250edo: Difference between revisions

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==Theory==

250edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val| 250 396 580 '''701''' '''864''' '''924''' … }}.

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=== ~~Divisors~~ ===

=== Subsets and supersets ===

250edo has subset edos {{EDOs| 2, 5, 10, 25, 50, 125 }}.

Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.

==Regular temperament properties==

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

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

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

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

! rowspan="2" |Optimal<br>8ve Stretch (¢)

! colspan="2" |Tuning Error

|-

![[TE error|Absolute]] (¢)

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

|-

|2.3

|{{monzo|-198 125}}

|{{val|250 396}}

| 0.3644

| 0.3645

| 7.59

|-

|2.3.5

|15625/15552, {{monzo|-34 20 1}}

|{{val|250 396 580}}

| 0.5752

| 0.4213

| 8.78

|}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|250}}
+==Theory==
 edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val| 250 396 580 '''701''' '''864''' '''924''' … }}.
@@ Line 11: / Line 11: @@
 {{Harmonics in equal|250}}
-=== Divisors ===
+=== Subsets and supersets ===
 edo has subset edos {{EDOs| 2, 5, 10, 25, 50, 125 }}.
 Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.
+==Regular temperament properties==
+{| class="wikitable center-4 center-5 center-6"
+! rowspan="2" |[[Subgroup]]
+! rowspan="2" |[[Comma list|Comma List]]
+! rowspan="2" |[[Mapping]]
+! rowspan="2" |Optimal<br>8ve Stretch (¢)
+! colspan="2" |Tuning Error
+|-
+![[TE error|Absolute]] (¢)
+![[TE simple badness|Relative]] (%)
+|-
+|2.3
+|{{monzo|-198 125}}
+|{{val|250 396}}
+| 0.3644
+| 0.3645
+| 7.59
+|-
+|2.3.5
+|15625/15552, {{monzo|-34 20 1}}
+|{{val|250 396 580}}
+| 0.5752
+| 0.4213
+| 8.78
+|}