30edo: Difference between revisions
→Notations: added ups and downs notation |
→Theory: + ''See regular temperament for more about what all this means and how to use it.'' |
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{{ED intro}} | {{ED intro}} | ||
== Theory == | == Theory == | ||
=== Harmonics === | |||
{{Harmonics in equal|30}} | {{Harmonics in equal|30}} | ||
=== RTT === | |||
''See [[regular temperament]] for more about what all this means and how to use it.'' | |||
Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament. | Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament. | ||
[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]] | [[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]] | ||
However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30. | However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30. | ||
Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8. | Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for [[pelogic]] (5-limit mavila), which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8. | ||
=== Subsets and supersets === | === Subsets and supersets === | ||