7760
| 701.7760
|
|-
|-
| 9/7
| 9/7
Line 1,382: Line 1,457:
| 385.9654
| 385.9654
| 701.7524
| 701.7524
|
|-
|-
| 15/11
| 15/11
Line 1,387: Line 1,463:
| 385.9891
| 385.9891
| 701.6481
| 701.6481
|
|-
|-
| 6/5 <br>(5-limit minimax)
| 6/5
| 231.5954
| 231.5954
| 385.9924
| 385.9924
| 701.6336
| 701.6336
| 5-limit minimax
|-
|-
| 11/9
| 11/9
Line 1,397: Line 1,475:
| 386.0088
| 386.0088
| 701.5612
| 701.5612
|
|-
|-
| 7/6
| 7/6
Line 1,402: Line 1,481:
| 386.0187
| 386.0187
| 701.5179
| 701.5179
|
|-
|-
| 5/4
| 5/4
Line 1,407: Line 1,487:
| 386.3137
| 386.3137
| 700.2197
| 700.2197
|
|}
|}


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