Argyria
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).
| Interval information |
(Young's) tinge
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.