150ed6
| ← 149ed6 | 150ed6 | 151ed6 → |
150 equal divisions of the 6th harmonic (abbreviated 150ed6) is a nonoctave tuning system that divides the interval of 6/1 into 150 equal parts of about 20.7 ¢ each. Each step represents a frequency ratio of 61/150, or the 150th root of 6.
Theory
150ed6 is very nearly identical to 58edo, but with the 6/1 rather than the 2/1 being just, which compresses the octave by about 0.577 cents. Like 58edo, 150ed6 is consistent to the 18-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.58 | +0.58 | -1.15 | +5.45 | +0.00 | +1.97 | -1.73 | +1.15 | +4.87 | +5.30 | -0.58 |
| Relative (%) | -2.8 | +2.8 | -5.6 | +26.3 | +0.0 | +9.5 | -8.4 | +5.6 | +23.5 | +25.6 | -2.8 | |
| Steps (reduced) |
58 (58) |
92 (92) |
116 (116) |
135 (135) |
150 (0) |
163 (13) |
174 (24) |
184 (34) |
193 (43) |
201 (51) |
208 (58) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.61 | +1.39 | +6.02 | -2.31 | -3.87 | +0.58 | -10.31 | +4.29 | +2.54 | +4.72 | -10.19 | -1.15 |
| Relative (%) | +27.1 | +6.7 | +29.1 | -11.2 | -18.7 | +2.8 | -49.8 | +20.7 | +12.3 | +22.8 | -49.3 | -5.6 | |
| Steps (reduced) |
215 (65) |
221 (71) |
227 (77) |
232 (82) |
237 (87) |
242 (92) |
246 (96) |
251 (101) |
255 (105) |
259 (109) |
262 (112) |
266 (116) | |
Subsets and supersets
Since 150 factors into primes as 2 × 3 × 52, 92ed6 contains subset ed6's 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75.