Rainy–didacus equivalence continuum: Difference between revisions

Inthar (talk | contribs)
Correct ratio for Rainy comma
Godtone (talk | contribs)
m correct equivalence used; smaller ratio is the one that goes to the power of n
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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 ([[3136/3125]])<sup>''n''</sup> ~ [[2100875/2097152]] 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 ([[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]].


{| class="wikitable center-1 center-2"
{| class="wikitable center-1 center-2"