@@ Line 1: / Line 1: @@
-See [[Ragismic_microtemperaments#Ennealimmal|Ragismic microtemperaments]].
+{{URWTC}}
-[[Category:soft_redirect]]
+'''Ennealimmal temperament''' is a [[regular temperament]] with a period of {{frac|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 [[Septiennealimmal clan #Ennealimmal]] for technical data.
+Ennealimmal scales are built from a ''period'' (which is exactly {{frac|1|9}} of an octave), and a ''generator'' (which is approximately 49 cents and represents several small intervals including 36/35). Depending on the size of the generator and the period in steps, the above listed edos make sense:
+{| class="wikitable"
+|- style="white-space: nowrap;"
+! Period (steps) !! Generator (steps) !! Generator (cents)<br />(pure octave) !! Edo
+|-
+| 3 || 1 || 44.444 || 27
+|-
+| 11 || 4 || 48.485 || 99
+|-
+| 30 || 11 || 48.889 || 270
+|-
+| 19 || 7 || 49.123 || 171
+|-
+| 8 || 3 || 50.000 || 72
+|-
+| 5 || 2 || 53.333 || 45
+|}
+== Interval chain ==
+{| class="wikitable"
+|+ style="font-size: 105%;" | Generator based off 11-limit ennealimmal
+|- style="white-space: nowrap;"
+! 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
+|-
+! &minus;1
+| 84.430
+| 217.764
+| 351.097
+| 484.430
+| 617.764
+| 751.097
+| 884.430
+| 1017.764
+| 1151.097
+|-
+! &minus;2
+| 35.527
+| 168.861
+| 302.194
+| 435.527
+| 568.861
+| 702.194
+| 835.527
+| 968.861
+| 1102.194
+|-
+! &minus;3
+| 1186.624
+| 119.958
+| 253.291
+| 386.624
+| 519.958
+| 653.291
+| 786.624
+| 919.958
+| 1053.291
+|-
+! &minus;4
+| 1137.721
+| 71.055
+| 204.388
+| 337.721
+| 471.055
+| 604.388
+| 737.721
+| 871.055
+| 1004.388
+|-
+! &minus;5
+| 1088.818
+| 22.152
+| 155.485
+| 288.818
+| 422.152
+| 555.485
+| 688.818
+| 822.152
+| 955.485
+|-
+! &minus;6
+| 1039.915
+| 1173.249
+| 106.582
+| 239.915
+| 373.249
+| 506.582
+| 639.915
+| 773.249
+| 906.582
+|-
+! &minus;7
+| 991.012
+| 1124.346
+| 57.679
+| 191.012
+| 324.346
+| 457.679
+| 591.012
+| 724.346
+| 857.679
+|-
+! &minus;8
+| 942.109
+| 1075.443
+| 8.776
+| 142.109
+| 275.443
+| 408.776
+| 542.109
+| 675.443
+| 808.776
+|-
+! &minus;9
+| 893.206
+| 1026.540
+| 1159.873
+| 93.206
+| 226.540
+| 359.873
+| 493.206
+| 626.540
+| 759.873
+|-
+! &minus;10
+| 844.303
+| 977.637
+| 1110.970
+| 44.303
+| 177.637
+| 310.970
+| 444.303
+| 577.637
+| 710.970
+|-
+! &minus;11
+| 795.400
+| 928.734
+| 1062.067
+| 1195.400
+| 128.734
+| 262.067
+| 395.400
+| 528.734
+| 662.067
+|-
+! &minus;12
+| 746.497
+| 879.831
+| 1013.164
+| 1146.497
+| 79.831
+| 213.164
+| 346.497
+| 479.831
+| 613.164
+|-
+! &minus;13
+| 697.594
+| 830.928
+| 964.261
+| 1097.594
+| 30.928
+| 164.261
+| 297.594
+| 430.928
+| 564.261
+|-
+! &minus;14
+| 648.691
+| 782.025
+| 915.358
+| 1048.691
+| 1182.025
+| 115.358
+| 248.691
+| 382.025
+| 515.358
+|-
+! &minus;15
+| 599.788
+| 733.122
+| 866.455
+| 999.788
+| 1133.122
+| 66.455
+| 199.788
+| 333.122
+| 466.455
+|-
+! &minus;16
+| 550.885
+| 684.219
+| 817.552
+| 950.885
+| 1084.219
+| 17.552
+| 150.885
+| 284.219
+| 417.552
+|-
+! &minus;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 &amp; 270) &ndash; tempering out 2401/2400, 4375/4374, 5632/5625
+* Ennealimmia (171 &amp; 270) &ndash; tempering out 2401/2400, 4375/4374, 131072/130977
+* Ennealimnic (72 &amp; 99e) &ndash; tempering out 243/242, 441/440, 4375/4356
+* Ennealiminal (72 &amp; 171e) &ndash; tempering out 385/384, 1375/1372, 4375/4374
+== Scales ==
+* [[Ennealimmal27]] &ndash; proper [[18L 9s]]. Ninth-octave analog of haplotonic scale
+* [[Ennealimmal45]] &ndash; improper [[27L 18s]]. Ninth-octave analog of mega-haplotonic scale
+** [[Ennealimmal45trans]] &ndash; symmetric 5-limit transversal version
+* [[Ennealimmal72]] &ndash; proper [[27L 45s]]. Ninth-octave analog of albitonic scale
+* [[Ennealimmal99]] &ndash; proper [[72L 27s]]. Ninth-octave analog of chromatic scale
+* [[Ennealimmal171]] &ndash; [[99L 72s]] scale. The boundary of propriety is [[270edo]].
+== Music ==
+; [[Gene Ward Smith]]
+* [https://archive.org/details/fingers_201403 ''The 45000 fingers of Dr. S''] (2003) – Ennealimmal[54] in TOP tuning
+[[Category:Ennealimmal| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Breedsmic temperaments]]
+[[Category:Ragismic microtemperaments]]
+[[Category:Landscape microtemperaments]]

Ennealimmal: Difference between revisions