Schismic–Mercator equivalence continuum: Difference between revisions

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The '''syntonic-chromatic equivalence continuum''' is a continuum of temperaments which equate a number of [[32805/32768|schismas (32805/32768)]] with [[Mercator's comma|Mercator's comma ({{monzo|-84 53}})]].

All temperaments in the continuum satisfy (32805/32768)<sup>''n''</sup> ~ {{monzo|-84 53}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[~~meantone~~]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[53edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them).

All temperaments in the continuum satisfy (32805/32768)<sup>''n''</sup> ~ {{monzo|-84 53}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[schismic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[53edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them).

For a similar but simpler concept, see [[Syntonic-chromatic equivalence continuum]].

== Counterschismic ==

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 The '''syntonic-chromatic equivalence continuum''' is a continuum of temperaments which equate a number of [[32805/32768|schismas (32805/32768)]] with [[Mercator's comma|Mercator's comma ({{monzo|-84 53}})]].
-All temperaments in the continuum satisfy (32805/32768)<sup>''n''</sup> ~ {{monzo|-84 53}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[meantone]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[53edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them).
+All temperaments in the continuum satisfy (32805/32768)<sup>''n''</sup> ~ {{monzo|-84 53}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[schismic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[53edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them).
+For a similar but simpler concept, see [[Syntonic-chromatic equivalence continuum]].
 == Counterschismic ==