Archytas–limmic equivalence continuum: Difference between revisions

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The '''~~Archytas-diatonic~~ equivalence continuum''' or ~~the~~ '''~~septimal-diatonic~~ equivalence continuum''' is a continuum of [[2.3.7 subgroup]] temperaments which equate a number of [[64/63|Archytas commas (64/63)]] with the [[256/243|limma (256/243)]].

The '''Archytas–diatonic equivalence continuum''', or '''septimal–diatonic equivalence continuum''', is a continuum of [[2.3.7 subgroup]] temperaments which equate a number of [[64/63|Archytas commas (64/63)]] with the [[256/243|limma (256/243)]].

All temperaments in the continuum satisfy {{nowrap|(64/63)<sup>''n''</sup> ~ 256/243}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[archy]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.7 subgroup temperaments supported by [[5edo]] (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 3.3093…, and temperaments near this tend to be the most accurate ones.

Revision as of 14:44, 18 December 2024 view source ArrowHead294 (talk \| contribs) 15,232 edits m ArrowHead294 moved page Archytas-diatonic equivalence continuum to Archytas–diatonic equivalence continuum: The dash in titles like these should be an en dash, not a hyphen-minus, since "Archytas" does not modify "diatonic" ← Older edit		Revision as of 14:45, 18 December 2024 view source ArrowHead294 (talk \| contribs) 15,232 edits mNo edit summary Newer edit →
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	The '''~~Archytas-diatonic~~ equivalence continuum''' or ~~the~~ '''~~septimal-diatonic~~ equivalence continuum''' is a continuum of [[2.3.7 subgroup]] temperaments which equate a number of [[64/63\|Archytas commas (64/63)]] with the [[256/243\|limma (256/243)]].		The '''Archytas–diatonic equivalence continuum''', or '''septimal–diatonic equivalence continuum''', is a continuum of [[2.3.7 subgroup]] temperaments which equate a number of [[64/63\|Archytas commas (64/63)]] with the [[256/243\|limma (256/243)]].

	All temperaments in the continuum satisfy {{nowrap\|(64/63)<sup>''n''</sup> ~ 256/243}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[archy]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.7 subgroup temperaments supported by [[5edo]] (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 3.3093…, and temperaments near this tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|(64/63)<sup>''n''</sup> ~ 256/243}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[archy]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.7 subgroup temperaments supported by [[5edo]] (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 3.3093…, and temperaments near this tend to be the most accurate ones.