Archytas–diatonic equivalence continuum: Difference between revisions
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Created page with "The '''Archytas-diatonic equivalence continuum''' is a continuum of 2.3.7-limit temperaments which equate a number of Archytas commas (64/63) with the 256/243|limm..." |
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The '''Archytas-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''' 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)]]. | ||
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 [[ | 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). | ||
[[Category:5edo]] | [[Category:5edo]] | ||
Revision as of 15:59, 16 March 2021
The Archytas-diatonic equivalence continuum is a continuum of 2.3.7-limit temperaments which equate a number of Archytas commas (64/63) with the limma (256/243).
All temperaments in the continuum satisfy (64/63)n ~ 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).