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| '''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 a low-complexity but high-accuracy [[extension]] to the 2.3.5.13 [[subgroup]], sometimes known as '''cata'''. | | '''Kleismic''' may refer to: |
| | * [[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 |
| | * [[Hanson and cata]], for the unextended rank-2 2.3.5 and 2.3.5.13 temperaments |
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| 7-limit extensions include [[keemun]], [[catalan]], [[catakleismic]], [[countercata]], and [[metakleismic]].
| | {{Disambiguation}} |
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| For technical data, see [[Kleismic family #Hanson]].
| | [[Category:Kleismic]] |
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| == Interval chain ==
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| In the following table, odd harmonics 1–15 are labeled in '''bold'''.
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| {| class="wikitable center-1 right-2"
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| ! #
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| ! Cents*
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| ! Approximate Ratios
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| |-
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| | 0
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| | 0.0
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| | '''1/1'''
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| |-
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| | 1
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| | 317.1
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| | 6/5
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| |-
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| | 2
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| | 634.2
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| | 13/9
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| |-
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| | 3
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| | 950.3
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| | 26/15
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| |-
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| | 4
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| | 68.4
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| | 25/24, 26/25, 27/26
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| |-
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| | 5
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| | 385.6
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| | '''5/4'''
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| |-
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| | 6
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| | 702.7
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| | '''3/2'''
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| |-
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| | 7
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| | 1019.8
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| | 9/5
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| |-
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| | 8
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| | 136.9
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| | 13/12, 14/13, 27/25
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| |-
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| | 9
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| | 454.0
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| | 13/10
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| |-
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| | 10
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| | 771.1
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| | 25/16
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| |-
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| | 11
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| | 1088.2
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| | '''15/8'''
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| |-
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| | 12
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| | 205.3
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| | '''9/8'''
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| |-
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| | 13
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| | 522.4
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| | 27/20
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| |-
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| | 14
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| | 839.6
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| | '''13/8''', 21/13
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| |-
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| | 15
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| | 1156.7
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| | 39/20
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| |-
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| | 16
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| | 273.8
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| | 75/64
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| |-
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| | 17
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| | 590.9
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| | 45/32
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| |-
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| | 18
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| | 908.0
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| | 27/16
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| |-
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| | 19
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| | 25.1
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| | 65/64, 81/80
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| |}
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| <nowiki>*</nowiki> in 2.3.5.13-subgroup [[CTE tuning]]
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| == Scales ==
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| * [[Cata7]]
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| * [[Cata11]]
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| * [[Cata15]]
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| * [[Cata19]]
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| == Music ==
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| ; [[Petr Pařízek]]
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| * [https://web.archive.org/web/20201127013042/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3 ''Hanson Improv'']
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| ; [[Chris Vaisvil]]
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| * [http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3 ''In Hanson11'']
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| == External links ==
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| * [http://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale''], by [[David Keenan]]
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| [[Category:Temperaments]]
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| [[Category:Hanson]] <!-- main article -->
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| [[Category:Cata| ]] <!-- main article -->
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| [[Category:Kleismic| ]] <!-- main article -->
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| [[Category:Kleismic family]] | |
