250edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|250}} | {{EDO intro|250}} | ||
==Theory== | |||
== 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''' … }}. | 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''' … }}. | ||
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 | 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. | ||
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. | 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. | ||
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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. | 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== | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! 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 error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3.5.7.11 | ||
| | | 441/440, 4125/4096, 14641/14580, 15625/15552 | ||
|{{ | | {{mapping| 250 396 580 701 864 }} (250de) | ||
| 0. | | +0.8703 | ||
| 0. | | 0.4930 | ||
| | | 10.3 | ||
|- | |- | ||
|2.3.5 | | 2.3.5.7.11 | ||
| | | 225/224, 243/242, 4375/4356, 589824/588245 | ||
|{{ | | {{mapping| 250 396 580 701 864 }} (250) | ||
| 0. | | +0.2503 | ||
| 0. | | 0.5149 | ||
| | | 10.7 | ||
|} | |} | ||