Argyria: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 41503/41472

~~| Monzo = -9 -4 0 3 2~~

| Name = argyria, (Young's) tinge

~~| Cents = 1.2936~~

| Color name = 1ooz<sup>3</sup>2, Lolotrizo comma

| Name = (Young's) tinge

| Comma = yes

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

In [[just intonation]], '''41503/41472''' is the comma between three [[8/7]]'s (693.522 cents) and two [[11/9]]'s (694.816 cents), measuring 1.294 cents<ref>Gayle Young, "The Pitch Organization of ''Harmonium for James Tenney''", Perspectives of New Music, vol. 26, no. 2, summer 1988, pp. 204–12. Stable URL: http://www.jstor.org/stable/833190</ref> and casually once referred to as "the tinge"<ref>Gayle Young, private e-mail to Todd Harrop, 24 June 2018.</ref>.

In [[just intonation]], '''41503/41472''', the '''argyria''', is the [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]]) [[comma]] between three [[8/7]]'s (693.522 cents) and two [[11/9]]'s (694.816 cents), measuring 1.294 cents<ref>Gayle Young, "The Pitch Organization of ''Harmonium for James Tenney''", Perspectives of New Music, vol. 26, no. 2, summer 1988, pp. 204–12. Stable URL: http://www.jstor.org/stable/833190</ref> and casually once referred to as "the '''tinge'''"<ref>Gayle Young, private e-mail to Todd Harrop, 24 June 2018.</ref>. It is the difference of [[1029/1024]] and [[243/242]] and therefore is the [[Don Page comma]] between the intervals [[11/9]] and [[8/7]]; in terms of [[S-expression]]s, this translates to (S7/S8)/(S9/S11), and by virtue of the equivalence ([[36/35]] = S6) = ([[64/63]] = S8)⋅([[81/80]] = S9), also to ([[121/120]] = S11)/([[1728/1715]] = S6/S7).

It ~~factors into two superparticular commas:~~ [[~~2401~~/~~2400~~]] × [[~~3025~~/~~3024~~]].

It is also the difference of [[385/384]] and [[540/539]]. Those two ratios make up [[225/224]]. Therefore, tempering it out guarantees that 225/224 is split into two, each for 385/384~540/539.

It factors into two superparticular commas: ([[2401/2400]])⋅([[3025/3024]]).

== Temperaments ==

[[Tempering out]] this comma in the full 11-limit results in the rank-4 argyric temperament (→ [[Catalog of rank-4 temperaments #Argyric (41503/41472)]]), and in the 2.3.7.11 subgroup, the rank-3 argyrian temperament.

== Etymology ==

This comma was named the argyria by [[Lériendil]] in 2024, on the pattern of the [[olympia]] and alongside the [[elysia]], after Argyre Planitia on Mars.

== References ==

~~== See Also ==~~

[[Category:Commas named after place names]]

* [[Gallery of just intervals]]

* [[Unnoticeable comma]]

~~[[Category:11-limit]]~~

[[Category:~~Unnoticable comma~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 41503/41472
-| Monzo = -9 -4 0 3 2
+| Name = argyria, (Young's) tinge
-| Cents = 1.2936
+| Color name = 1ooz<sup>3</sup>2, Lolotrizo comma
-| Name = (Young's) tinge
+| Comma = yes
-| Color name =
-| FJS name =
-| Sound =
 }}
-In [[just intonation]], '''41503/41472''' is the comma between three [[8/7]]'s (693.522 cents) and two [[11/9]]'s (694.816 cents), measuring 1.294 cents<ref>Gayle Young, "The Pitch Organization of ''Harmonium for James Tenney''", Perspectives of New Music, vol. 26, no. 2, summer 1988, pp. 204–12. Stable URL: http://www.jstor.org/stable/833190</ref> and casually once referred to as "the tinge"<ref>Gayle Young, private e-mail to Todd Harrop, 24 June 2018.</ref>.
+In [[just intonation]], '''41503/41472''', the '''argyria''', is the [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]]) [[comma]] between three [[8/7]]'s (693.522 cents) and two [[11/9]]'s (694.816 cents), measuring 1.294 cents<ref>Gayle Young, "The Pitch Organization of ''Harmonium for James Tenney''", Perspectives of New Music, vol. 26, no. 2, summer 1988, pp. 204–12. Stable URL: http://www.jstor.org/stable/833190</ref> and casually once referred to as "the '''tinge'''"<ref>Gayle Young, private e-mail to Todd Harrop, 24 June 2018.</ref>. It is the difference of [[1029/1024]] and [[243/242]] and therefore is the [[Don Page comma]] between the intervals [[11/9]] and [[8/7]]; in terms of [[S-expression]]s, this translates to (S7/S8)/(S9/S11), and by virtue of the equivalence ([[36/35]] = S6) = ([[64/63]] = S8)⋅([[81/80]] = S9), also to ([[121/120]] = S11)/([[1728/1715]] = S6/S7).
-It factors into two superparticular commas: [[2401/2400]] × [[3025/3024]].
+It is also the difference of [[385/384]] and [[540/539]]. Those two ratios make up [[225/224]]. Therefore, tempering it out guarantees that 225/224 is split into two, each for 385/384~540/539.
+It factors into two superparticular commas: ([[2401/2400]])⋅([[3025/3024]]).
+== Temperaments ==
+[[Tempering out]] this comma in the full 11-limit results in the rank-4 argyric temperament (→ [[Catalog of rank-4 temperaments #Argyric (41503/41472)]]), and in the 2.3.7.11 subgroup, the rank-3 argyrian temperament.
+== Etymology ==
+This comma was named the argyria by [[Lériendil]] in 2024, on the pattern of the [[olympia]] and alongside the [[elysia]], after Argyre Planitia on Mars.
+== References ==
 <references/>
-== See Also ==
+[[Category:Commas named after place names]]
-* [[Gallery of just intervals]]
-* [[Unnoticeable comma]]
-[[Category:11-limit]]
-[[Category:Unnoticable comma]]