2025/2023
Ratio | 2025/2023 |
Factorization | 3^{4} × 5^{2} × 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 (log_{2} nd) | 21.966 |
Weil height (log_{2} max(n, d)) | 21.9674 |
Wilson height (sopfr (nd)) | 63 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.22555 bits |
Comma size | unnoticeable |
S-expression | S15 / S17 |
open this interval in xen-calc |
The fidesma, with a ratio of 2025/2023 (also 3.5.7.17 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.
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 fidesmic temperament, or in the the 3.5.7.17 subgroup, the rank-3 fidic temperament.
Etymology
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.