8019/8000: Difference between revisions

In the full 11-limit, tempering it out leads to the rank-4 '''trimitone temperament''' (→ [[Rank-4 temperament #Trimitone]]). Due to the factorization above, it extends neatly to the 13-limit.  

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 (or equivalently 12&53) 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). This temperament is therefore great for 8:9:10:11:12 chords. 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 ==

* [[Small comma]]