Kleismic: Difference between revisions
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{{Redirect|Hanson and cata|the rank-2 temperament family|Kleismic family}} | |||
{{Redirect|Hanson and cata|the rank-3 temperament family|Kleismic rank-three family}} | |||
'''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'''. | '''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'''. | ||