Rodan: Difference between revisions
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Cleanup; bold prime harmonics; clarify tuning spectrum table |
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| Line 1: | Line 1: | ||
See | See [[Gamelismic clan #Rodan]] for more information. | ||
Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363] | Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363] | ||
Gencom map: [ | Gencom map: [{{val| 1 1 -1 3 6 8 8 }}, {{val| 0 3 17 -1 -13 -22 -20 }}] | ||
== Interval | == Interval chain == | ||
{| class="wikitable center- | Primes harmonics are in '''bold'''. | ||
{| class="wikitable center-1 right-2" | |||
! rowspan="2" | # | ! rowspan="2" | # | ||
! rowspan="2" | Cents* | ! rowspan="2" | Cents* | ||
| Line 21: | Line 23: | ||
| 1 | | 1 | ||
| 234.482 | | 234.482 | ||
| 8/7 | | '''8/7''' | ||
| | | | ||
|- | |- | ||
| Line 31: | Line 33: | ||
| 3 | | 3 | ||
| 703.446 | | 703.446 | ||
| 3/2 | | '''3/2''' | ||
| | | | ||
|- | |- | ||
| Line 41: | Line 43: | ||
| 5 | | 5 | ||
| 1172.411 | | 1172.411 | ||
| 63/32 | | 63/32, 160/81 | ||
| | | | ||
|- | |- | ||
| Line 66: | Line 68: | ||
| 10 | | 10 | ||
| 1144.821 | | 1144.821 | ||
| 27/14 | | 27/14, 35/18, 64/33 | ||
| 33/17 | | 33/17 | ||
|- | |- | ||
| Line 76: | Line 78: | ||
| 12 | | 12 | ||
| 413.786 | | 413.786 | ||
| 14/11 | | 14/11, 81/64, 80/63 | ||
| 33/26 | | 33/26 | ||
|- | |- | ||
| 13 | | 13 | ||
| 648.268 | | 648.268 | ||
| 16/11 | | '''16/11''' | ||
| | | | ||
|- | |- | ||
| Line 91: | Line 93: | ||
| 15 | | 15 | ||
| 1117.232 | | 1117.232 | ||
| 21/11 | | 21/11, 40/21 | ||
| | | | ||
|- | |- | ||
| Line 101: | Line 103: | ||
| 17 | | 17 | ||
| 386.196 | | 386.196 | ||
| 5/4 | | '''5/4''' | ||
| | | | ||
|- | |- | ||
| Line 112: | Line 114: | ||
| 855.161 | | 855.161 | ||
| 18/11 | | 18/11 | ||
| 64/39 | | 64/39, 28/17 | ||
|- | |- | ||
| 20 | | 20 | ||
| 1089.643 | | 1089.643 | ||
| 15/8 | | 15/8 | ||
| 32/17 | | '''32/17''' | ||
|- | |- | ||
| 21 | | 21 | ||
| Line 127: | Line 129: | ||
| 358.607 | | 358.607 | ||
| 27/22 | | 27/22 | ||
| 16/13 | | '''16/13''', 21/17 | ||
|} | |} | ||
<nowiki>*</nowiki> in 13-limit POTE tuning | <nowiki>*</nowiki> in 13-limit POTE tuning | ||
| Line 137: | Line 139: | ||
! Eigenmonzo | ! Eigenmonzo | ||
! Fifth | ! Fifth | ||
! | ! Comments | ||
|- | |- | ||
| 8/7 | | 8/7 | ||
| Line 169: | Line 171: | ||
| 7/5 | | 7/5 | ||
| 702.915 | | 702.915 | ||
| 7 and 9 limit minimax | | 7- and 9-odd-limit minimax | ||
|- | |- | ||
| 11/9 | | 11/9 | ||
| 703.041 | | 703.041 | ||
| 11 limit minimax | | 11-odd-limit minimax | ||
|- | |- | ||
| (75\128) | | (75\128) | ||
| Line 181: | Line 183: | ||
| 18/13 | | 18/13 | ||
| 703.220 | | 703.220 | ||
| 13 and 15 limit minimax | | 13- and 15-odd-limit minimax | ||
|- | |- | ||
| 16/15 | | 16/15 | ||
| Line 209: | Line 211: | ||
| 5/4 | | 5/4 | ||
| 703.467 | | 703.467 | ||
| 5 limit minimax | | 5-odd-limit minimax | ||
|- | |- | ||
| 11/10 | | 11/10 | ||
| Line 233: | Line 235: | ||
| 18/17 | | 18/17 | ||
| 703.726 | | 703.726 | ||
| 17 limit minimax | | 17-odd-limit minimax | ||
|- | |- | ||
| 17/15 | | 17/15 | ||
Revision as of 09:02, 7 March 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
Primes harmonics are in bold.
| # | Cents* | Approximate Ratios | |
|---|---|---|---|
| 11-limit | 13- and 17-limit | ||
| 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 | 27/16 | 22/13 |
| 10 | 1144.821 | 27/14, 35/18, 64/33 | 33/17 |
| 11 | 179.304 | 10/9 | |
| 12 | 413.786 | 14/11, 81/64, 80/63 | 33/26 |
| 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 | 15/14 | 14/13 |
| 22 | 358.607 | 27/22 | 16/13, 21/17 |
* in 13-limit POTE tuning
Spectrum of Rodan Tunings by Eigenmonzos
| Eigenmonzo | 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 |