Ennealimmal: Difference between revisions

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interval chain (uses 36/35 as the generator, not 5/3)
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See [[Ragismic microtemperaments #Ennealimmal]] for more technical data.
See [[Ragismic microtemperaments #Ennealimmal]] for more technical data.
== Interval chain ==
{| class="wikitable"
|+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
|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 extensions ==

Revision as of 08:07, 18 September 2022

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)
0 133.333 266.666 400 533.333 666.666 800 933.333 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

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