2025/2023: Difference between revisions

The '''fidesma''' is an [[unnoticeable comma|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{{cent}}, 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. 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. No music is known to have been composed in this temperament to date, but it may receive some attention during 2025.

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'''.  

This comma's name come from both Latin "fidēs" (meaning "chord"<ref>[[Wiktionary: fides #Etymology 2]]</ref>) and Latin fīdēs (meaning "you will rely on"<ref>[[Wiktionary: fido #Latin]]</ref>), 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.