Superkleismic: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 1: / Line 1: @@
-'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit|7-]], [[11-limit|11-]], and [[13-limit]]. It is a member of [[shibboleth family]] as well as of the [[gamelismic clan]]. It also [[extension|extends]] [[orgone]]. The minor-third generator of superkleismic is ~6.3 cents sharp of [[6/5]], even wider than the [[Kleismic family|kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you [[orgone]]. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11, 15, or 26 notes are available.
+'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[square superparticular|S5/S6]] = [[875/864]], the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out S7/S8 = [[1029/1024]], the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments|keemic temperament]]. It extends extremely easily to the [[11-limit]] as well, by tempering out S10 = [[100/99]] (as well as [[385/384]] and [[441/440]]) so that two generators reach [[16/11]], which serves to [[extension|extend]] the structure of [[orgone]] in the 2.7.11 subgroup. Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]].
+The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.
 See [[Shibboleth family #Superkleismic]] for more technical data.
@@ Line 9: / Line 11: @@
 ! #
 ! Cents*
-! Approximate ratios
+! Approximate 11-limit ratios
+! 13-limit extension
 |-
 | 0
 | 0.0
 | '''1/1'''
+|
 |-
 | 1
 | 322.0
 | 6/5
+|
 |-
 | 2
 | 644.0
-| 13/9, '''16/11'''
+| '''16/11'''
+| 13/9
 |-
 | 3
 | 966.0
 | '''7/4'''
+|
 |-
 | 4
 | 88.0
 | 21/20, 22/21
+|
 |-
 | 5
 | 410.0
 | 14/11
+|
 |-
 | 6
 | 732.0
-| 20/13, '''32/21'''
+| '''32/21'''
+| 20/13
 |-
 | 7
 | 1053.9
-| 11/6, 24/13
+| 11/6
+| 24/13
 |-
 | 8
 | 175.9
 | 10/9, 11/10
+|
 |-
 | 9
 | 497.9
 | '''4/3'''
+|
 |-
 | 10
 | 819.9
 | '''8/5'''
+|
 |-
 | 11
 | 1141.9
-| 35/18, 48/25, 52/27, 64/33
+| 35/18, 48/25, 64/33
+| 52/27
 |-
 | 12
 | 263.9
 | 7/6
+|
 |-
 | 13
 | 585.9
 | 7/5
+|
 |-
 | 14
 | 907.9
+|
 | 22/13
 |-
 | 15
 | 29.9
-| 40/39, 49/48, 56/55, 64/63
+| 49/48, 56/55, 64/63
+| 40/39
 |-
 | 16
 | 351.9
-| 11/9, '''16/13'''
+| 11/9
+| '''16/13'''
 |-
 | 17
 | 673.9
 | 22/15, 40/27
+|
 |-
 | 18
 | 995.9
 | '''16/9'''
+|
 |-
 | 19
 | 117.9
-| 14/13, '''16/15'''
+| '''16/15'''
+| 14/13
 |-
 | 20
 | 439.9
 | 32/25, 35/27
+|
 |-
 | 21
 | 761.8
 | 14/9
+|
 |-
 | 22
 | 1083.8
 | 28/15
+|
 |-
 | 23
 | 205.8
-| 28/25, 44/39
+| 28/25
+| 44/39
 |-
 | 24
 | 527.8
 | 49/36
+|
 |-
 | 25
 | 849.8
-| 44/27, 64/39
+| 44/27
+| 64/39
 |-
 | 26
 | 1171.8
-| 49/25, 88/45, 128/65, 160/81
+| 49/25, 88/45, 160/81
+| 128/65
 |}
 <nowiki>*</nowiki> in 13-limit CWE tuning