User:VectorGraphics/Porcupine family: Difference between revisions

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{{interwiki|de=Porcupine|en=Porcupine family|es=|ja=}}{{Technical data page}}The '''porcupine family''' of [[Regular temperament|temperaments]] [[Tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis. This comma splits 4/3 into three equal parts, and 6/5 makes up two of those parts. Thus, the generator is mapped to 10/9. Mathematically, {{nowrap|(10/9)3 {{=}} (4/3)⋅(250/243)}}, and {{nowrap|(10/9)5 {{=}} (8/5)⋅(250/243)2}}. [[22edo|3\22]] is a very recommendable generator, and [[Mos scale|mos scales]] of 7, 8 and 15 notes make for some nice scale possibilities.

The '''porcupine family''' of [[Regular temperament|temperaments]] [[Tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis. This comma splits 4/3 into three equal parts, and 6/5 makes up two of those parts. Thus, the generator is mapped to 10/9. Mathematically, {{nowrap|(10/9)3 {{=}} (4/3)⋅(250/243)}}, and {{nowrap|(10/9)5 {{=}} (8/5)⋅(250/243)2}}. [[22edo|3\22]] is a very recommendable generator, and [[Mos scale|mos scales]] of 7, 8 and 15 notes make for some nice scale possibilities.

It most naturally manifests as a [[2.3.5.11 subgroup]] temperament, where it tempers out [[100/99]] and [[55/54]] equating the generator to 11/10 as well as 10/9.

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-{{interwiki|de=Porcupine|en=Porcupine family|es=|ja=}}{{Technical data page}}The '''porcupine family''' of [[Regular temperament|temperaments]] [[Tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis. This comma splits 4/3 into three equal parts, and 6/5 makes up two of those parts. Thus, the generator is mapped to 10/9. Mathematically, {{nowrap|(10/9)<sup>3</sup> {{=}} (4/3)⋅(250/243)}}, and {{nowrap|(10/9)<sup>5</sup> {{=}} (8/5)⋅(250/243)<sup>2</sup>}}. [[22edo|3\22]] is a very recommendable generator, and [[Mos scale|mos scales]] of 7, 8 and 15 notes make for some nice scale possibilities.
+{{interwiki|de=Porcupine|en=Porcupine family|es=|ja=}}{{Technical data page}}
+The '''porcupine family''' of [[Regular temperament|temperaments]] [[Tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis. This comma splits 4/3 into three equal parts, and 6/5 makes up two of those parts. Thus, the generator is mapped to 10/9. Mathematically, {{nowrap|(10/9)<sup>3</sup> {{=}} (4/3)⋅(250/243)}}, and {{nowrap|(10/9)<sup>5</sup> {{=}} (8/5)⋅(250/243)<sup>2</sup>}}. [[22edo|3\22]] is a very recommendable generator, and [[Mos scale|mos scales]] of 7, 8 and 15 notes make for some nice scale possibilities.
 It most naturally manifests as a [[2.3.5.11 subgroup]] temperament, where it tempers out [[100/99]] and [[55/54]] equating the generator to 11/10 as well as 10/9.