3L 5s
3L 5s or antioneirotonic (/oʊnaɪrəˈtɒnɪk/ oh-ny-rə-TON-ik or /ənaɪrə-/ ə-ny-rə-) refers to the structure of octave-equivalent MOS scales with generators ranging from 1\3 (one degrees of 3edo = 400¢) to 3\8 (three degrees of 8edo = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is named antioneirotonic because it is the oneirotonic (5L 3s) MOS pattern with large and small steps switched.
There are two significant harmonic entropy minima with this MOS pattern. Sensi, in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. Squares, in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.
| Generator | Cents | Comments | |||||
|---|---|---|---|---|---|---|---|
| 1\3 | 400 | ||||||
| 8\23 | 417.39 | ||||||
| 7\20 | 420 | ||||||
| 6\17 | 423.53 | L/s = 4 | |||||
| 17\48 | 425 | Squares is around here | |||||
| 11\31 | 425.81 | ||||||
| 427.73 | L/s = pi | ||||||
| 5\14 | 428.57 | L/s = 3 | |||||
| 430.41 | L/s = e | ||||||
| 14\39 | 430.77 | ||||||
| 23\64 | 431.25 | ||||||
| 9\25 | 432 | ||||||
| 4\11 | 436.36 | Boundary of propriety:
generators larger than this are proper | |||||
| 439.23 | |||||||
| 11\30 | 440 | ||||||
| 29\79 | 440.51 | Unnamed golden temperament | |||||
| 18\49 | 440.82 | ||||||
| 441.185 | |||||||
| 7\19 | 442.11 | Optimum rank range (L/s=3/2) sensi | |||||
| 17\46 | 443.48 | Sensi is around here | |||||
| 10\27 | 444.44 | ||||||
| 13\35 | 445.71 | ||||||
| 16\43 | 446.51 | ||||||
| 3\8 | 450 | ||||||