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| | 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]] | |||
* [[Category:11-limit]] | * [[Category:11-limit]] | ||
* [[Category:Small comma]] | |||
* [[Category:Ratio]] | * [[Category:Ratio]] | ||
Revision as of 04:43, 6 April 2021
| Interval information |
8019/8000 is a comma in the 2.3.5.11 subgroup, equal to (11/8)/(10/9)3.
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)3 and (9/8)3 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)3 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- or 13-limit, it is closely related to bischismic, which also tempers 3136/3125.