8019/8000: Difference between revisions

'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 11-limit (also 2.3.5.11 [[subgroup]]) by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)³.  Furthermore, it is also the interval separating the [[syntonic comma]] and the [[ptolemisma]].

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]]