31edf
| ← 30edf | 31edf | 32edf → |
(convergent)
(convergent)
31 equal divisions of the perfect fifth (abbreviated 31edf or 31ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 31 equal parts of about 22.6 ¢ each. Each step represents a frequency ratio of (3/2)1/31, or the 31st root of 3/2.
Theory
31edf is almost identical to 53edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 0.1166 cents. Like 53edo, 31edf is consistent to the 10-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.12 | +0.12 | +0.23 | -1.14 | +0.23 | +5.09 | +0.35 | +0.23 | -1.02 | -7.52 | +0.35 |
| Relative (%) | +0.5 | +0.5 | +1.0 | -5.0 | +1.0 | +22.5 | +1.5 | +1.0 | -4.5 | -33.2 | +1.5 | |
| Steps (reduced) |
53 (22) |
84 (22) |
106 (13) |
123 (30) |
137 (13) |
149 (25) |
159 (4) |
168 (13) |
176 (21) |
183 (28) |
190 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.36 | +5.20 | -1.02 | +0.47 | +8.73 | +0.35 | -2.68 | -0.90 | +5.20 | -7.40 | +6.22 | +0.47 |
| Relative (%) | -10.4 | +23.0 | -4.5 | +2.1 | +38.6 | +1.5 | -11.8 | -4.0 | +23.0 | -32.7 | +27.5 | +2.1 | |
| Steps (reduced) |
196 (10) |
202 (16) |
207 (21) |
212 (26) |
217 (0) |
221 (4) |
225 (8) |
229 (12) |
233 (16) |
236 (19) |
240 (23) |
243 (26) | |