Ennealimmal

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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 based off 11-limit ennealimmal
Generator Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 (0)
0 133.333 266.666 400.000 533.333 666.666 800.000 933.333 1066.666 1200.000
-1 84.430 217.764 351.097 484.430 617.764 751.097 884.430 1017.764 1151.097
-2 35.527 168.861 302.194 435.527 568.861 702.194 835.527 968.861 1102.194
-3 1186.624 119.958 253.291 386.624 519.958 653.291 786.624 919.958 1053.291
-4 1137.721 71.055 204.388 337.721 471.055 604.388 737.721 871.055 1004.388
-5 1088.818 22.152 155.485 288.818 422.152 555.485 688.818 822.152 955.485
-6 1039.915 1173.249 106.582 239.915 373.249 506.582 639.915 773.249 906.582
-7 991.012 1124.346 57.679 191.012 324.346 457.679 591.012 724.346 857.679
-8 942.109 1075.443 8.776 142.109 275.443 408.776 542.109 675.443 808.776
-9 893.206 1026.540 1159.873 93.206 226.540 359.873 493.206 626.540 759.873
-10 844.303 977.637 1110.970 44.303 177.637 310.970 444.303 577.637 710.970
-11 795.400 928.734 1062.067 1195.400 128.734 262.067 395.400 528.734 662.067
-12 746.497 879.831 1013.164 1146.497 79.831 213.164 346.497 479.831 613.164
-13 697.594 830.928 964.261 1097.594 30.928 164.261 297.594 430.928 564.261
-14 648.691 782.025 915.358 1048.691 1182.025 115.358 248.691 382.025 515.358
-15 599.788 733.122 866.455 999.788 1133.122 66.455 199.788 333.122 466.455
-16 550.885 684.219 817.552 950.885 1084.219 17.552 150.885 284.219 417.552
-17 501.982 635.316 768.649 901.982 1035.316 1168.649 101.982 235.316 368.649

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