Diaschismic–gothmic equivalence continuum: Difference between revisions

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The '''diaschismic-gothic equivalence continuum''', also referrable as the ''diaschismic-tetracot equivalence continuum'', ''kleismic-tetracot equivalence continuum'', ''diaschismic-würschmidt equivalence continuum'', ''diaschismic-kleismic equivalence continuum'', or ''kleismic-würschmidt equivalence continuum'', is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] that describes the set of all [[5-limit]] temperaments supported by [[34edo]].

The '''diaschismic-gothic equivalence continuum''', also referrable to as the ''diaschismic-tetracot equivalence continuum'', ''kleismic-tetracot equivalence continuum'', ''diaschismic-würschmidt equivalence continuum'', ''diaschismic-kleismic equivalence continuum'', or ''kleismic-würschmidt equivalence continuum'', is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] that describes the set of all [[5-limit]] temperaments supported by [[34edo]].

All temperaments in the continuum satisfy (2048/2025)<sup>''n''</sup> ~ {{monzo| 27 -17 }}, equating a number of [[2048/2025|diaschismas (2048/2025)]] with the [[gothic comma]]. Varying ''n'' results in different temperaments listed in the table below. It converges to [[diaschismic]] 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 [[tempering out|tempers out]] both commas and thus tempers out all combinations of them. The just value of ''n'' is approximately 3.41464…, and temperaments having ''n'' near this value tend to be the most accurate ones.

Revision as of 23:51, 23 July 2024 view source Lériendil (talk \| contribs) 8,046 edits m Lériendil moved page Diaschismic-gothmic equivalence continuum to Diaschismic-gothic equivalence continuum ← Older edit		Revision as of 23:53, 23 July 2024 view source Lériendil (talk \| contribs) 8,046 edits No edit summary Newer edit →
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	The '''diaschismic-gothic equivalence continuum''', also referrable as the ''diaschismic-tetracot equivalence continuum'', ''kleismic-tetracot equivalence continuum'', ''diaschismic-würschmidt equivalence continuum'', ''diaschismic-kleismic equivalence continuum'', or ''kleismic-würschmidt equivalence continuum'', is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] that describes the set of all [[5-limit]] temperaments supported by [[34edo]].		The '''diaschismic-gothic equivalence continuum''', also referrable to as the ''diaschismic-tetracot equivalence continuum'', ''kleismic-tetracot equivalence continuum'', ''diaschismic-würschmidt equivalence continuum'', ''diaschismic-kleismic equivalence continuum'', or ''kleismic-würschmidt equivalence continuum'', is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] that describes the set of all [[5-limit]] temperaments supported by [[34edo]].

	All temperaments in the continuum satisfy (2048/2025)<sup>''n''</sup> ~ {{monzo\| 27 -17 }}, equating a number of [[2048/2025\|diaschismas (2048/2025)]] with the [[gothic comma]]. Varying ''n'' results in different temperaments listed in the table below. It converges to [[diaschismic]] 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 [[tempering out\|tempers out]] both commas and thus tempers out all combinations of them. The just value of ''n'' is approximately 3.41464…, and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in the continuum satisfy (2048/2025)<sup>''n''</sup> ~ {{monzo\| 27 -17 }}, equating a number of [[2048/2025\|diaschismas (2048/2025)]] with the [[gothic comma]]. Varying ''n'' results in different temperaments listed in the table below. It converges to [[diaschismic]] 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 [[tempering out\|tempers out]] both commas and thus tempers out all combinations of them. The just value of ''n'' is approximately 3.41464…, and temperaments having ''n'' near this value tend to be the most accurate ones.