Tertiaseptal: Difference between revisions
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Cmloegcmluin (talk | contribs) →Tuning spectrum by Eigenmonzos: improve and standardize tuning spectra tables |
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| Line 988: | Line 988: | ||
<sup>a</sup> in 11-limit POTE tuning | <sup>a</sup> in 11-limit POTE tuning | ||
== Tuning | == Tuning spectra == | ||
=== Tertiaseptal === | === Tertiaseptal === | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
|- | |- | ||
! | ! [[eigenmonzo|eigenmonzo<br>(unchanged interval]]) | ||
! | ! septimal <br>whole tone (¢) | ||
! | ! major third<br>(¢) | ||
! | ! 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 | | 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 | | 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 | | 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 | | 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<br>(unchanged interval) | ||
! | ! septimal <br>whole tone (¢) | ||
! | ! major third<br>(¢) | ||
! | ! 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 | | 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 | | 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 | | 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 | | 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<br>(unchanged interval) | ||
! | ! septimal <br>whole tone (¢) | ||
! | ! major third<br>(¢) | ||
! | ! 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 | | 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 | | 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 | ||
| | |||
|} | |} | ||
Revision as of 00:21, 30 September 2021
Tertiaseptal is a temperament for the 7, 11, 13, and 17 limit. EDOs that support tertiaseptal include 31edo, 140edo, and 171edo.
See Breedsmic temperaments #Tertiaseptal for more information.
Interval chain
Tertiaseptal and tertia
| generator | cents value a (octave-reduced) |
17-limit ratio (octave-reduced) | |
|---|---|---|---|
| tertiaseptal (31&171) |
tertia (31&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 | 8/7 | |
| 4 | 308.8 | 117/98, 140/117 | |
| 5 | 386.0 | 5/4 | |
| 6 | 463.1 | 17/13 | |
| 7 | 540.3 | 175/128 | 15/11, 175/128 |
| 8 | 617.5 | 10/7 | |
| 9 | 694.7 | 112/75 | |
| 10 | 771.9 | 25/16 | |
| 11 | 849.1 | 44/27, 80/49, 49/30, 85/52, 18/11 | 80/49, 49/30, 85/52 |
| 12 | 926.3 | 128/75 | |
| 13 | 1003.5 | 25/14 | |
| 14 | 1080.7 | 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 | 16/15 | |
| 18 | 189.4 | 39/35 | |
| 19 | 266.6 | 7/6 | |
| 20 | 343.8 | 39/32 | 39/32, 11/9 |
| 21 | 421.0 | 51/40 | 14/11, 51/40 |
| 22 | 498.2 | 4/3 | |
| 23 | 575.4 | 39/28 | |
| 24 | 652.6 | 35/24 | 16/11, 35/24 |
| 25 | 729.8 | 32/21 | |
| 26 | 807.0 | 51/32 | 35/22, 51/32 |
| 27 | 884.2 | 5/3 | |
| 28 | 961.4 | 68/39 | |
| 29 | 1038.6 | 51/28 | 20/11, 51/28 |
| 30 | 1115.7 | 40/21, 21/11 | 40/21 |
| 31 | 1192.9 | ||
| 32 | 70.1 | 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 | 25/21 | |
| 36 | 378.9 | 56/45, 96/77 | 56/45 |
| 37 | 456.1 | 13/10 | |
| 38 | 533.3 | 34/25, 15/11 | 34/25 |
| 39 | 610.5 | 64/45 | |
| 40 | 687.7 | 52/35 | |
| 41 | 764.8 | 14/9 | |
| 42 | 842.0 | 13/8 | |
| 43 | 919.2 | 17/10 | |
| 44 | 996.4 | 16/9 | |
| 45 | 1073.6 | 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 | 17/16 | |
| 49 | 182.4 | 10/9 | |
| 50 | 259.6 | 65/56, 64/55 | 65/56 |
| 51 | 336.8 | 17/14 | |
| 52 | 414.0 | 80/63, 14/11 | 80/63 |
| 53 | 491.1 | 65/49 | |
| 54 | 568.3 | 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 | 26/15 | |
| 60 | 1031.5 | 136/75, 20/11 | 136/75 |
| 61 | 1108.7 | 91/48, 256/135 | |
| 62 | 1185.9 | 208/105 | 196/99, 208/105 |
| 63 | 63.1 | 28/27 | |
| 64 | 140.3 | 13/12 | |
| 65 | 217.4 | 17/15, 25/22 | 17/15 |
| 66 | 294.6 | 32/27 | 13/11, 32/27 |
| 67 | 371.8 | 26/21 | |
| 68 | 449.0 | 35/27 | |
| 69 | 526.2 | 65/48 | |
| 70 | 603.4 | 17/12 | |
| 71 | 680.6 | 40/27 | |
| 72 | 757.8 | 65/42 | 17/11, 65/42 |
| 73 | 835.0 | 34/21 | |
| 74 | 912.2 | 56/33 | |
| 75 | 989.4 | 39/22 | 136/77, 85/48 |
| 76 | 1066.6 | 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 | 52/45 | |
| 82 | 329.7 | 40/33 | |
| 83 | 406.9 | 91/72 | |
| 84 | 484.1 | 119/90 | |
| 85 | 561.3 | 112/81 | |
| 86 | 638.5 | 13/9 | |
| 87 | 715.7 | 68/45, 50/33 | 68/45 |
| 88 | 792.8 | 128/81 | 52/33, 128/81 |
| 89 | 870.0 | 119/72 | |
| 90 | 947.2 | 140/81 | |
| 91 | 1024.4 | 65/36 | |
| 92 | 1101.6 | 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 | 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 | 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 | |
a in 7-limit POTE tuning
Hemitert
| generator | cents value a (octave-reduced) |
11-limit ratio (octave-reduced) |
|---|---|---|
| 1 | 38.6 | 45/44 |
| 2 | 77.2 | 256/245 |
| 3 | 115.8 | |
| 4 | 154.4 | 35/32 |
| 5 | 193.0 | |
| 6 | 231.6 | 8/7 |
| 7 | 270.2 | |
| 8 | 308.8 | |
| 9 | 347.4 | 11/9 |
| 10 | 386.0 | 5/4 |
| 11 | 424.6 | |
| 12 | 463.1 | 64/49 |
| 13 | 501.7 | |
| 14 | 540.3 | |
| 15 | 578.9 | |
| 16 | 617.5 | 10/7 |
| 17 | 656.1 | |
| 18 | 694.7 | |
| 19 | 733.3 | |
| 20 | 771.9 | 25/16 |
| 21 | 810.5 | |
| 22 | 849.1 | |
| 23 | 887.7 | |
| 24 | 926.3 | |
| 25 | 964.9 | |
| 26 | 1003.5 | 25/14 |
| 27 | 1042.1 | |
| 28 | 1080.7 | 28/15 |
| 29 | 1119.3 | 21/11 |
| 30 | 1157.9 | |
| 31 | 1196.5 | |
| 32 | 35.1 | 50/49, 49/48 |
| 33 | 73.7 | |
| 34 | 112.2 | 16/15 |
| 35 | 150.8 | 12/11 |
| 36 | 189.4 | |
| 37 | 228.0 | |
| 38 | 266.6 | 7/6 |
| 39 | 305.2 | |
| 40 | 343.8 | |
| 41 | 382.4 | |
| 42 | 421.0 | |
| 43 | 459.6 | |
| 44 | 498.2 | 4/3 |
| 45 | 536.8 | 15/11 |
| 46 | 575.4 | |
| 47 | 614.0 | |
| 48 | 652.6 | |
| 49 | 691.2 | |
| 50 | 729.8 | 32/21 |
| 51 | 768.4 | |
| 52 | 807.0 | |
| 53 | 845.6 | |
| 54 | 884.2 | 5/3 |
| 55 | 922.8 | |
| 56 | 961.4 | |
| 57 | 999.9 | |
| 58 | 1038.5 | |
| 59 | 1077.1 | |
| 60 | 1115.7 | 40/21 |
| 61 | 1154.3 | |
| 62 | 1192.9 | |
| 63 | 31.5 | |
| 64 | 70.1 | 25/24 |
| 65 | 108.7 | |
| 66 | 147.3 | |
| 67 | 185.9 | |
| 68 | 224.5 | |
| 69 | 263.1 | |
| 70 | 301.7 | |
| 71 | 340.3 | |
| 72 | 378.9 | |
| 73 | 417.5 | 14/11 |
| 74 | 456.1 | |
| 75 | 494.7 | |
| 76 | 533.3 | |
| 77 | 571.9 | |
| 78 | 610.5 | |
| 79 | 649.1 | 16/11 |
| 80 | 687.6 | |
| 81 | 726.2 | |
| 82 | 764.8 | 14/9 |
| 83 | 803.4 | |
| 84 | 842.0 | |
| 85 | 880.6 | |
| 86 | 919.2 | |
| 87 | 957.8 | |
| 88 | 996.4 | 16/9 |
| 89 | 1035.0 | 20/11 |
| 90 | 1073.6 | |
| 91 | 1112.2 | |
| 92 | 1150.8 | |
| 93 | 1189.4 | |
| 94 | 28.0 | 64/63 |
| 95 | 66.6 | |
| 96 | 105.2 | |
| 97 | 143.8 | |
| 98 | 182.4 | 10/9 |
a in 11-limit POTE tuning
Tuning spectra
Tertiaseptal
| eigenmonzo (unchanged interval) |
septimal whole tone (¢) |
major third (¢) |
perfect fifth (¢) |
comments |
|---|---|---|---|---|
| 8/7 | 231.1741 | 385.2902 | 704.7233 | |
| 13/10 | 231.4228 | 385.7046 | 702.8998 | |
| 14/13 | 231.4468 | 385.7446 | 702.7236 | |
| 16/13 | 231.4663 | 385.7771 | 702.5807 | |
| 15/13 | 231.4708 | 385.7847 | 702.5475 | |
| 16/15 | 231.4820 | 385.8033 | 702.4654 | |
| 13/12 | 231.4956 | 385.8260 | 702.3656 | |
| 18/13 | 231.5099 | 385.8499 | 702.2606 | |
| 20/17 | 231.5331 | 385.8886 | 702.0903 | |
| 17/14 | 231.5370 | 385.8950 | 702.0618 | |
| 17/15 | 231.5394 | 385.8990 | 702.0445 | |
| 15/14 | 231.5480 | 385.9133 | 701.9816 | |
| 4/3 | 231.5516 | 385.9193 | 701.9550 | |
| 18/17 | 231.5558 | 385.9264 | 701.9239 | |
| 24/17 | 231.5572 | 385.9286 | 701.9142 | |
| 7/5 | 231.5579 | 385.9299 | 701.9085 | 7, 9-limit minimax |
| 17/16 | 231.5597 | 385.9329 | 701.8954 | |
| 10/9 | 231.5757 | 385.9596 | 701.7779 | |
| 9/7 | 231.5792 | 385.9654 | 701.7524 | |
| 6/5 | 231.5954 | 385.9924 | 701.6336 | 5-limit minimax |
| 7/6 | 231.6112 | 386.0187 | 701.5179 | |
| 13/11 | 231.6250 | 386.0417 | 701.4164 | 13, 15, 17-limit minimax |
| 22/17 | 231.6593 | 386.0989 | 701.1648 | |
| 11/8 | 231.7463 | 386.2438 | 700.5272 | |
| 11/10 | 231.7498 | 386.2496 | 700.5016 | 11-limit minimax |
| 14/11 | 231.7793 | 386.2988 | 700.2851 | |
| 5/4 | 231.7882 | 386.3137 | 700.2197 | |
| 15/11 | 231.8645 | 386.4409 | 699.6601 | |
| 12/11 | 231.8761 | 386.4602 | 699.5753 | |
| 17/13 | 232.2139 | 387.0231 | 697.0983 | |
| 11/9 | 232.5251 | 387.5418 | 694.8159 |
Tertia
| eigenmonzo (unchanged interval) |
septimal whole tone (¢) |
major third (¢) |
perfect fifth (¢) |
comments |
|---|---|---|---|---|
| 12/11 | 225.9556 | 376.5926 | 742.9924 | |
| 15/11 | 230.1218 | 383.5363 | 712.4404 | |
| 14/11 | 231.0726 | 385.1209 | 705.4678 | |
| 11/8 | 231.0853 | 385.1421 | 705.3748 | |
| 8/7 | 231.1741 | 385.2902 | 704.7233 | |
| 11/10 | 231.2065 | 385.3441 | 704.4860 | |
| 13/11 | 231.3277 | 385.5462 | 703.5968 | |
| 22/17 | 231.4016 | 385.6693 | 703.0552 | |
| 13/10 | 231.4228 | 385.7046 | 702.8998 | |
| 14/13 | 231.4468 | 385.7446 | 702.7236 | |
| 16/13 | 231.4663 | 385.7771 | 702.5807 | |
| 15/13 | 231.4708 | 385.7847 | 702.5475 | |
| 16/15 | 231.4820 | 385.8033 | 702.4654 | |
| 13/12 | 231.4956 | 385.8260 | 702.3656 | |
| 18/13 | 231.5099 | 385.8499 | 702.2606 | 13, 15, 17-limit minimax |
| 20/17 | 231.5331 | 385.8886 | 702.0903 | |
| 17/14 | 231.5370 | 385.8950 | 702.0618 | |
| 17/15 | 231.5394 | 385.8990 | 702.0445 | |
| 15/14 | 231.5480 | 385.9133 | 701.9816 | |
| 4/3 | 231.5516 | 385.9193 | 701.9550 | 11-limit minimax |
| 18/17 | 231.5558 | 385.9264 | 701.9239 | |
| 24/17 | 231.5572 | 385.9286 | 701.9142 | |
| 7/5 | 231.5579 | 385.9299 | 701.9085 | 7, 9-limit minimax |
| 17/16 | 231.5597 | 385.9329 | 701.8954 | |
| 10/9 | 231.5757 | 385.9596 | 701.7779 | |
| 9/7 | 231.5792 | 385.9654 | 701.7524 | |
| 6/5 | 231.5954 | 385.9924 | 701.6336 | 5-limit minimax |
| 7/6 | 231.6112 | 386.0187 | 701.5179 | |
| 5/4 | 231.7882 | 386.3137 | 700.2197 | |
| 11/9 | 232.1112 | 386.8520 | 697.8513 | |
| 17/13 | 232.2139 | 387.0231 | 697.0983 |
Hemitert
| eigenmonzo (unchanged interval) |
septimal whole tone (¢) |
major third (¢) |
perfect fifth (¢) |
comments |
|---|---|---|---|---|
| 8/7 | 231.1741 | 385.2902 | 704.7233 | |
| 16/15 | 231.4820 | 385.8033 | 702.4654 | |
| 12/11 | 231.5378 | 385.8963 | 702.0563 | |
| 11/8 | 231.5455 | 385.9091 | 701.9999 | |
| 15/14 | 231.5480 | 385.9133 | 701.9816 | |
| 4/3 | 231.5516 | 385.9193 | 701.9550 | |
| 7/5 | 231.5579 | 385.9299 | 701.9085 | 7, 9, 11-limit minimax |
| 11/10 | 231.5727 | 385.9546 | 701.7998 | |
| 10/9 | 231.5757 | 385.9596 | 701.7779 | |
| 14/11 | 231.5760 | 385.9600 | 701.7760 | |
| 9/7 | 231.5792 | 385.9654 | 701.7524 | |
| 15/11 | 231.5934 | 385.9891 | 701.6481 | |
| 6/5 | 231.5954 | 385.9924 | 701.6336 | 5-limit minimax |
| 11/9 | 231.6053 | 386.0088 | 701.5612 | |
| 7/6 | 231.6112 | 386.0187 | 701.5179 | |
| 5/4 | 231.7882 | 386.3137 | 700.2197 |