Schismic–Mercator equivalence continuum: Difference between revisions
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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). | 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 | For a similar but perhaps more intuitive and practical concept, see [[Syntonic-chromatic equivalence continuum]]. | ||
{| class="wikitable center-1 center-2" | |||
|+ Temperaments in the continuum | |||
|- | |||
! rowspan="2" | ''n'' | |||
! rowspan="2" | Temperament | |||
! colspan="2" | Comma | |||
|- | |||
! Ratio | |||
! Monzo | |||
|- | |||
| 0 | |||
| [[Mercator's comma|Mercator]] | |||
| | |||
| {{monzo|-84 53}} | |||
|- | |||
| 1 | |||
| Counterschismic | |||
| | |||
| {{monzo|-69 45 -1}} | |||
|- | |||
| 2 | |||
| [[Very high accuracy temperaments#Monzismic|Monzismic]] | |||
| | |||
| [[Monzisma|{{monzo|54 -37 2}}]] | |||
|- | |||
| 3 | |||
| [[Tricot]] | |||
| | |||
| {{monzo| 39 -29 3}} | |||
|- | |||
| 4 | |||
| [[Vulture]] | |||
| | |||
| {{monzo| 24 -21 4 }} | |||
|- | |||
| 5 | |||
| [[Amity]] | |||
| [[1600000/1594323]] | |||
| {{monzo| 9 -13 5 }} | |||
|- | |||
| 6 | |||
| [[Kleismic]] | |||
| [[15625/15552]] | |||
| {{monzo|-6 -5 6}} | |||
|- | |||
| 7 | |||
| [[Orson]] | |||
| [[Semicomma|2109375/2097152]] | |||
| {{monzo|-21 3 7 }} | |||
|- | |||
| … | |||
| … | |||
| … | |||
| … | |||
|- | |||
| ∞ | |||
| [[Schismic]] | |||
| [[32805/32768]] | |||
| {{monzo| -15 8 1}} | |||
|} | |||
== Counterschismic == | == Counterschismic == | ||