Syntonic–Archytas equivalence continuum: Difference between revisions
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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. | ||
{| class="wikitable center-1 center-2" | |||
|+ Temperament families in the continuum | |||
|- | |||
! rowspan="2" | ''n'' | |||
! rowspan="2" | Temperament family | |||
! colspan="2" | Comma | |||
|- | |||
! Ratio | |||
! Monzo | |||
|- | |||
| 0 | |||
| [[Archytas clan|Archy]] | |||
| [[64/63]] | |||
| {{monzo|6 -2 0 -1}} | |||
|- | |||
| 1 | |||
| [[Hemifamity family|Hemifamity]] | |||
| [[5120/5103]] | |||
| {{monzo|1 5 1 -4}} | |||
|- | |||
| ∞ | |||
| [[Meantone family|Meantone]] | |||
| [[81/80]] | |||
| {{monzo| -4 4 -1 0}} | |||
|} | |||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||