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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 a low-complexity but high-accuracy [[extension]] to the 2.3.5.13 [[subgroup]], sometimes known as '''cata'''.  
* [[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


{{Disambiguation}}
7-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]]
 
== Tuning spectrum ==
 
== Scales ==
* [[Cata7]]
* [[Cata11]]
* [[Cata15]]
* [[Cata19]]
 
== Music ==
; [[Petr Pařízek]]
* [https://web.archive.org/web/20201127013042/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]]

Revision as of 09:20, 16 September 2024

Hanson is a rank-2 temperament of the kleismic family, characterized by the vanishing of the kleisma. It is generated by a classical minor third (6/5), six of which make a 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.

7-limit extensions include keemun, catalan, catakleismic, countercata, and metakleismic.

For technical data, see Kleismic family #Hanson.

Interval chain

In the following table, odd harmonics 1–15 are labeled in bold.

# 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

* in 2.3.5.13-subgroup CTE tuning

Tuning spectrum

Scales

Music

Petr Pařízek
Chris Vaisvil

External links

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