1000edo: Difference between revisions

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~~The '''~~1000 ~~edo''' divides the octave in 1000 equal parts of exactly 1.2 [[cent]]s, or 1 [[millioctave]] each. It is notable mostly because it is the equal division corresponding to millioctaves.~~

1000edo is notable mostly because it is the equal division corresponding to millioctaves.

== 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 luna comma, 274877906944/274658203125 and senior comma, {{Monzo| -17 62 -35 }}. 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 ===

=== Subsets and supersets ===

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}}.

~~{{primes~~ in ~~edo|1000|columns=~~11}}

[[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.

==Regular temperament properties==

{| class="wikitable center-4 center-5 center-6"

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 {{Infobox ET}}
-The '''1000 edo''' divides the octave in 1000 equal parts of exactly 1.2 [[cent]]s, or 1 [[millioctave]] each. It is notable mostly because it is the equal division corresponding to millioctaves.
+{{EDO intro|1000}}
+edo is notable mostly because it is the equal division corresponding to millioctaves.
+== 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 luna comma, 274877906944/274658203125 and senior comma, {{Monzo| -17 62 -35 }}. 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 ===
+{{harmonics in equal|1000}}
+=== Subsets and supersets ===
+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}}.
-{{primes in edo|1000|columns=11}}
+[[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.
 ==Regular temperament properties==
 {| class="wikitable center-4 center-5 center-6"