Rodan: Difference between revisions
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Cmloegcmluin (talk | contribs) →Spectrum of rodan tunings by eigenmonzos: improve and standardize tuning spectra tables |
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* [[Rodan41opt]] | * [[Rodan41opt]] | ||
== | == Tuning spectrum == | ||
{| class="wikitable center-all | {| class="wikitable center-all" | ||
|- | |- | ||
! | ! ET<br>generator | ||
! | ! [[eigenmonzo|eigenmonzo<br>(unchanged interval]]) | ||
! | ! fifth<br>(¢) | ||
! comments | |||
|- | |- | ||
| | |||
| 8/7 | | 8/7 | ||
| 693.522 | | 693.522 | ||
| | | | ||
|- | |- | ||
| | |||
| 17/13 | | 17/13 | ||
| 696.642 | | 696.642 | ||
| | | | ||
|- | |- | ||
| | |||
| 7/6 | | 7/6 | ||
| 699.847 | | 699.847 | ||
| | | | ||
|- | |- | ||
| | |||
| 9/7 | | 9/7 | ||
| 700.750 | | 700.750 | ||
| | | | ||
|- | |- | ||
| | |||
| 4/3 | | 4/3 | ||
| 701.955 | | 701.955 | ||
| | | | ||
|- | |- | ||
| | | [[41edo|24\41]] | ||
| | |||
| 702.439 | | 702.439 | ||
| | | | ||
|- | |- | ||
| | |||
| 15/14 | | 15/14 | ||
| 702.778 | | 702.778 | ||
| | | | ||
|- | |- | ||
| | |||
| 7/5 | | 7/5 | ||
| 702.915 | | 702.915 | ||
| 7- and 9-odd-limit minimax | | 7- and 9-odd-limit minimax | ||
|- | |- | ||
| | |||
| 11/9 | | 11/9 | ||
| 703.041 | | 703.041 | ||
| 11-odd-limit minimax | | 11-odd-limit minimax | ||
|- | |- | ||
| | | [[128edo|75\128]] | ||
| | |||
| 703.125 | | 703.125 | ||
| | | | ||
|- | |- | ||
| | |||
| 18/13 | | 18/13 | ||
| 703.220 | | 703.220 | ||
| 13- and 15-odd-limit minimax | | 13- and 15-odd-limit minimax | ||
|- | |- | ||
| | |||
| 16/15 | | 16/15 | ||
| 703.240 | | 703.240 | ||
| | | | ||
|- | |- | ||
| | |||
| 12/11 | | 12/11 | ||
| 703.244 | | 703.244 | ||
| | | | ||
|- | |- | ||
| | |||
| 15/11 | | 15/11 | ||
| 703.359 | | 703.359 | ||
| | | | ||
|- | |- | ||
| | |||
| 13/12 | | 13/12 | ||
| 703.371 | | 703.371 | ||
| | | | ||
|- | |- | ||
| | |||
| 15/13 | | 15/13 | ||
| 703.410 | | 703.410 | ||
| | | | ||
|- | |- | ||
| | | [[87edo|51\87]] | ||
| | |||
| 703.448 | | 703.448 | ||
| | | | ||
|- | |- | ||
| | |||
| 5/4 | | 5/4 | ||
| 703.467 | | 703.467 | ||
| 5-odd-limit minimax | | 5-odd-limit minimax | ||
|- | |- | ||
| | |||
| 11/10 | | 11/10 | ||
| 703.500 | | 703.500 | ||
| | | | ||
|- | |- | ||
| | |||
| 13/10 | | 13/10 | ||
| 703.522 | | 703.522 | ||
| | | | ||
|- | |- | ||
| | |||
| 11/8 | | 11/8 | ||
| 703.542 | | 703.542 | ||
| | | | ||
|- | |- | ||
| | |||
| 16/13 | | 16/13 | ||
| 703.564 | | 703.564 | ||
| | | | ||
|- | |- | ||
| | |||
| 13/11 | | 13/11 | ||
| 703.597 | | 703.597 | ||
| | | | ||
|- | |- | ||
| | |||
| 18/17 | | 18/17 | ||
| 703.726 | | 703.726 | ||
| 17-odd-limit minimax | | 17-odd-limit minimax | ||
|- | |- | ||
| | |||
| 17/15 | | 17/15 | ||
| 703.748 | | 703.748 | ||
| | | | ||
|- | |- | ||
| | | [[133edo|78\133]] | ||
| | |||
| 703.759 | | 703.759 | ||
| | | | ||
|- | |- | ||
| | |||
| 6/5 | | 6/5 | ||
| 703.791 | | 703.791 | ||
| | | | ||
|- | |- | ||
| | |||
| 20/17 | | 20/17 | ||
| 703.894 | | 703.894 | ||
| | | | ||
|- | |- | ||
| | |||
| 24/17 | | 24/17 | ||
| 703.956 | | 703.956 | ||
| | | | ||
|- | |- | ||
| | |||
| 17/16 | | 17/16 | ||
| 704.257 | | 704.257 | ||
| | | | ||
|- | |- | ||
| | |||
| 10/9 | | 10/9 | ||
| 704.292 | | 704.292 | ||
| | | | ||
|- | |- | ||
| | | [[46edo|27\46]] | ||
| | |||
| 704.348 | | 704.348 | ||
| | | | ||
|- | |- | ||
| | |||
| 14/11 | | 14/11 | ||
| 704.377 | | 704.377 | ||
Revision as of 00:27, 30 September 2021
See Gamelismic clan #Rodan for more information.
Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363]
Gencom map: [⟨1 1 -1 3 6 8 8], ⟨0 3 17 -1 -13 -22 -20]]
Interval chain
Prime harmonics are in bold.
| # | Cents* | Approximate Ratios | |
|---|---|---|---|
| 13-limit | 17-limit extension | ||
| 0 | 0.000 | 1/1 | |
| 1 | 234.482 | 8/7 | |
| 2 | 468.964 | 21/16 | 17/13 |
| 3 | 703.446 | 3/2 | |
| 4 | 937.929 | 12/7 | |
| 5 | 1172.411 | 63/32, 160/81 | |
| 6 | 206.893 | 9/8 | |
| 7 | 441.375 | 9/7 | 22/17 |
| 8 | 675.857 | 40/27 | |
| 9 | 910.339 | 22/13, 27/16, 33/28 | |
| 10 | 1144.821 | 27/14, 35/18, 64/33 | 33/17 |
| 11 | 179.304 | 10/9 | |
| 12 | 413.786 | 14/11, 33/26, 80/63 | |
| 13 | 648.268 | 16/11 | |
| 14 | 882.750 | 5/3 | |
| 15 | 1117.232 | 21/11, 40/21 | |
| 16 | 151.714 | 12/11 | |
| 17 | 386.196 | 5/4 | |
| 18 | 620.679 | 10/7 | |
| 19 | 855.161 | 18/11, 64/39 | 28/17 |
| 20 | 1089.643 | 15/8 | 32/17 |
| 21 | 124.125 | 14/13, 15/14 | |
| 22 | 358.607 | 16/13, 27/22 | 21/17 |
| 23 | 593.088 | 45/32 | 24/17 |
| 24 | 827.570 | 21/13 | |
| 25 | 1062.052 | 24/13 | |
* in 13-limit POTE tuning
Chords
Scales
Tuning spectrum
| ET generator |
eigenmonzo (unchanged interval) |
fifth (¢) |
comments |
|---|---|---|---|
| 8/7 | 693.522 | ||
| 17/13 | 696.642 | ||
| 7/6 | 699.847 | ||
| 9/7 | 700.750 | ||
| 4/3 | 701.955 | ||
| 24\41 | 702.439 | ||
| 15/14 | 702.778 | ||
| 7/5 | 702.915 | 7- and 9-odd-limit minimax | |
| 11/9 | 703.041 | 11-odd-limit minimax | |
| 75\128 | 703.125 | ||
| 18/13 | 703.220 | 13- and 15-odd-limit minimax | |
| 16/15 | 703.240 | ||
| 12/11 | 703.244 | ||
| 15/11 | 703.359 | ||
| 13/12 | 703.371 | ||
| 15/13 | 703.410 | ||
| 51\87 | 703.448 | ||
| 5/4 | 703.467 | 5-odd-limit minimax | |
| 11/10 | 703.500 | ||
| 13/10 | 703.522 | ||
| 11/8 | 703.542 | ||
| 16/13 | 703.564 | ||
| 13/11 | 703.597 | ||
| 18/17 | 703.726 | 17-odd-limit minimax | |
| 17/15 | 703.748 | ||
| 78\133 | 703.759 | ||
| 6/5 | 703.791 | ||
| 20/17 | 703.894 | ||
| 24/17 | 703.956 | ||
| 17/16 | 704.257 | ||
| 10/9 | 704.292 | ||
| 27\46 | 704.348 | ||
| 14/11 | 704.377 |