2025/2023

Interval information

Ratio	2025/2023
Factorization	34 × 52 × 7-1 × 17-2
Monzo	[0 4 2 -1 0 0 -2⟩
Size in cents	1.710706¢
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{nd}[/math])	~1.22555 bits
Comma size	unnoticeable
S-expression	S15 / S17
open this interval in xen-calc

The fidesma is an unnoticeable 17-limit (specifically 3.5.7.17-subgroup) comma with a ratio of 2025/2023, the difference between two 17/15 wide wholetones 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 (1701/1700)(2500/2499), and in the 23-limit, (2024/2023)(2025/2024), hinting at an extension of fidesmic to the 2.3.5.7.11.17.23 subgroup. No music is known to have been composed in this temperament to date, but it may receive some attention while the year number of the Gregorian calendar progresses to 2025.

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") and Latin fīdēs (meaning "you will rely on"), 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.