Ennealimmal
Ennealimmal temperament has a period of 1/9 octave and tempers out 2401/2400 and 4375/4374. EDOs that support ennealimmal include EDOs 27, 45, 72, 99, 171, 270, 441, and 612.
See Ragismic microtemperaments #Ennealimmal for more technical data.
Interval chain
| Generator | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 | Period 6 | Period 7 | Period 8 | Period 9 (0) |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 133.333 | 266.666 | 400 | 533.333 | 666.666 | 800 | 933.333 | 1066.666 | 1200 |
| -1 | 84.43 | 217.763 | 351.097 | 484.43 | 617.763 | 751.097 | 884.43 | 1017.763 | 1151.097 |
| -2 | 35.527 | 168.86 | 302.194 | 435.527 | 568.86 | 702.194 | 835.527 | 968.86 | 1102.194 |
| -3 | 1186.624 | 119.957 | 253.291 | 386.624 | 519.957 | 653.291 | 786.624 | 919.957 | 1053.291 |
| -4 | 1137.721 | 71.054 | 204.388 | 337.721 | 471.054 | 604.388 | 737.721 | 871.054 | 1004.388 |
| -5 | 1088.818 | 22.151 | 155.485 | 288.818 | 422.151 | 555.485 | 688.818 | 822.151 | 955.485 |
| -6 | 1039.915 | 1173.248 | 106.582 | 239.915 | 373.248 | 506.582 | 639.915 | 773.248 | 906.582 |
| -7 | 991.012 | 1124.345 | 57.679 | 191.012 | 324.345 | 457.679 | 591.012 | 724.345 | 857.679 |
| -8 | 942.109 | 1075.442 | 8.776 | 142.109 | 275.442 | 408.776 | 542.109 | 675.442 | 808.776 |
| -9 | 893.206 | 1026.539 | 1159.873 | 93.206 | 226.539 | 359.873 | 493.206 | 626.539 | 759.873 |
| -10 | 844.303 | 977.636 | 1110.97 | 44.303 | 177.636 | 310.97 | 444.303 | 577.636 | 710.97 |
| -11 | 795.4 | 928.733 | 1062.067 | 1195.4 | 128.733 | 262.067 | 395.4 | 528.733 | 662.067 |
| -12 | 746.497 | 879.83 | 1013.164 | 1146.497 | 79.83 | 213.164 | 346.497 | 479.83 | 613.164 |
| -13 | 697.594 | 830.927 | 964.261 | 1097.594 | 30.927 | 164.261 | 297.594 | 430.927 | 564.261 |
| -14 | 648.691 | 782.024 | 915.358 | 1048.691 | 1182.024 | 115.358 | 248.691 | 382.024 | 515.358 |
| -15 | 599.788 | 733.121 | 866.455 | 999.788 | 1133.121 | 66.455 | 199.788 | 333.121 | 466.455 |
| -16 | 550.885 | 684.218 | 817.552 | 950.885 | 1084.218 | 17.552 | 150.885 | 284.218 | 417.552 |
| -17 | 501.982 | 635.315 | 768.649 | 901.982 | 1035.315 | 1168.649 | 101.982 | 235.315 | 368.649 |
Ennealimmal extensions
Ennealimmal temperament has various extensions to the 11-limit. These are all members of the ennealimmal family, but in addition they are linear temperaments:
- Ennealimmal (99e & 270) - tempering out 2401/2400, 4375/4374, 5632/5625
- Ennealimmia (171 & 270) - tempering out 2401/2400, 4375/4374, 131072/130977
- Ennealimnic (72 & 99e) - tempering out 243/242, 441/440, 4375/4356
- Ennealiminal (72 & 171e) - tempering out 385/384, 1375/1372, 4375/4374
Scales
- Ennealimmal27 - proper 18L 9s. Ninth-octave analog of haplotonic scale
- Ennealimmal45 - improper 27L 18s. Ninth-octave analog of mega-haplotonic scale
- Ennealimmal45trans - symmetric 5-limit transversal version
- Ennealimmal72 - proper 27L 45s. Ninth-octave analog of albitonic scale
- Ennealimmal99 - proper 72L 27s. Ninth-octave analog of chromatic scale
- Ennealimmal171 - 99L 72s scale. The boundary of propriety is 270EDO.