16ed5/2: Difference between revisions
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Coincidentally, 133 steps of the pyrite edX of this size exceed 11 octaves by only 2.978¢. | Coincidentally, 133 steps of the pyrite edX of this size exceed 11 octaves by only 2.978¢. | ||
== 16ed5/2 as a generator == | |||
'''<font style="font-size: 1.35em">Trisa-quingu (12&121)</font>'''<br> | |||
'''<font style="font-size: 1.2em">5-limit</font>'''<br> | |||
Comma: {{monzo|37 -16 -5}}<br> | |||
Mapping: [{{val|1 2 1}}, {{val|0 -5 16}}]<br> | |||
POTE generator: ~135/128 = 99.267<br> | |||
Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc<br> | |||
Badness: 0.444506<br><br> | |||
'''<font style="font-size: 1.35em">[[Octagar temperaments #Quintupole|Quintupole]] (12&121)</font>'''<br> | |||
{{See also|34ed7 #34ed7 as a generator}} | |||
'''<font style="font-size: 1.2em">7-limit</font>'''<br> | |||
Comma list: 4000/3969, 458752/455625<br> | |||
Mapping: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]<br> | |||
POTE generator: ~135/128 = 99.175<br> | |||
Vals: 12, 97, 109, 121<br> | |||
Badness: 0.111620<br><br> | |||
'''<font style="font-size: 1.2em">11-limit</font>'''<br> | |||
Comma list: 896/891, 1375/1372, 4375/4356<br> | |||
Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]<br> | |||
POTE generator: ~132/125 = 99.156<br> | |||
Vals: 12, 109, 121, 351bde, 472bdee<br> | |||
Badness: 0.056501<br><br> | |||
'''<font style="font-size: 1.35em">[[Marvel temperaments|12&85 temperament]]</font>'''<br> | |||
'''<font style="font-size: 1.2em">7-limit</font>'''<br> | |||
Comma list: 225/224, 7812500/7411887<br> | |||
Mapping: [{{val|1 2 1 1}}, {{val|0 -5 16 22}}]<br> | |||
POTE generator: ~21/20 = 98.994<br> | |||
Vals: 12, 73c, 85, 97d<br> | |||
Badness: 0.192498<br><br> | |||
'''<font style="font-size: 1.2em">11-limit</font>'''<br> | |||
Comma list: 100/99, 225/224, 85184/84035<br> | |||
Mapping: [{{val|1 2 1 1 0}}, {{val|0 -5 16 22 42}}]<br> | |||
POTE generator: ~21/20 = 98.954<br> | |||
Vals: 12, 73ce, 85, 97d<br> | |||
Badness: 0.104353<br><br> | |||
[[Category:EdX]] | |||
[[Category:Nonoctave]] | |||
Revision as of 22:12, 13 July 2021
This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval
Intervals
| Degrees | Enneatonic | ed38\29 | Golden | ed5/2 | ed(7φ+6)\5(φ+1) | ed4\3=r¢ | ||
|---|---|---|---|---|---|---|---|---|
| 1 | 1#/2b | F#/Gb | 98.276 | 98.3795 | 99.145 | 99.2705 | 100 | |
| 2 | 2 | G | 196.552 | 196.759 | 198.289 | 198.541 | 200 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | 294.828 | 295.138 | 297.433 | 297.8115 | 300 |
| 4 | 3 | J | A | 393.103 | 393.518 | 396.578 | 397.082 | 400 |
| 5 | 3#/4b | J#/Ab | A#/Bb | 491.379 | 491.897 | 495.723 | 496.3525 | 500 |
| 6 | 4 | A | B | 589.655 | 590.277 | 594.868 | 595.623 | 600 |
| 7 | 5 | B | H | 687.931 | 688.656 | 694.012 | 694.894 | 700 |
| 8 | 5#/6b | B#/Hb | H#/Cb | 786.207 | 787.036 | 793.157 | 794.164 | 800 |
| 9 | 6 | H | C | 884.483 | 885.415 | 892.3015 | 893.435 | 900 |
| 10 | 6#/7b | H#/Cb | C#/Db | 982.759 | 983.795 | 991.446 | 992.705 | 1000 |
| 11 | 7 | C | D | 1081.0345 | 1082.174 | 1090.591 | 1091.976 | 1100 |
| 12 | 7#/8b | C#/Db | D#/Sb | 1179.31 | 1180.554 | 1189.735 | 1191.246 | 1200 |
| 13 | 8 | D | S | 1277.586 | 1278.933 | 1288.88 | 1290.517 | 1300 |
| 14 | 8#/9b | D#/Eb | S#/Eb | 1375.862 | 1377.313 | 1388.0245 | 1389.787 | 1400 |
| 15 | 9 | E | 1474.138 | 1475.692 | 1487.169 | 1489.058 | 1500 | |
| 16 | 1 | F | 1572.414 | 1574.0715 | 1586.314 | 1588.328 | 1600 | |
Coincidentally, 133 steps of the pyrite edX of this size exceed 11 octaves by only 2.978¢.
16ed5/2 as a generator
Trisa-quingu (12&121)
5-limit
Comma: [37 -16 -5⟩
Mapping: [⟨1 2 1], ⟨0 -5 16]]
POTE generator: ~135/128 = 99.267
Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc
Badness: 0.444506
Quintupole (12&121)
7-limit
Comma list: 4000/3969, 458752/455625
Mapping: [⟨1 2 1 0], ⟨0 -5 16 34]]
POTE generator: ~135/128 = 99.175
Vals: 12, 97, 109, 121
Badness: 0.111620
11-limit
Comma list: 896/891, 1375/1372, 4375/4356
Mapping: [⟨1 2 1 0 -1], ⟨0 -5 16 34 54]]
POTE generator: ~132/125 = 99.156
Vals: 12, 109, 121, 351bde, 472bdee
Badness: 0.056501
12&85 temperament
7-limit
Comma list: 225/224, 7812500/7411887
Mapping: [⟨1 2 1 1], ⟨0 -5 16 22]]
POTE generator: ~21/20 = 98.994
Vals: 12, 73c, 85, 97d
Badness: 0.192498
11-limit
Comma list: 100/99, 225/224, 85184/84035
Mapping: [⟨1 2 1 1 0], ⟨0 -5 16 22 42]]
POTE generator: ~21/20 = 98.954
Vals: 12, 73ce, 85, 97d
Badness: 0.104353