17100edo: Difference between revisions

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~~== Theory ==~~

This ~~EDO~~'s step size is the relative cent of [[171edo]]. It notably provides the optimal patent val for 13-limit [[harmonisma|harmonismic]] temperament, tempering out [[10648/10647]].

This edo's step size is the [[relative cent]] of [[171edo]], an excellent [[7-limit]] [[microtemperament]]. It also notably provides the [[optimal patent val]] for [[13-limit]] [[harmonisma|harmonismic]] temperament, which [[tempering out|tempers out]] [[10648/10647]].

=== ~~Subsets and Supersets~~ ===

Since 17100 = 22 * 32 * 52 * 19, it contains subset edos {{edos| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, and 8550.}}

=== Prime harmonics ===

=== Subsets and supersets ===

Since 17100 factors into primes as {{nowrap| 22 × 32 × 52 × 19 }}, 17100edo contains subset edos {{EDOs| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, and 8550 }}.

[[Category:Harmonismic]]

[[Category:171edo]]

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 {{Infobox ET}}
 {{ED intro}}
-== Theory ==
-This EDO's step size is the relative cent of [[171edo]]. It notably provides the optimal patent val for 13-limit [[harmonisma|harmonismic]] temperament, tempering out [[10648/10647]].
+This edo's step size is the [[relative cent]] of [[171edo]], an excellent [[7-limit]] [[microtemperament]]. It also notably provides the [[optimal patent val]] for [[13-limit]] [[harmonisma|harmonismic]] temperament, which [[tempering out|tempers out]] [[10648/10647]].
-=== Subsets and Supersets ===
-Since 17100 = 2<sup>2</sup> * 3<sup>2</sup> * 5<sup>2</sup> * 19, it contains subset edos {{edos| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, and 8550.}}
+=== Prime harmonics ===
 {{Harmonics in equal|17100}}
+=== Subsets and supersets ===
+Since 17100 factors into primes as {{nowrap| 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 19 }}, 17100edo contains subset edos {{EDOs| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, and 8550 }}.
 [[Category:Harmonismic]]
 [[Category:171edo]]