8019/8000: Difference between revisions

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'''8019/8000''' is a comma in the 2.3.5.11 subgroup, equal to ([[11/8]])/([[10/9]])<sup>3</sup>.
'''8019/8000''' is a [[comma]] in the 2.3.5.11 subgroup, equal to ([[11/8]])/([[10/9]])<sup>3</sup>.


== Temperaments ==
== Temperaments ==
In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family#Bischismic|Bischismic]], which also tempers [[3136/3125]].
In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic|bischismic]], which also tempers [[3136/3125]].


== See also ==
== See also ==
* [[Small comma]]


* [[Unnoticeable comma]]
* [[Category:11-limit]]
* [[Category:11-limit]]
* [[Category:Small comma]]
* [[Category:Ratio]]
* [[Category:Ratio]]