250edo: Difference between revisions

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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~~. Being a small multiple of~~ [[10edo]]~~, it equates 13/8 with 0.~~7 ~~octaves~~. 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''' … }}.

== 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''' … }}.

~~In addition, in the~~ patent val in the 11-limit, ~~it is a tuning for~~ the [[Minortonic family#Seminar|seminar]] temperament.

The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s the [[Minortonic family #Seminar|seminar]] temperament.

~~=== Divisors ===~~

The 250deff… val tempers out [[441/440]], 4125/4096, [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.

~~250edo has subset edos {{EDOs|1~~, 2, 5, 10, 25, ~~50, 125}}.~~

~~Since 2.3.5.7 harmonics~~ in the ~~patent val 250edo come from 125edo~~, and ~~11.13 harmonics~~ in the ~~patent val come from 50edo, this system is worthy of being considered as a superset of these two temperaments~~.

=== Odd harmonics ===

=== 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]]

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

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

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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

|-

| 2.3.5.7.11

| 441/440, 4125/4096, 14641/14580, 15625/15552

| {{mapping| 250 396 580 701 864 }} (250de)

| +0.8703

| 0.4930

| 10.3

|-

| 2.3.5.7.11

| 225/224, 243/242, 4375/4356, 589824/588245

| {{mapping| 250 396 580 701 864 }} (250)

| +0.2503

| 0.5149

| 10.7

|}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|250}}
+{{ED intro}}
-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. Being a small multiple of [[10edo]], it equates 13/8 with 0.7 octaves. 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''' … }}.
+== 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''' … }}.
-In addition, in the patent val in the 11-limit, it is a tuning for the [[Minortonic family#Seminar|seminar]] temperament.
+The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s the [[Minortonic family #Seminar|seminar]] temperament.
-=== Divisors ===
+The 250deff… val tempers out [[441/440]], 4125/4096, [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.
-edo has subset edos {{EDOs|1, 2, 5, 10, 25, 50, 125}}.
-Since 2.3.5.7 harmonics in the patent val 250edo come from 125edo, and 11.13 harmonics in the patent val come from 50edo, this system is worthy of being considered as a superset of these two temperaments.
 === Odd harmonics ===
 {{Harmonics in equal|250}}
+=== 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]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3.5.7.11
+| 441/440, 4125/4096, 14641/14580, 15625/15552
+| {{mapping| 250 396 580 701 864 }} (250de)
+| +0.8703
+| 0.4930
+| 10.3
+|-
+| 2.3.5.7.11
+| 225/224, 243/242, 4375/4356, 589824/588245
+| {{mapping| 250 396 580 701 864 }} (250)
+| +0.2503
+| 0.5149
+| 10.7
+|}