236edo: Difference between revisions

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== Theory ==

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The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.

The 236dghin val (using the second-best mappings of primes 7, 17, 19, 23, and 43) makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[45-odd-limit]]. This works best with a stretched octave.

=== Prime harmonics ===

{{Harmonics in equal|236|start=12|columns=11|collapsed=1|title=Approximation of prime harmonics in 236edo (continued)}}

=== Subsets and supersets ===

Since 236 factors into 22 × 53, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

Since 236 factors into 22 × 59, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

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| 6144/6125, 19683/19600, 390625/388962

| {{mapping| 236 374 548 663 }}

| -0.1830

| −0.1830

| 0.03883

| 7.64

|}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|236}}
+{{ED intro}}
 == Theory ==
@@ Line 6: / Line 6: @@
 The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.
+The 236dghin val (using the second-best mappings of primes 7, 17, 19, 23, and 43) makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[45-odd-limit]]. This works best with a stretched octave.
 === Prime harmonics ===
-{{Harmonics in equal|236}}
+{{Harmonics in equal|236|columns=11}}
+{{Harmonics in equal|236|start=12|columns=11|collapsed=1|title=Approximation of prime harmonics in 236edo (continued)}}
 === Subsets and supersets ===
-Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.
+Since 236 factors into 2<sup>2</sup> × 59, 236edo has subset edos {{EDOs| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 27: / Line 31: @@
 | 6144/6125, 19683/19600, 390625/388962
 | {{mapping| 236 374 548 663 }}
-| -0.1830
+| −0.1830
 | 0.03883
 | 7.64
 |}