Diarithmedia

Interval information

Ratio	25921/25920
Subgroup monzo	2.3.5.7.23 [-6 -4 -1 2 2⟩
Size in cents	0.06679015¢
Name	diarithmedia
Color name	23oozzg3 bitwethozo-agu 3rd
FJS name	[math]\text{P1}^{7,7,23,23}_{5}[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	29.3236
Weil height (log2 max(n, d))	29.3237
Wilson height (sopfr(nd))	89
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19986 bits
Comma size	unnoticeable
S-expressions	S161, S46 / S48
open this interval in xen-calc

25921/25920, the diarithmedia, is a 23-limit and 2.3.5.7.23-subgroup square superparticular comma of about 0.067 cents. It is the difference between 161/160 and 162/161, and between 49/45 and (24/23)², and therefore tempering this comma out splits the syntonic comma, 81/80 into exact halves alongside 49/45. As a further consequence, it equates 161/144, the "arithmetic meantone" (being the arithmetic mean of 9/8 and 10/9) with 180/161 and splits 5/4 in half, providing a way to use hemithirds without equating 9/8 and 10/9 together.

Etymology

The name diarithmetic media was proposed by Flora Canou in 2023, for being the separatrix between an arithmetic-mean interval and an inverse-arithmetic-mean interval. It was shortened to diarithmedia by Lériendil in 2024.

See also

• Unnoticeable comma
• List of superparticular intervals
• 161/144
• Meantone