Ennealimmal: Difference between revisions

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Royalmilktea (talk | contribs)
autopatrolled, emailconfirmed
64 edits
interval chain (uses 36/35 as the generator, not 5/3)
Royalmilktea (talk | contribs)
autopatrolled, emailconfirmed
64 edits
interval chain changes (decimal places, rounding)
Line 20: Line 20:
|133.333
|133.333
|266.666
|266.666
|400
|400.000
|533.333
|533.333
|666.666
|666.666
|800
|800.000
|933.333
|933.333
|1066.666
|1066.666
|1200
|1200.000
|-
|-
!-1
!-1
|84.43
|84.430
|217.763
|217.764
|351.097
|351.097
|484.43
|484.430
|617.763
|617.764
|751.097
|751.097
|884.43
|884.430
|1017.763
|1017.764
|1151.097
|1151.097
|-
|-
!-2
!-2
|35.527
|35.527
|168.86
|168.861
|302.194
|302.194
|435.527
|435.527
|568.86
|568.861
|702.194
|702.194
|835.527
|835.527
|968.86
|968.861
|1102.194
|1102.194
|-
|-
!-3
!-3
|1186.624
|1186.624
|119.957
|119.958
|253.291
|253.291
|386.624
|386.624
|519.957
|519.958
|653.291
|653.291
|786.624
|786.624
|919.957
|919.958
|1053.291
|1053.291
|-
|-
!-4
!-4
|1137.721
|1137.721
|71.054
|71.055
|204.388
|204.388
|337.721
|337.721
|471.054
|471.055
|604.388
|604.388
|737.721
|737.721
|871.054
|871.055
|1004.388
|1004.388
|-
|-
!-5
!-5
|1088.818
|1088.818
|22.151
|22.152
|155.485
|155.485
|288.818
|288.818
|422.151
|422.152
|555.485
|555.485
|688.818
|688.818
|822.151
|822.152
|955.485
|955.485
|-
|-
!-6
!-6
|1039.915
|1039.915
|1173.248
|1173.249
|106.582
|106.582
|239.915
|239.915
|373.248
|373.249
|506.582
|506.582
|639.915
|639.915
|773.248
|773.249
|906.582
|906.582
|-
|-
!-7
!-7
|991.012
|991.012
|1124.345
|1124.346
|57.679
|57.679
|191.012
|191.012
|324.345
|324.346
|457.679
|457.679
|591.012
|591.012
|724.345
|724.346
|857.679
|857.679
|-
|-
!-8
!-8
|942.109
|942.109
|1075.442
|1075.443
|8.776
|8.776
|142.109
|142.109
|275.442
|275.443
|408.776
|408.776
|542.109
|542.109
|675.442
|675.443
|808.776
|808.776
|-
|-
!-9
!-9
|893.206
|893.206
|1026.539
|1026.540
|1159.873
|1159.873
|93.206
|93.206
|226.539
|226.540
|359.873
|359.873
|493.206
|493.206
|626.539
|626.540
|759.873
|759.873
|-
|-
!-10
!-10
|844.303
|844.303
|977.636
|977.637
|1110.97
|1110.970
|44.303
|44.303
|177.636
|177.637
|310.97
|310.970
|444.303
|444.303
|577.636
|577.637
|710.97
|710.970
|-
|-
!-11
!-11
|795.4
|795.400
|928.733
|928.734
|1062.067
|1062.067
|1195.4
|1195.400
|128.733
|128.734
|262.067
|262.067
|395.4
|395.400
|528.733
|528.734
|662.067
|662.067
|-
|-
!-12
!-12
|746.497
|746.497
|879.83
|879.831
|1013.164
|1013.164
|1146.497
|1146.497
|79.83
|79.831
|213.164
|213.164
|346.497
|346.497
|479.83
|479.831
|613.164
|613.164
|-
|-
!-13
!-13
|697.594
|697.594
|830.927
|830.928
|964.261
|964.261
|1097.594
|1097.594
|30.927
|30.928
|164.261
|164.261
|297.594
|297.594
|430.927
|430.928
|564.261
|564.261
|-
|-
!-14
!-14
|648.691
|648.691
|782.024
|782.025
|915.358
|915.358
|1048.691
|1048.691
|1182.024
|1182.025
|115.358
|115.358
|248.691
|248.691
|382.024
|382.025
|515.358
|515.358
|-
|-
!-15
!-15
|599.788
|599.788
|733.121
|733.122
|866.455
|866.455
|999.788
|999.788
|1133.121
|1133.122
|66.455
|66.455
|199.788
|199.788
|333.121
|333.122
|466.455
|466.455
|-
|-
!-16
!-16
|550.885
|550.885
|684.218
|684.219
|817.552
|817.552
|950.885
|950.885
|1084.218
|1084.219
|17.552
|17.552
|150.885
|150.885
|284.218
|284.219
|417.552
|417.552
|-
|-
!-17
!-17
|501.982
|501.982
|635.315
|635.316
|768.649
|768.649
|901.982
|901.982
|1035.315
|1035.316
|1168.649
|1168.649
|101.982
|101.982
|235.315
|235.316
|368.649
|368.649
|}
|}

Revision as of 19:50, 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)
0 133.333 266.666 400.000 533.333 666.666 800.000 933.333 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

Retrieved from "https://en.xen.wiki/index.php?title=Ennealimmal&oldid=95522"