2000edo: Difference between revisions

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== 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]].

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]].

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.

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=== Prime harmonics ===

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

== Regular temperament properties ==

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

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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| [[Calcium]]

|-

|80

| 80

|619\2000 (19\2000)

| 619\2000 (19\2000)

|371.4 (11.4)

| 371.4 (11.4)

|2275/1836 (?)

| 2275/1836 (?)

|[[Mercury]]

| [[Mercury]]

|}

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

[[Category:29-limit]]

@@ Line 3: / Line 3: @@
 == 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]].
+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]].
 = 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.
@@ Line 9: / Line 9: @@
 === Prime harmonics ===
 {{Harmonics in equal|2000|columns=13}}
-[[Category:Equal divisions of the octave|####]]
 == Regular temperament properties ==
@@ Line 18: / Line 16: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 30: / Line 28: @@
 | [[Calcium]]
 |-
-|80
+| 80
-|619\2000<br>(19\2000)
+| 619\2000<br>(19\2000)
-|371.4<br>(11.4)
+| 371.4<br>(11.4)
-|2275/1836<br>(?)
+| 2275/1836<br>(?)
-|[[Mercury]]
+| [[Mercury]]
 |}
-<!-- 4-digit number -->
+[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
 [[Category:29-limit]]