Diarithmedia
| Ratio | 25921/25920 |
| Subgroup monzo | 2.3.5.7.23 [-6 -4 -1 2 2⟩ |
| Size in cents | 0.066790149¢ |
| 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.