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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This is also supported by [[229edo]]. | This is also supported by [[229edo]]. | ||
= Polyraider (rank-2, 7&1171, 2.3.5.11.f2.f3) = | |||
''Note: f2, f3 refer to the first 2 modes of a bar, or approximately 2.75653 and 5.40281. '' | |||
Premise: What is the next tuning that does what 11EDT does but better? Can it be possible to join it with 11EDT? | |||
== First part, solved == | |||
The next tuning that approximates the first few harmonics of a string and a bar better than 11EDT up to relative error is [[1171edo]]. It is notable for having a very accurate 2.3.5.11 subgroup. | |||
== Mapping == | |||
The mapping which I prefer to use (not Hermite normal form) is: | |||
<pre> | |||
[ 7 11 16 24 10 17] | |||
[-12 -3 15 -5 23 -23] | |||
</pre> | |||
This is because the mapping [https://sintel.pythonanywhere.com/result?subgroup=30.2.3.11.275653%2F100000.540281%2F100000&reduce=on&weights=weil&target=&edos=34+5746&submit_edo=submit&commas= Sintel's temperament finder] gives is very complex, with generator ranges reaching 297. | |||
Note that [[34ed30]] or [[3ed27/20]] are possible "spines" for this temperament. | |||