282edo: Difference between revisions

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| Consistency = 29

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The '''282 equal divisions of the octave''' ('''282edo'''), or the '''282(-tone) equal temperament''' ('''282tet''', '''282et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 282 parts of 4.~~2553~~ [[cent]]s each.

The '''282 equal divisions of the octave''' ('''282edo'''), or the '''282(-tone) equal temperament''' ('''282tet''', '''282et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 282 parts of about 4.26 [[cent]]s each.

== Theory ==

282edo is the smallest equal temperament uniquely [[consistent]] through to the [[23-odd-limit]], and also the smallest consistent to the [[29-odd-limit]]. It shares the same 3rd, 7th, and 13th harmonics with [[94edo]] (282 = 3 × 94), as well as [[11/10]] and [[20/17]] (supporting the [[Stearnsmic clan #Garistearn|garistearn]] temperament). It has a distinct sharp tendency for odd harmonics up to 29. It tempers out ~~16875~~/~~16807~~, [[~~19683~~/~~19600~~]] ~~and 65625/65536~~ in the 7-limit, and [[540/539]] and 5632/5625 in the 11-limit, so that it provides the [[optimal patent val]] for the [[jupiter]] temperament; it also tempers out [[4000/3993]] and 234375/234256, providing the optimal patent val for [[septisuperfourth]] temperament. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079.

282edo is the smallest equal temperament uniquely [[consistent]] through to the [[23-odd-limit]], and also the smallest consistent to the [[29-odd-limit]]. It shares the same 3rd, 7th, and 13th harmonics with [[94edo]] (282 = 3 × 94), as well as [[11/10]] and [[20/17]] (supporting the [[Stearnsmic clan #Garistearn|garistearn]] temperament). It has a distinct sharp tendency for odd harmonics up to 29. It tempers out [[6144/6125]] (porwell), 118098/117649 (stearnsma), and [[250047/250000]] (landscape comma) in the 7-limit, and [[540/539]] and 5632/5625 in the 11-limit, so that it provides the [[optimal patent val]] for the [[jupiter]] temperament; it also tempers out [[4000/3993]] and 234375/234256, providing the optimal patent val for [[septisuperfourth]] temperament. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].

=== Prime harmonics ===

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[[Category:Equal divisions of the octave]]

[[Category:29-limit]]

[[Category:Septisuperfourth]]

[[Category:Jupiter]]

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 | Consistency = 29
 }}
-The '''282 equal divisions of the octave''' ('''282edo'''), or the '''282(-tone) equal temperament''' ('''282tet''', '''282et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 282 parts of 4.2553 [[cent]]s each.
+The '''282 equal divisions of the octave''' ('''282edo'''), or the '''282(-tone) equal temperament''' ('''282tet''', '''282et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 282 parts of about 4.26 [[cent]]s each.
 == Theory ==
-edo is the smallest equal temperament uniquely [[consistent]] through to the [[23-odd-limit]], and also the smallest consistent to the [[29-odd-limit]]. It shares the same 3rd, 7th, and 13th harmonics with [[94edo]] (282 = 3 × 94), as well as [[11/10]] and [[20/17]] (supporting the [[Stearnsmic clan #Garistearn|garistearn]] temperament). It has a distinct sharp tendency for odd harmonics up to 29. It tempers out 16875/16807, [[19683/19600]] and 65625/65536 in the 7-limit, and [[540/539]] and 5632/5625 in the 11-limit, so that it provides the [[optimal patent val]] for the [[jupiter]] temperament; it also tempers out [[4000/3993]] and 234375/234256, providing the optimal patent val for [[septisuperfourth]] temperament. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079.
+edo is the smallest equal temperament uniquely [[consistent]] through to the [[23-odd-limit]], and also the smallest consistent to the [[29-odd-limit]]. It shares the same 3rd, 7th, and 13th harmonics with [[94edo]] (282 = 3 × 94), as well as [[11/10]] and [[20/17]] (supporting the [[Stearnsmic clan #Garistearn|garistearn]] temperament). It has a distinct sharp tendency for odd harmonics up to 29. It tempers out [[6144/6125]] (porwell), 118098/117649 (stearnsma), and [[250047/250000]] (landscape comma) in the 7-limit, and [[540/539]] and 5632/5625 in the 11-limit, so that it provides the [[optimal patent val]] for the [[jupiter]] temperament; it also tempers out [[4000/3993]] and 234375/234256, providing the optimal patent val for [[septisuperfourth]] temperament. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].
 === Prime harmonics ===
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 | [[Sextile]]
 |}
 [[Category:Equal divisions of the octave]]
 [[Category:29-limit]]
+[[Category:Septisuperfourth]]
+[[Category:Jupiter]]