2025/2023: Difference between revisions

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The '''fidesma''' is a [[3.5.7.17 subgroup]] [[~~unnoticeable~~ 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.

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.

It factors into [[1701/1700]] × [[2500/2499]] (and, ~~of course,~~ [[2024/2023]] × [[2025/2024]]), ~~extending fidic temperament~~ 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 [[Wikipedia:Gregorian calendar|Gregorian calendar]] progresses to 2025.

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 [[Wikipedia:Gregorian calendar|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 ==

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-The '''fidesma''' is a [[3.5.7.17 subgroup]] [[unnoticeable 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.
+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.
-It factors into [[1701/1700]] × [[2500/2499]] (and, of course, [[2024/2023]] × [[2025/2024]]), extending fidic temperament 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 [[Wikipedia:Gregorian calendar|Gregorian calendar]] progresses to 2025.
+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 [[Wikipedia:Gregorian calendar|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 ==