Zudilisma
Jump to navigation
Jump to search
| This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations, or conceptual frameworks. |
| 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{nd}[/math]) |
~1.19982 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.