150ed6
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| ← 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 6th harmonic rather than the octave being just, which compresses the octave by about 0.577 cents. Like 58edo, 150ed6 is consistent to the 18-integer-limit. The prime harmonics 3, 5, 7, 11, and 13, which are tuned sharp in 58edo, remain sharp here, but less so. The 17, which is flat to begin with, becomes slightly worse.
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.