112edo
112EDO has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the patent fifth- is identical to the perfect fifth of 56edo, a great inverse gentle fifth where +5 fifths gives a near-just 28:27 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of 7edo) and +9 fifths gives a close approximation to 17:21.
One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from 17edo, but sharing a similar structure.
Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as circulating temperaments.
| Tones | Pattern | L:s |
|---|---|---|
| 5 | 2L 3s | 23:22 |
| 6 | 4L 2s | 19:18 |
| 7 | 7edo | equal |
| 8 | 8edo | |
| 9 | 4L 5s | 13:12 |
| 10 | 2L 8s | 12:11 |
| 11 | 2L 9s | 11:10 |
| 12 | 4L 8s | 10:9 |
| 13 | 8L 5s | 9:8 |
| 14 | 14edo | equal |
| 15 | 6L 9s | 8:7 |
| 16 | 16edo | equal |
| 17 | 10L 7s | 7:6 |
| 18 | 4L 14s | |
| 19 | 17L 2s | 6:5 |
| 20 | 12L 8s | |
| 21 | 7L 14s | |
| 22 | 2L 20s | |
| 23 | 20L 3s | 5:4 |
| 24 | 16L 8s | |
| 25 | 12L 13s | |
| 26 | 8L 18s | |
| 27 | 4L 23s | |
| 28 | 28edo | equal |
| 29 | 25L 4s | 4:3 |
| 30 | 22L 8s | |
| 31 | 19L 12s | |
| 32 | 16L 16s | |
| 33 | 13L 20s | |
| 34 | 10L 24s | |
| 35 | 7L 28s | |
| 36 | 4L 32s | |
| 37 | 1L 36s | |
| 38 | 36L 2s | 3:2 |
| 39 | 34L 5s | |
| 40 | 32L 8s | |
| 41 | 30L 11s | |
| 42 | 28L 14s | |
| 43 | 26L 17s | |
| 44 | 24L 20s | |
| 45 | 22L 23s | |
| 46 | 20L 26s | |
| 47 | 18L 29s | |
| 48 | 16L 32s | |
| 49 | 14L 35s | |
| 50 | 12L 38s | |
| 51 | 10L 41s | |
| 52 | 8L 44s | |
| 53 | 6L 47s | |
| 54 | 4L 50s | |
| 55 | 2L 53s | |
| 56 | 56edo | equal |
| 57 | 55L 2s | 2:1 |
| 58 | 54L 4s | |
| 59 | 53L 6s | |
| 60 | 52L 8s | |
| 61 | 51L 10s | |
| 62 | 50L 12s | |
| 63 | 49L 14s | |
| 64 | 48L 16s | |
| 65 | 47L 18s | |
| 66 | 46L 20s | |
| 67 | 45L 22s | |
| 68 | 44L 24s | |
| 69 | 43L 26s | |
| 70 | 42L 28s | |
| 71 | 41L 30s | |
| 72 | 40L 32s | |
| 73 | 39L 34s | |
| 74 | 38L 36s | |
| 75 | 37L 38s | |
| 76 | 36L 40s | |
| 77 | 35L 42s | |
| 78 | 34L 44s | |
| 79 | 33L 46s | |
| 80 | 32L 48s | |
| 81 | 31L 50s | |
| 82 | 30L 52s | |
| 83 | 29L 54s | |
| 84 | 28L 56s | |
| 85 | 27L 58s | |
| 86 | 26L 60s | |
| 87 | 25L 62s | |
| 88 | 24L 64s | |
| 89 | 23L 66s |