2.3.17.19 subgroup: Difference between revisions
DesertFreeze (talk | contribs) Created page with "The 2.3.17.19 subgroup is arguably quite significant to 12edo. Its fifth, minor second, and minor third almost perfectly correspond to the octave-reduced harmonics of 3, 17, and 19, respectively. 12edo's patent val for this subgroup is |12 19 25 27⟩. {{Stub}}" |
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The 2.3.17.19 subgroup is arguably quite significant to [[12edo]]. Its fifth, minor second, and minor third almost perfectly correspond to the octave-reduced harmonics of 3, 17, and 19, respectively. 12edo's patent val for this subgroup is |12 19 | The '''2.3.17.19 subgroup''' (a.k.a. ''sana'' in [[color notation]]) consists of [[just intonation]] [[Interval|intervals]] such that the only [[prime factor]]<nowiki/>s in all [[Ratio|ratios]] are 2, 3, 17 and 19. This subgroup is a [[Rank and codimension|rank-4]] system, and can be modeled in a 3-dimensional [[lattice]], with the primes 2, 3, 17 and [[19/1|19]] represented by each dimension. The prime [[2/1|2]] does not appear in typical lattices because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a seventh dimension is needed. | ||
The 2.3.17.19 subgroup is arguably quite significant to [[12edo]], as it is the subgroup it does best with difference. Its fifth, minor second, and minor third almost perfectly correspond to the octave-reduced harmonics of 3, 17, and 19, respectively. 12edo's patent val for this subgroup is {{val|12 19 49 51}}. | |||
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