Kleismic: Difference between revisions

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-'''Kleismic''' may refer to:
+'''Hanson''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] of the [[kleismic family]], characterized by the vanishing of the [[15625/15552|kleisma]]. It is [[generator|generated]] by a [[6/5|classical minor third (6/5)]], six of which make a [[3/1|twelfth (3/1)]]. This naturally gives us hemitwelfths at only 3 generator steps, which can be interpreted as [[26/15]] (and thus hemifourths as [[15/13]]), resulting in '''cata''', a low-complexity but high-accuracy [[extension]] to the 2.3.5.13 [[subgroup]].
-* [[Kleismic rank three family]], for the rank-3 kleismic temperament and its associated family
-* [[Kleismic family]], for the rank-2 hanson temperament and its associated family
-{{Disambiguation}}
+-limit extensions include [[keemun]], [[catalan]], [[catakleismic]], [[countercata]], and [[metakleismic]].
-[[Category:Kleismic]]
+For technical data, see [[Kleismic family #Hanson]].
+== Interval chain ==
+In the following table, odd harmonics 1–15 are labeled in '''bold'''.
+{| class="wikitable center-1 right-2"
+! #
+! Cents*
+! Approximate Ratios
+|-
+| 0
+| 0.0
+| '''1/1'''
+|-
+| 1
+| 317.1
+| 6/5
+|-
+| 2
+| 634.2
+| 13/9
+|-
+| 3
+| 950.3
+| 26/15
+|-
+| 4
+| 68.4
+| 25/24, 26/25, 27/26
+|-
+| 5
+| 385.6
+| '''5/4'''
+|-
+| 6
+| 702.7
+| '''3/2'''
+|-
+| 7
+| 1019.8
+| 9/5
+|-
+| 8
+| 136.9
+| 13/12, 14/13, 27/25
+|-
+| 9
+| 454.0
+| 13/10
+|-
+| 10
+| 771.1
+| 25/16
+|-
+| 11
+| 1088.2
+| '''15/8'''
+|-
+| 12
+| 205.3
+| '''9/8'''
+|-
+| 13
+| 522.4
+| 27/20
+|-
+| 14
+| 839.6
+| '''13/8''', 21/13
+|-
+| 15
+| 1156.7
+| 39/20
+|-
+| 16
+| 273.8
+| 75/64
+|-
+| 17
+| 590.9
+| 45/32
+|-
+| 18
+| 908.0
+| 27/16
+|-
+| 19
+| 25.1
+| 65/64, 81/80
+|}
+<nowiki>*</nowiki> in 2.3.5.13-subgroup [[CTE tuning]]
+== Scales ==
+* [[Cata7]]
+* [[Cata11]]
+* [[Cata15]]
+* [[Cata19]]
+== Music ==
+; [[Petr Pařízek]]
+* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3 ''Hanson Improv'']
+; [[Chris Vaisvil]]
+* [http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3 ''In Hanson11'']
+== External links ==
+* [http://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale''], by [[David Keenan]]
+[[Category:Temperaments]]
+[[Category:Hanson]] <!-- main article -->
+[[Category:Cata| ]] <!-- main article -->
+[[Category:Kleismic| ]] <!-- main article -->
+[[Category:Kleismic family]]