147ed12
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| ← 146ed12 | 147ed12 | 148ed12 → |
(convergent)
(semiconvergent)
147 equal divisions of the 12th harmonic (abbreviated 147ed12) is a nonoctave tuning system that divides the interval of 12/1 into 147 equal parts of about 29.3 ¢ each. Each step represents a frequency ratio of 121/147, or the 147th root of 12.
Theory
147ed12 is almost identical to 41edo, but with the 12th harmonic rather than the octave being just. The octave is about 0.135 ¢ compressed. Like 41edo, 147ed12 is consistent to the 16-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.1 | +0.3 | -0.3 | -6.1 | +0.1 | -3.4 | -0.4 | +0.5 | -6.3 | +4.3 | +0.0 |
| Relative (%) | -0.5 | +0.9 | -0.9 | -21.0 | +0.5 | -11.5 | -1.4 | +1.8 | -21.4 | +14.7 | +0.0 | |
| Steps (reduced) |
41 (41) |
65 (65) |
82 (82) |
95 (95) |
106 (106) |
115 (115) |
123 (123) |
130 (130) |
136 (136) |
142 (142) |
147 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.8 | -3.5 | -5.9 | -0.5 | +11.6 | +0.4 | -5.4 | -6.4 | -3.1 | +4.2 | -14.2 | -0.1 |
| Relative (%) | +26.5 | -11.9 | -20.1 | -1.8 | +39.5 | +1.4 | -18.5 | -21.9 | -10.5 | +14.3 | -48.7 | -0.5 | |
| Steps (reduced) |
152 (5) |
156 (9) |
160 (13) |
164 (17) |
168 (21) |
171 (24) |
174 (27) |
177 (30) |
180 (33) |
183 (36) |
185 (38) |
188 (41) | |