2025/2023
2025/2023, the fidesma, is an unnoticeable 17-limit (specifically 3.5.7.17-subgroup) comma with a size of about 1.71 cents. It is the difference between two 17/15 wide wholetones and a 9/7 supermajor third.
| Interval information |
susuruyoyo negative 3rd
It is the superpyth counterpart of 1445/1444, tempered out in any scale where the fifth 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. However, the fidesma can be conceptualized in other ways, such as being the amount by which two instances of 18/17 exceed 28/25.
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.
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.