2000edo: Difference between revisions

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== Theory ==

2000edo is distinctly [[consistent]] through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are 1578 and [[1889edo]].

2000edo is distinctly [[consistent]] through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are 1578 and [[1889edo]], and in the 19-limit, nothing smaller defeats it.

2000 = 2<sup>4</sup> × 5<sup>3</sup> , and its divisors are {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000}}. From these, [[1000edo]] is notable because it carries the interval size measure [[millioctave]]. It is argued that cutting millioctaves in half makes for a better interval measuring system, in light of 2000edo's high consistency limit, which introduces just interval approximations not present in 1000edo. In addition, 2000edo inherits its fifth from [[200edo]], where it is semiconvergent.

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== Regular temperament properties ==

2000edo has the smallest relative error than any previous ~~temperament~~ in the 19-limit. It is only bettered by [[2460edo]].

2000edo has the smallest relative error than any previous equal temperaments in the 19-limit. It is only bettered by [[2460edo]].

=== Rank-2 temperaments ===

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 == Theory ==
-edo is distinctly [[consistent]] through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are 1578 and [[1889edo]].
+edo is distinctly [[consistent]] through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are 1578 and [[1889edo]], and in the 19-limit, nothing smaller defeats it.
 = 2<sup>4</sup> × 5<sup>3</sup> , and its divisors are {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000}}. From these, [[1000edo]] is notable because it carries the interval size measure [[millioctave]]. It is argued that cutting millioctaves in half makes for a better interval measuring system, in light of 2000edo's high consistency limit, which introduces just interval approximations not present in 1000edo. In addition, 2000edo inherits its fifth from [[200edo]], where it is semiconvergent.
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 == Regular temperament properties ==
-edo has the smallest relative error than any previous temperament in the 19-limit. It is only bettered by [[2460edo]].
+edo has the smallest relative error than any previous equal temperaments in the 19-limit. It is only bettered by [[2460edo]].
 === Rank-2 temperaments ===