2000edo: Difference between revisions

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{{EDO intro|2000}} It 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, the first edo to do so being [[2460edo]].

2000 = 24 × 53~~; some of~~ its divisors are ~~[[10edo~~|10]], ~~[[16edo|~~16]], ~~[[25edo|~~25]], ~~[[50edo|~~50]], ~~[[80edo|~~80]], ~~[[100edo|~~100]], ~~[[125edo|~~125~~]] and~~ [[~~200edo|200~~]]~~. Also there~~ is the ~~1000 division of~~ [[millioctave]]~~s, where it might be~~ argued that cutting ~~these~~ in half makes for a better system.

== Theory ==

It 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]].

2000 = 24 × 53 , 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.

=== Prime harmonics ===

[[Category:Equal divisions of the octave|####]]

[[Category:Equal divisions of the octave|####]]

== Regular temperament properties ==

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

=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

! Periods per octave

! Generator (reduced)

! Cents (reduced)

! Associated ratio

! Temperaments

|-

| 20

| 287\2000 (87\2000)

| 172.2 (52.2)

| 169/153 (?)

| [[Calcium]]

|}

[[Category:29-limit]]

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 {{Infobox ET}}
-{{EDO intro|2000}} It 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, the first edo to do so being [[2460edo]].
+{{EDO intro|2000}}
-= 2<sup>4</sup> × 5<sup>3</sup>; some of its divisors are [[10edo|10]], [[16edo|16]], [[25edo|25]], [[50edo|50]], [[80edo|80]], [[100edo|100]], [[125edo|125]] and [[200edo|200]]. Also there is the 1000 division of [[millioctave]]s, where it might be argued that cutting these in half makes for a better system.
+== Theory ==
+It 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]].
+= 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.
 === Prime harmonics ===
 {{Harmonics in equal|2000|columns=13}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+[[Category:Equal divisions of the octave|####]]
+== Regular temperament properties ==
+edo has the smallest relative error than any previous temperament in the 19-limit. It is only bettered by [[2460edo]].
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+! Periods<br>per octave
+! Generator<br>(reduced)
+! Cents<br>(reduced)
+! Associated<br>ratio
+! Temperaments
+|-
+| 20
+| 287\2000<br>(87\2000)
+| 172.2<br>(52.2)
+| 169/153<br>(?)
+| [[Calcium]]
+|}
+<!-- 4-digit number -->
 [[Category:29-limit]]