Archytas–diatonic 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~~-limit~~ 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 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)]].

All temperaments in the continuum satisfy (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 [[Just intonation subgroup|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.

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	The '''Archytas-diatonic equivalence continuum''' or the '''septimal-diatonic equivalence continuum''' is a continuum of 2.3.7~~-limit~~ 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 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)]].

	All temperaments in the continuum satisfy (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 [[Just intonation subgroup\|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 (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 [[Just intonation subgroup\|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.