27edo
From XenReference
27edo, or 27 equal divisions of the octave, is the equal tuning with a step size of (1200/27) ≈ 44.4¢, 27 of which stack to the perfect octave 2/1. It is best known as a Superpyth tuning alongside 22edo with a distinct sharp tendency in the 7-limit, and approximating prime 13 well instead of 11.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +9.2 | +13.7 | +9.0 | -18.0 | +3.9 | -16.1 | +13.6 | -6.1 | -7.4 | +10.5 | +15.3 | +15.4 | +21.8 | +1.2 | +15.4 |
| Relative (%) | 0.0 | +20.6 | +30.8 | +20.1 | -40.5 | +8.8 | -36.1 | +30.6 | -13.6 | -16.5 | +23.7 | +34.5 | +34.6 | +49.1 | +2.6 | +34.6 | |
| Steps (reduced) |
27 (0) |
43 (16) |
63 (9) |
76 (22) |
93 (12) |
100 (19) |
110 (2) |
115 (7) |
122 (14) |
131 (23) |
134 (26) |
141 (6) |
145 (10) |
147 (12) |
150 (15) |
155 (20) | |
Useful aberrismic scales in 27edo include blackdye, pinedye, and their mutual superset trackdye.
Ground's chord table
This table uses ground's interval name shorthand.
| fif | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 17\27 | (sj 1inv) |
sensic simic |
sensic taphric |
(um 2inv) | ||||||||
| 16\27 | um | m | n | j | sj | |||||||
| 15\27 | tim | tm | dm | dj | tj | tlj | ||||||
| 14\27 | classic dim. |
|||||||||||
| 13\27 | otonal dim. |
|||||||||||
Multiples
54edo
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +9.2 | -8.5 | +9.0 | +4.2 | +3.9 | +6.2 | -8.6 | -6.1 | -7.4 | +10.5 | -6.9 | -6.8 | -0.4 | +1.2 | -6.8 |
| Relative (%) | 0.0 | +41.2 | -38.4 | +40.3 | +19.1 | +17.6 | +27.7 | -38.8 | -27.2 | -33.1 | +47.3 | -31.0 | -30.8 | -1.8 | +5.2 | -30.8 | |
| Steps (reduced) |
54 (0) |
86 (32) |
125 (17) |
152 (44) |
187 (25) |
200 (38) |
221 (5) |
229 (13) |
244 (28) |
262 (46) |
268 (52) |
281 (11) |
289 (19) |
293 (23) |
300 (30) |
309 (39) | |
81edo
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -5.7 | -1.1 | -5.9 | -3.2 | +3.9 | -1.3 | -1.2 | -6.1 | -7.4 | -4.3 | +0.5 | +0.6 | +7.0 | +1.2 | +0.6 |
| Relative (%) | 0.0 | -38.2 | -7.6 | -39.6 | -21.4 | +26.4 | -8.4 | -8.2 | -40.9 | -49.6 | -29.0 | +3.4 | +3.8 | +47.3 | +7.8 | +3.8 | |
| Steps (reduced) |
81 (0) |
128 (47) |
188 (26) |
227 (65) |
280 (37) |
300 (57) |
331 (7) |
344 (20) |
366 (42) |
393 (69) |
401 (77) |
422 (17) |
434 (29) |
440 (35) |
450 (45) |
464 (59) | |
