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]])3. In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] ~~due to the schisma equating three [[9/8]]'s with a [[64/45]]. This combination may be desirable~~ as it gives lower-complexity interpretations ~~of the most complex tritones in~~ the [[5-limit]]~~: those corresponding to~~ (10/9)3 and [[729/512|(9/8)3]], the ~~similarity~~ being ~~due to both~~ stacking ~~three of one of the two simplest 5-limit whole~~ tones. For ~~tempering both~~, ~~[[118edo]] and~~ [[183edo]] ~~are~~ recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones.

'''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 [[729/512|(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. 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 ==

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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>. In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] due to the schisma equating three [[9/8]]'s with a [[64/45]]. This combination may be desirable as it gives lower-complexity interpretations of the most complex tritones in the [[5-limit]]: those corresponding to (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]], the similarity being due to both stacking three of one of the two simplest 5-limit whole tones. For tempering both, [[118edo]] and [[183edo]] are recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones.
+'''8019/8000''' is a comma in the 2.3.5.11 subgroup, equal to ([[11/8]])/([[10/9]])<sup>3</sup>.
+== 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]].
 == See also ==