User:2^67-1/Derivation of some temperaments: Difference between revisions
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This page details the derivation of some temperaments I have created. | This page details the derivation of some temperaments I have created. | ||
= | = Grand Undetrita (rank-3, 7&b22&b176, 2.3.5.7.11.13.17.19.23.31.47.127) = | ||
Premise: [[11edt]] is a superb exotemperament in the 2.3.5.11 subgroup. What if we expanded that? | Premise: [[11edt]] is a superb exotemperament in the 2.3.5.11 subgroup. What if we expanded that? | ||
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== Restrictions == | == Restrictions == | ||
=== No-23s === | |||
If one removes 23, we get the three-patent-val-EDO-defined temperament 7&111&236: | If one removes 23, we get the three-patent-val-EDO-defined temperament 7&111&236: | ||
<pre> | <pre> | ||
[ 7 11 16 20 24 26 29 30 | [ 7 11 16 20 24 26 29 30 35 39 49] | ||
[ 0 0 0 -1 0 | [ 0 0 0 -1 0 -1 -1 -1 -1 -1 -1] | ||
[-1 0 2 0 0 3 -2 0 | [-1 0 2 0 0 3 -2 0 -2 1 0] | ||
</pre> | </pre> | ||
In this tuning, [[236edo]] makes the semitone 17 steps and the fine tuning increment 2 steps. | In this tuning, [[236edo]] makes the semitone 17 steps and the fine tuning increment 2 steps. Note that the semitone is ''still'' 1/2 the [[11edt]] step. | ||
=== 2.3.5.7.11.13.19 === | |||
Since 17, 23, 31, 47, and 127 are close to 16 (or 18), 24, 32, 48, and 128, it is more difficult to use them in harmony. Restricting it further to 2.3.5.7.11.13.19 gives: | |||
<pre> | |||
[ 7 11 16 20 24 26 30] | |||
[ 0 0 0 -1 0 -1 -1] | |||
[-1 0 2 0 0 3 0] | |||
</pre> | |||
This is also supported by [[229edo]]. | |||