Single-pitch tuning: Difference between revisions
→Music: Chris Vaisvil's ''0-EDO for Orchestra'' (2021): Really in 1edo, so moved there |
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== In equal tunings == | == In equal tunings == | ||
{{Infobox ET|0edo}} | {{Infobox ET|0edo}}{{todo|fix template|description=The step size is wrong; it shouldn't be zero cents, but rather infinite or undefined.}} | ||
Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of any finite interval. | Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of any finite interval. | ||
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== In regular temperament theory == | == In regular temperament theory == | ||
Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ]. | Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ]. Since it maps all intervals to the same pitch, it [[tempering out|tempers out]] all commas and is [[consistent]] in all [[limit]]s. | ||
Single-pitch tuning can also be considered a rank-0 temperament in the empty subgroup, which contains no primes. It tempers no commas and the pitch represents only the [[1/1|unison]], so it is also empty-subgroup JI. (Tempering everything and tempering nothing are the same in this case, because there is nothing to temper.) This is closer to representing how single-pitch tuning is actually used, when it is used at all. | |||
Both are examples of [[trivial temperament]]s. | |||
== Music == | == Music == | ||
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; [[No Clue Music]] | ; [[No Clue Music]] | ||
* [https://www.youtube.com/watch?v=g-WXe2mvAPk ''0 EDO Experiment''] (2024) | * [https://www.youtube.com/watch?v=g-WXe2mvAPk ''0 EDO Experiment''] (2024) | ||
[[Category:Limiting cases]] | [[Category:Limiting cases]] | ||
[[Category:Trivial temperaments]] | [[Category:Trivial temperaments]] | ||