Rainy–didacus equivalence continuum: Difference between revisions

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The '''rainy–didacus continuum''' is the [[equivalence continuum|continuum]] of [[2.5.7 subgroup]] temperaments which equate a number of [[rainy comma]]s with the [[didacus comma]] ([[3136/3125]]), and thus is the continuum of all 2.5.7 subgroup temperaments supported by [[31edo]], which tempers both and thus tempers all linear combinations of them. If one wants to use all of these simultaneously but wants more accurate tuning than [[31edo]], [[31st-octave temperaments]] extending [[birds]] may be interesting.

The '''rainy–didacus continuum''' is the [[equivalence continuum|continuum]] of [[2.5.7 subgroup]] temperaments which equate a number of [[rainy comma]]s with the [[didacus comma]] ([[3136/3125]]), and thus is the continuum of all 2.5.7 subgroup temperaments supported by [[31edo]], which tempers both and thus tempers all linear combinations of them. If one wants to use all of these simultaneously but wants more accurate tuning than [[31edo]] for the other primes, then [[31st-octave temperaments]] extending [[birds]] may be interesting.

All temperaments in the continuum satisfy {{nowrap|([[2100875/2097152]])<sup>''n''</sup> ~ ([[3136/3125]])}} for some rational value of ''n''. The just value of ''n'' is approximately 1.981... so that {{nowrap|''n'' {{=}} 2}} is especially close to the [[JIP]].

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{{Optimal ET sequence|legend=1|31, 224, 255, 286, 317, 348, 379, 410, 789}}

[[Badness]] (Sintel): ?

[[Badness]] (Sintel): 0.0148

[[Category:31edo]]

[[Category:Equivalence continua]]

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-The '''rainy–didacus continuum''' is the [[equivalence continuum|continuum]] of [[2.5.7 subgroup]] temperaments which equate a number of [[rainy comma]]s with the [[didacus comma]] ([[3136/3125]]), and thus is the continuum of all 2.5.7 subgroup temperaments supported by [[31edo]], which tempers both and thus tempers all linear combinations of them. If one wants to use all of these simultaneously but wants more accurate tuning than [[31edo]], [[31st-octave temperaments]] extending [[birds]] may be interesting.
+The '''rainy–didacus continuum''' is the [[equivalence continuum|continuum]] of [[2.5.7 subgroup]] temperaments which equate a number of [[rainy comma]]s with the [[didacus comma]] ([[3136/3125]]), and thus is the continuum of all 2.5.7 subgroup temperaments supported by [[31edo]], which tempers both and thus tempers all linear combinations of them. If one wants to use all of these simultaneously but wants more accurate tuning than [[31edo]] for the other primes, then [[31st-octave temperaments]] extending [[birds]] may be interesting.
 All temperaments in the continuum satisfy {{nowrap|([[2100875/2097152]])<sup>''n''</sup> ~ ([[3136/3125]])}} for some rational value of ''n''. The just value of ''n'' is approximately 1.981... so that {{nowrap|''n'' {{=}} 2}} is especially close to the [[JIP]].
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 | {{monzo| -69 0 14 13 }}
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+| …
 | …
 | …
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 {{Optimal ET sequence|legend=1|31, 224, 255, 286, 317, 348, 379, 410, 789}}
-[[Badness]] (Sintel): ?
+[[Badness]] (Sintel): 0.0148
 [[Category:31edo]]
 [[Category:Equivalence continua]]