1000edo: Difference between revisions

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== Theory ==

1000edo is related to 200edo, but the [[patent val]]s differ on the mapping for 5 and 7. In the [[5-limit]], it tempers out {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -17 62 -35 }} (senior comma). In the [[7-limit]], it tempers out [[4375/4374]], 201768035/201326592, and 165288374272/164794921875, leading to the [[lunatic]] temperament and [[seniority]] temperament. It also tempers out [[3025/3024]], [[9801/9800]], and 391314/390625 in the [[11-limit]]; [[1001/1000]], [[4225/4224]], 4459/4455, and [[10648/10647]] in the [[13-limit]], leading to the [[deca]] temperament and [[donar]] temperament.

1000edo is related to 200edo, but the [[patent val]]s differ on the mapping for [[5/1|5]] and [[7/1|7]]. In the [[5-limit]], it tempers out {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -17 62 -35 }} (senior comma). In the [[7-limit]], it tempers out [[4375/4374]], 201768035/201326592, and 165288374272/164794921875, leading to the [[lunatic]] temperament and [[seniority]] temperament. It also tempers out [[3025/3024]], [[9801/9800]], and 391314/390625 in the [[11-limit]]; [[1001/1000]], [[4225/4224]], 4459/4455, and [[10648/10647]] in the [[13-limit]], leading to the [[deca]] temperament and [[donar]] temperament.

=== Prime harmonics ===

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1000edo carries the interval size measure ''millioctave'' and has subset edos {{EDOs| 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 }}.

[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for ~~the 2.~~7.11.13.17.23 ~~subgroup~~.

[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for harmonics 7, [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[23/1|23]].

== Regular temperament properties ==

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 == Theory ==
-edo is related to 200edo, but the [[patent val]]s differ on the mapping for 5 and 7. In the [[5-limit]], it tempers out {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -17 62 -35 }} (senior comma). In the [[7-limit]], it tempers out [[4375/4374]], 201768035/201326592, and 165288374272/164794921875, leading to the [[lunatic]] temperament and [[seniority]] temperament. It also tempers out [[3025/3024]], [[9801/9800]], and 391314/390625 in the [[11-limit]]; [[1001/1000]], [[4225/4224]], 4459/4455, and [[10648/10647]] in the [[13-limit]], leading to the [[deca]] temperament and [[donar]] temperament.
+edo is related to 200edo, but the [[patent val]]s differ on the mapping for [[5/1|5]] and [[7/1|7]]. In the [[5-limit]], it tempers out {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| -17 62 -35 }} (senior comma). In the [[7-limit]], it tempers out [[4375/4374]], 201768035/201326592, and 165288374272/164794921875, leading to the [[lunatic]] temperament and [[seniority]] temperament. It also tempers out [[3025/3024]], [[9801/9800]], and 391314/390625 in the [[11-limit]]; [[1001/1000]], [[4225/4224]], 4459/4455, and [[10648/10647]] in the [[13-limit]], leading to the [[deca]] temperament and [[donar]] temperament.
 === Prime harmonics ===
@@ Line 13: / Line 13: @@
 edo carries the interval size measure ''millioctave'' and has subset edos {{EDOs| 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 }}.
-[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for the 2.7.11.13.17.23 subgroup.
+[[2000edo]], which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for harmonics 7, [[11/1|11]], [[13/1|13]], [[17/1|17]], and [[23/1|23]].
 == Regular temperament properties ==