Schismic–countercommatic equivalence continuum: Difference between revisions
Explain the significance of the countercomma |
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The ''' | The '''schismic–countercommatic equivalence continuum''' is a continuum of 5-limit temperaments which equate a number of [[32805/32768|schismas (32805/32768)]] with the [[41-comma|Pythagorean countercomma ({{monzo| 65 -41 }})]]. This continuum is theoretically interesting in that these are all [[5-limit]] [[microtemperament]]s [[support]]ed by [[41edo]]. | ||
All temperaments in the continuum satisfy (32805/32768)<sup>''n''</sup> ~ {{monzo| 65 -41 }}. 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 41edo due to it being the unique equal temperament that [[tempering out|tempers out]] both commas and thus tempers out all combinations of them. The just value of ''n'' is approximately 10.1575233481…, and temperaments having ''n'' near this value tend to be the most accurate ones. | All temperaments in the continuum satisfy (32805/32768)<sup>''n''</sup> ~ {{monzo| 65 -41 }}. 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 41edo due to it being the unique equal temperament that [[tempering out|tempers out]] both commas and thus tempers out all combinations of them. The just value of ''n'' is approximately 10.1575233481…, and temperaments having ''n'' near this value tend to be the most accurate ones. | ||
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* Etc. | * Etc. | ||
For a similar but perhaps more intuitive and practical concept, see [[ | For a similar but perhaps more intuitive and practical concept, see [[Schismic–Pythagorean equivalence continuum]]. | ||
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