2023edo: Difference between revisions

Line 5:

2023edo is enfactored in the 5-limit, with the same mapping as [[289edo]].

In the patent val, it is ~~good in~~ the ~~no-11s 17-limit, a property which it shares with~~ [[~~323edo~~]]~~. As such, a 2.3.5.7.13.17~~ temperament ~~can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}~~. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out.

In the 17-limit on the patent val, it is a tuning for the [[leaves]] temperament. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out.

If we impose a stricter harmonic approach, and require all errors to be below 25%, the subgroup consisting of first 7 such harmonics for 2023edo is 2.13.17.23.47.61.71.

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The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>.

== Regular temperament properties ==

=== Rank-2 temperaments ===

Note: 5-limit temperaments represented by 289edo are not included.

{| class="wikitable center-all left-4"

!Periods

per 8ve

!Generator

(Reduced)

!Cents

(Reduced)

!Associated

Ratio

!Temperament

|-

|17

|144\2023

(25\2023)

|85.417

(14.829)

|1024/975

(?)

|[[Leaves]]

|}

== Music ==

* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭, (Op. 2, No. 2)] by [[Eliora]]

* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭ Leaves, (Op. 2, No. 2)] by [[Eliora]]

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

[[Category:Quartismic]]

@@ Line 5: / Line 5: @@
 edo is enfactored in the 5-limit, with the same mapping as [[289edo]].
-In the patent val, it is good in the no-11s 17-limit, a property which it shares with [[323edo]]. As such, a 2.3.5.7.13.17 temperament can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out.
+In the 17-limit on the patent val, it is a tuning for the [[leaves]] temperament. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out.
 If we impose a stricter harmonic approach, and require all errors to be below 25%, the subgroup consisting of first 7 such harmonics for 2023edo is 2.13.17.23.47.61.71.
@@ Line 13: / Line 13: @@
 The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>.
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
+Note: 5-limit temperaments represented by 289edo are not included.
+{| class="wikitable center-all left-4"
+!Periods
+per 8ve
+!Generator
+(Reduced)
+!Cents
+(Reduced)
+!Associated
+Ratio
+!Temperament
+|-
+|17
+|144\2023
+(25\2023)
+|85.417
+(14.829)
+|1024/975
+(?)
+|[[Leaves]]
+|}
 == Music ==
-* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭, (Op. 2, No. 2)] by [[Eliora]]
+* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭ Leaves, (Op. 2, No. 2)] by [[Eliora]]
 [[Category:Equal divisions of the octave|####]]<!-- 4-digit number -->
 [[Category:Quartismic]]