Syntonic–Archytas equivalence continuum

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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 Archytas comma (64/63). This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by dominant temperament.

All temperaments in the continuum satisfy (81/80)n ~ 64/63. Varying n results in different temperament families listed in the table below. It converges to 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.