8019/8000: Difference between revisions
explained that/why 183edo may be less preferable to 118edo |
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== 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. 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 == | ||
Revision as of 02:37, 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.