Zudilisma
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| Ratio | 68630377364883/68630356164608 |
| Subgroup monzo | 2.3.7.23.397 [-30 29 -1 -1 -1⟩ |
| Size in cents | 0.00053478714¢ |
| Name | Zudilisma |
| Color name | L4397u23ur-5 |
| FJS name | [math]\text{dddd}{-4}_{7,23,397}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 91.9278 |
| Weil height (log2 max(n, d)) | 91.9278 |
| Wilson height (sopfr (nd)) | 574 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.3983 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
68630377364883/68630356164608, the Zudilisma, is a 2.3.7.23.397 subgroup ratio which is the difference between 127834/1 and a stack of 29 3/2.
It appears in the sequence of numbers where the fractional part of 1.5^n gets progressively closer to an integer than for any number before it - sequence A1267122 in OEIS. Said sequence was described by Zudilin, hence the name of the ratio.
If this ratio is taken as a comma to be tempered out, it will produce a temperament that very closely approximates Pythagorean tuning and, in diatonic notation, maps 63917/32768 as C - Cxx.