Diaschismic–gothmic equivalence continuum: Difference between revisions

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The '''diaschismic-tetracot equivalence continuum''' (which is the '''diaschismic-gothmic equivalence continuum''' with an offset of 2) 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-tetracot equivalence continuum''' (which is the '''diaschismic-gothmic equivalence continuum''' with offset 2) is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] describing 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|gothic comma (134217728/129140163)]]. At ''n'' = 2 (which we align with ''r'' = 0) we get '''tetracot''', which is an important offset for a number of reasons discussed later. 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 00:17, 24 July 2024 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,407 edits m Godtone moved page Diaschismic-gothic equivalence continuum to Diaschismic-tetracot equivalence continuum over redirect: avoid "gothic-"/"gothmic-" confusion by removing it as the main name, preferring diaschismic-tetracot as both play key roles; diaschisma for the reasons FloraC stated and tetracot for being the point at which inverting conveniently yields the kleisma^n-based continuum, as well as for other reasons such as diaschismic and tetracot tempering being the most strongly ch... ← Older edit		Revision as of 00:18, 24 July 2024 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,407 edits m simplify starting sentence Newer edit →
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	The '''diaschismic-tetracot equivalence continuum''' (which is the '''diaschismic-gothmic equivalence continuum''' with an offset of 2) 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-tetracot equivalence continuum''' (which is the '''diaschismic-gothmic equivalence continuum''' with offset 2) is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] describing 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\|gothic comma (134217728/129140163)]]. At ''n'' = 2 (which we align with ''r'' = 0) we get '''tetracot''', which is an important offset for a number of reasons discussed later. 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\|gothic comma (134217728/129140163)]]. At ''n'' = 2 (which we align with ''r'' = 0) we get '''tetracot''', which is an important offset for a number of reasons discussed later. 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.