2025/2023: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = fidesma

~~| Ratio = 2025/2023~~

| Color name = 17uuryy-3,<br>susuruyoyo negative 3rd

~~| Monzo = 0 4 2 -1 0 -2~~

| Comma = yes

~~| Cents = 1.710705~~

| Name =

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''2025/2023''', the '''fidesma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (specifically 3.5.7.17-[[subgroup]]) [[comma]] with a size of about 1.71 [[cent]]s. It is the difference between two [[17/15]] wide wholetones and a [[9/7]] supermajor third.

~~2025/2023 is the difference between two [[17/15]] wide whole tones and a 9/7 supermajor third.~~ 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 is the [[superpyth]] counterpart of [[1445/1444]], [[tempering out|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.

[[~~Category~~:17-~~limit~~]]

== Temperaments ==

[[~~Category~~:~~Interval ratio~~]]

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.

[[Category:~~Superparticular~~]]

[[Category:~~Unnoticeable comma~~]]

=== Fidic ===

[[Subgroup]]: 3.5.7.17

: mapping generators: ~3, ~5, ~45/17

[[Optimal tuning]]s:

* [[WE]]: ~3 = 1901.8290{{c}}, ~5/3 = 884.3495{{c}}, ~45/17 = 1684.4623{{c}}

* [[CWE]]: ~3 = 1901.9550{{c}}, ~5/3 = 884.3084{{c}}, ~45/17 = 1684.5363{{c}}

[[Badness]] (Sintel): 0.0269

=== Fidesmic ===

[[Subgroup]]: 2.3.5.7.11.13

[[Mapping]]:<br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 2 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~45/17, ~11, ~13

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8290{{c}}, ~5/4 = 386.1785{{c}}, ~45/34 = 484.4623{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5276{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8290{{c}}, ~5/4 = 386.1785{{c}}, ~45/34 = 484.4623{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5276{{c}}

{{Optimal ET sequence|legend=1| 17cg, 22, 27eg, 34d, 38df, 45efg, 49fg, 50, 60e, 72, 111, 121, 149, 159, 171, 183, 243e, 270, 354, 414, 441, 525, 597, 624, 684, 867, 966g, 1038, 1308g, 1402, 1833g, 2026g, 2551g }} *

<nowiki/>* [[optimal patent val]]: [[1905edo|1905]]

[[Badness]] (Sintel): 2.53

== Etymology ==

This comma was named by [[Aura]] in 2023. The name comes 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 chord]]s.

== References ==

[[Category:Fidesmic]]

[[Category:Commas named by translating something into another language]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = fidesma
-| Ratio = 2025/2023
+| Color name = 17uuryy-3,<br>susuruyoyo negative 3rd
-| Monzo = 0 4 2 -1 0 -2
+| Comma = yes
-| Cents = 1.710705
-| Name =
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''2025/2023''', the '''fidesma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (specifically 3.5.7.17-[[subgroup]]) [[comma]] with a size of about 1.71 [[cent]]s. It is the difference between two [[17/15]] wide wholetones and a [[9/7]] supermajor third.
-/2023 is the difference between two [[17/15]] wide whole tones and a 9/7 supermajor third. 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 is the [[superpyth]] counterpart of [[1445/1444]], [[tempering out|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.
-[[Category:17-limit]]
+== Temperaments ==
-[[Category:Interval ratio]]
+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.
-[[Category:Superparticular]]
-[[Category:Unnoticeable comma]]
+=== Fidic ===
+[[Subgroup]]: 3.5.7.17
+{{Mapping|legend=2| 1 0 0 2 | 0 1 0 1 | 0 0 2 -1 }}
+: mapping generators: ~3, ~5, ~45/17
+[[Optimal tuning]]s:
+* [[WE]]: ~3 = 1901.8290{{c}}, ~5/3 = 884.3495{{c}}, ~45/17 = 1684.4623{{c}}
+* [[CWE]]: ~3 = 1901.9550{{c}}, ~5/3 = 884.3084{{c}}, ~45/17 = 1684.5363{{c}}
+[[Optimal ET sequence]]: [[17edt|b17]], [[26edt|b26]], [[62edt|b62]], [[88edt|b88]], [[114edt|b114]], [[245edt|b245]], [[271edt|b271]], [[385edt|b385]], [[630edt|b630]], [[656edt|b656]], [[1015edt|b1015]], [[1400edt|b1400g]], [[2415edt|b2415g]], [[2686edt|b2686gg]], [[3071edt|b3071dgg]]
+[[Badness]] (Sintel): 0.0269
+=== Fidesmic ===
+[[Subgroup]]: 2.3.5.7.11.13
+[[Mapping]]:<br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 2 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~45/17, ~11, ~13
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8290{{c}}, ~5/4 = 386.1785{{c}}, ~45/34 = 484.4623{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5276{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8290{{c}}, ~5/4 = 386.1785{{c}}, ~45/34 = 484.4623{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5276{{c}}
+{{Optimal ET sequence|legend=1| 17cg, 22, 27eg, 34d, 38df, 45efg, 49fg, 50, 60e, 72, 111, 121, 149, 159, 171, 183, 243e, 270, 354, 414, 441, 525, 597, 624, 684, 867, 966g, 1038, 1308g, 1402, 1833g, 2026g, 2551g }} *
+<nowiki/>* [[optimal patent val]]: [[1905edo|1905]]
+[[Badness]] (Sintel): 2.53
+== Etymology ==
+This comma was named by [[Aura]] in 2023. The name comes 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 chord]]s.
+== References ==
+<references/>
+[[Category:Fidesmic]]
+[[Category:Commas named by translating something into another language]]