Gaster: Difference between revisions
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'''Gaster''' is a [[regular temperament]] that tempers out a plethora of [[unnoticeable comma]]s including {{monzo|-70 72 -19}} (quadbila-negu). The generator for this temperament is a gassormic tritone, [[55/39]], and from this it derives its name. Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 55/39 = 38/27 = 31/22 = 24/17, 26/19 = 41/30 = 56/41, etc.) Since it tempers out the mirkwai comma, it qualifies as a [[Mirkwai clan|mirkwai temperament]]. | '''Gaster''' is a [[regular temperament]] that tempers out a plethora of [[unnoticeable comma]]s including {{monzo|-70 72 -19}} ([[#Gaster comma|gaster comma]], quadbila-negu). The generator for this temperament is a gassormic tritone, [[55/39]], and from this it derives its name. Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 55/39 = 38/27 = 31/22 = 24/17, 26/19 = 41/30 = 56/41, etc.) Since it tempers out the mirkwai comma, it qualifies as a [[Mirkwai clan|mirkwai temperament]]. | ||
== Temperament data == | == Temperament data == | ||
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== Gaster comma == | == Gaster comma == | ||
'''Gaster comma''' is a 5-limit [[unnoticeable comma]] measuring about 0.7995 cents. It is the difference between a stack of seventeen [[9/8]]s and a stack of nineteen [[10/9]]s, (9/8)<sup>17</sup>/(10/9)<sup>19</sup> = {{monzo|-70 72 -19}} (quadbila-negu). Equal temperaments which temper out this comma include {{Vals| 111, 113, 224, 335, 559, 783, 1342, 1901, 3243 }} and others. | '''Gaster comma''' is a 5-limit [[unnoticeable comma]] measuring about 0.7995 cents. It is the difference between a stack of seventeen [[9/8]]s and a stack of nineteen [[10/9]]s, (9/8)<sup>17</sup>/(10/9)<sup>19</sup> = {{monzo|-70 72 -19}} (quadbila-negu). Equal temperaments which temper out this comma include {{Vals| 111, 113, 224, 335, 559, 783, 1342, 1901, 3243 }} and others. | ||
== See also == | == See also == | ||
* [[Mirkwai clan]] | * [[Mirkwai clan]] | ||
* [[Very high accuracy temperaments]] | |||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||