365edo/Eliora's approach: Difference between revisions
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{{Main|365edo}} | {{Main|365edo}} | ||
== Theory == | == Theory == | ||
As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. | As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. Therefore, each step is equal to 3.2854936 cents, and there are ''common octaves'' consisting of 365 steps and ''leap octaves'' consisting of 366 steps. The additional step does not amount to a JI mapping on its own, but rather resets the stretched octave to match the pure octave. Given that a standard gamut of music suitable for human hearing uses 8 octaves, this means 2 of them would be leap. | ||
=== Using a val with a selected octave stretch === | |||
In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close to the target value, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era. | |||
In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does. | In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does. | ||
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Mappings different from the patent val highlighted in '''bold'''. | Mappings different from the patent val highlighted in '''bold'''. | ||
=== Using a uniform map === | |||
One might take interval approximations directly in 365.24219edo. | |||
== Regular temperament properties == | == Regular temperament properties == | ||