Rainy–didacus equivalence continuum: Difference between revisions

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m ArrowHead294 moved page Rainy-didacus equivalence continuum to Rainy–didacus equivalence continuum: The dash in titles like these should be an en dash, not a hyphen-minus, since "Rainy" does not modify "didacus"
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The '''rainy-didacus continuum''' is the 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 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.


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


{| class="wikitable center-1 center-2"
{| class="wikitable center-1 center-2"
|+Temperaments in the continuum
|+ style="font-size: 105%;" | Temperaments in the continuum
|-
|-
! rowspan="2" | ''n''
! rowspan="2" | ''n''
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| {{monzo| -21 0 3 5 }}
| {{monzo| -21 0 3 5 }}
|}
|}
<nowiki>*</nowiki> note that [[ostara]] is contorted in the 2.5.7 subgroup, hence why this is not merely "2.5.7 ostara"; by contrast, neither "2.5.7 [[myna]]" nor "2.5.7 [[mohajira]]" are contorted.
<nowiki />* Note that [[ostara]] is contorted in the 2.5.7 subgroup, hence why this is not merely "2.5.7 ostara"; by contrast, neither "2.5.7 [[myna]]" nor "2.5.7 [[mohajira]]" are contorted.


== Temperaments ==
== Temperaments ==