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Interval information
Ratio 2025/2023
Factorization 34 × 52 × 7-1 × 17-2
Monzo [0 4 2 -1 0 0 -2
Size in cents 1.7107057¢
Name fidesma
Color name 17uuryy-3,
susuruyoyo negative 3rd
FJS name [math]\text{ddd}{-3}^{5,5}_{7,17,17}[/math]
Special properties reduced
Tenney height (log2 nd) 21.966
Weil height (log2 max(n, d)) 21.9674
Wilson height (sopfr (nd)) 63
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.41063 bits
Comma size unnoticeable
S-expression S15 / S17
open this interval in xen-calc

The fidesma, with a ratio of 2025/2023 (also subgroup) is the difference between two 17/15 wide whole tones and a 9/7 supermajor third. Measuring about 1.7 ¢, it is an unnoticeable comma. It is the superpyth counterpart of 1445/1444, tempered out in any scale where the 5th is sharp enough that two of them approximates 17/15 and four 9/7, most notably 22edo, which is very close to quarter comma superpyth.

It factors into two superparticular intervals: 1701/1700 × 2500/2499.


Tempering out this comma in the 17-limit results in the rank-6 fidesmic temperament, or in the the subgroup, the rank-3 fidic temperament.


This comma's name come from both Latin "fidēs" (meaning "chord"[1]) and Latin fīdēs (meaning "you will rely on"[2]), which is fitting because those who like more accurate forms of superpyth-like temperaments and scales frequently end up relying on the tempering of this comma for a number of essentially tempered chords.