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Interval information
Ratio 8019/8000
Factorization 2-6 × 36 × 5-3 × 11
Monzo [-6 6 -3 0 1
Size in cents 4.106806¢
Name trimitone comma
Color name L1og31, lalotrigu 1sn,
Lalotrigu comma
FJS name [math]\text{d1}^{11}_{5,5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 25.935
Weil height (log2 max(n, d)) 25.9384
Wilson height (sopfr (nd)) 56
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.51315 bits
Comma size small
S-expression S9 / S10
open this interval in xen-calc

8019/8000, the trimitone comma (for "triple minor (whole) tone"), is the comma in the 11-limit (also 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 13-limit, it factors neatly into (729/728)(1001/1000).


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 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 (or equivalently 12&53) temperament in the 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- or 13-limit, it is closely related to bischismic, which also tempers 3136/3125.

See also