Diaschismic–gothmic equivalence continuum: Difference between revisions

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The '''diaschismic-kleismic equivalence continuum''' is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] which equate a number of [[15625/15552|kleismas (15625/15552)]] with the [[393216/390625|~~Würschmidt_comma~~ (393216/390625)]].

The '''diaschismic-kleismic equivalence continuum''' is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] which equate a number of [[15625/15552|kleismas (15625/15552)]] with the [[393216/390625|Würschmidt comma (393216/390625)]].

All temperaments in the continuum satisfy (15625/15552)<sup>''n''</sup> ~ 393216/390625. Equivalently, we can offset ''n'' by 1, and equate a number of kleismas with the [[2048/2025|diaschisma (2048/2025)]], hence the name. Varying ''n'' results in different temperaments listed in the table below. It converges to [[Hanson_and_cata|hanson]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[34edo]] due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of ''n'' is 1.4117…, and temperaments near this tend to be the most accurate ones.

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	The '''diaschismic-kleismic equivalence continuum''' is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] which equate a number of [[15625/15552\|kleismas (15625/15552)]] with the [[393216/390625\|~~Würschmidt_comma~~ (393216/390625)]].		The '''diaschismic-kleismic equivalence continuum''' is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] which equate a number of [[15625/15552\|kleismas (15625/15552)]] with the [[393216/390625\|Würschmidt comma (393216/390625)]].

	All temperaments in the continuum satisfy (15625/15552)<sup>''n''</sup> ~ 393216/390625. Equivalently, we can offset ''n'' by 1, and equate a number of kleismas with the [[2048/2025\|diaschisma (2048/2025)]], hence the name. Varying ''n'' results in different temperaments listed in the table below. It converges to [[Hanson_and_cata\|hanson]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[34edo]] due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of ''n'' is 1.4117…, and temperaments near this tend to be the most accurate ones.		All temperaments in the continuum satisfy (15625/15552)<sup>''n''</sup> ~ 393216/390625. Equivalently, we can offset ''n'' by 1, and equate a number of kleismas with the [[2048/2025\|diaschisma (2048/2025)]], hence the name. Varying ''n'' results in different temperaments listed in the table below. It converges to [[Hanson_and_cata\|hanson]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[34edo]] due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of ''n'' is 1.4117…, and temperaments near this tend to be the most accurate ones.