Syntonic–Archytas equivalence continuum: Difference between revisions
Created page with "The '''breedsmic-syntonic equivalence continuum''' is a continuum of 7-limit rank-3 temperament families which equate a number of syntonic commas (81/80) with an 6..." |
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All temperaments in the continuum satisfy (81/80)<sup>''n''</sup> ~ 64/63. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Meantone family|meantone + za]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.267726433120519..., and temperaments having ''n'' near this value will be more accurate. | All temperaments in the continuum satisfy (81/80)<sup>''n''</sup> ~ 64/63. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Meantone family|meantone + za]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.267726433120519..., and temperaments having ''n'' near this value will be more accurate. | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||