Argyria: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 41503/41472 | | Ratio = 41503/41472 | ||
| Name = argyria, (Young's) tinge | |||
| Color name = 1ooz<sup>3</sup>2, Lolotrizo comma | |||
| Name = (Young's) tinge | | Comma = yes | ||
| Color name = | |||
| | |||
}} | }} | ||
In [[just intonation]], the comma between three [[8/7]]'s (693.522 cents) and two [[11/9]]'s (694.816 cents), measuring 1.294 cents< | 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 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/> | |||
[[Category: | [[Category:Commas named after place names]] | ||
Latest revision as of 04:50, 10 March 2026
| Interval information |
(Young's) tinge
In just intonation, 41503/41472, the argyria, is the unnoticeable 11-limit (specifically 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[1] and casually once referred to as "the tinge"[2]. 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-expressions, 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 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
- ↑ 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
- ↑ Gayle Young, private e-mail to Todd Harrop, 24 June 2018.