Kleismic family: Difference between revisions
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The [[5-limit]] parent comma for the '''kleismic family''' is [[15625/15552]], the kleisma. The [[generator]] is a [[6/5|classical minor third (6/5)]], and to get to the interval class of [[5/4|major thirds]] requires five of these, and so to get to [[3/2|fifths]] requires six. In fact, (6/5)<sup>5</sup> = 5/2 × 15625/15552. This 5-limit temperament (virtually a [[microtemperament]]) is sometimes called '''hanson''', and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]]. | The [[5-limit]] parent comma for the '''kleismic family''' is [[15625/15552]], the kleisma. The [[generator]] is a [[6/5|classical minor third (6/5)]], and to get to the interval class of [[5/4|major thirds]] requires five of these, and so to get to [[3/2|fifths]] requires six. In fact, (6/5)<sup>5</sup> = 5/2 × 15625/15552. This 5-limit temperament (virtually a [[microtemperament]]) is sometimes called '''hanson''', and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]]. | ||