Generator sequence: Difference between revisions
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Given a lattice generated by ''E'' and the generators in the recipe, there exists a map π that identifies all non-imperfect generators. We may choose π so that the MOS's period and generator are linearly independent, and thus ''m'' = ''n''. The images π(''u'') and π(''v'') also satisfy Ψ(π(''u'')) = Ψ(π(''v'')) > 0 and are a stack of ''n'' resp. ''m'' MOS generators (all of which are perfect). Hence Ψ(π(''u'')) = Ψ(π(''v'')) = ''mg + pE''. This expression corresponds to a well-defined number of steps, given the generator ''g'' and the period ''E'' of the MOS, hence ''u'' and ''v'' must subtend the same number of steps. | Given a lattice generated by ''E'' and the generators in the recipe, there exists a map π that identifies all non-imperfect generators. We may choose π so that the MOS's period and generator are linearly independent, and thus ''m'' = ''n''. The images π(''u'') and π(''v'') also satisfy Ψ(π(''u'')) = Ψ(π(''v'')) > 0 and are a stack of ''n'' resp. ''m'' MOS generators (all of which are perfect). Hence Ψ(π(''u'')) = Ψ(π(''v'')) = ''mg + pE''. This expression corresponds to a well-defined number of steps, given the generator ''g'' and the period ''E'' of the MOS, hence ''u'' and ''v'' must subtend the same number of steps. | ||
== JI scales from | == JI scales obtained from guided generator sequences == | ||
Only CS sizes at least 5 are listed. Todo: check for larger CS sizes. | Only CS sizes at least 5 are listed. Todo: check for larger CS sizes. | ||
* The Zarlino series, GS(5/4, 6/5) = GS(4:5:6): 5, 7, 10, 17, 24, 41, 65 | * The Zarlino series, GS(5/4, 6/5) = GS(4:5:6): 5, 7, 10, 17, 24, 41, 65 | ||