Kleismic: Difference between revisions
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'''Kleismic''' is a high-accuracy 2.3.5 temperament that equates a stack of six 6/5 minor thirds to one 3/1. Via a [[canonical extension|structurally induced]] extension to 2.3.5.13, it equates three 6/5's to one semitwelfth [[26/15]] and equates 25/24 to 26/25 and 27/26. | '''Kleismic''', 2.3.5.13[15 & 19], is a high-accuracy 2.3.5 temperament that equates a stack of six 6/5 minor thirds to one 3/1. Via a [[canonical extension|structurally induced]] extension to 2.3.5.13, it equates three 6/5's to one semitwelfth [[26/15]] and equates 25/24 to 26/25 and 27/26. | ||
Kleismic harmony is naturally based on splitting 5/3 into 4/3 and 5/4 thus making 3:4:5 or 12:15:18 triads. Indeed, Kleismic[15] (4L11s) can be constructed from the [[generator sequence]] GS(3:4:5)[19] by tempering out four kleismas. | Kleismic harmony is naturally based on splitting 5/3 into 4/3 and 5/4 thus making 3:4:5 or 12:15:18 triads. Indeed, Kleismic[15] (4L11s) can be constructed from the [[generator sequence]] GS(3:4:5)[19] by tempering out four kleismas. | ||
{{cat|Temperaments}}{{Navbox regtemp}} | {{cat|Temperaments}}{{Navbox regtemp}} | ||
Revision as of 07:50, 25 February 2026
| Kleismic |
325/324, 625/624 (2.3.5.13)
2.3.5.13 15-odd-limit: 2.35¢
2.3.5.13 15-odd-limit: 15 notes
Kleismic, 2.3.5.13[15 & 19], is a high-accuracy 2.3.5 temperament that equates a stack of six 6/5 minor thirds to one 3/1. Via a structurally induced extension to 2.3.5.13, it equates three 6/5's to one semitwelfth 26/15 and equates 25/24 to 26/25 and 27/26.
Kleismic harmony is naturally based on splitting 5/3 into 4/3 and 5/4 thus making 3:4:5 or 12:15:18 triads. Indeed, Kleismic[15] (4L11s) can be constructed from the generator sequence GS(3:4:5)[19] by tempering out four kleismas.
