2023edo: Difference between revisions

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== Theory ==

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.

It 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.

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.

In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].

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

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

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

[[Category:Quartismic]]

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 == Theory ==
 {{Harmonics in equal|2023}}
-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.
+It 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.
+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.
 In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].
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 The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+[[Category:Equal divisions of the octave|####]]<!-- 4-digit number -->
 [[Category:Quartismic]]