Argyria: Difference between revisions

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[[Category:11-limit]]
[[Category:11-limit]]
[[Category:Unnoticeable comma]]
[[Category:Unnoticeable commas]]

Revision as of 22:01, 20 March 2022

Interval information
Ratio 41503/41472
Factorization 2-9 × 3-4 × 73 × 112
Monzo [-9 -4 0 3 2⟩
Size in cents 1.293601¢
Name (Young's) tinge
FJS name [math]\displaystyle{ \text{d2}^{7,7,7,11,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 30.6808
Weil norm (log2 max(n, d)) 30.6819
Wilson norm (sopfr(nd)) 73
Open this interval in xen-calc

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[1] and casually once referred to as "the tinge"[2]. So it is the difference of 1029/1024 and 243/242. Besides, 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.

See also

Notes

  1. ↑ 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
  2. ↑ Gayle Young, private e-mail to Todd Harrop, 24 June 2018.
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