160ed6
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| ← 159ed6 | 160ed6 | 161ed6 → |
160 equal divisions of the 6th harmonic (abbreviated 160ed6) is a nonoctave tuning system that divides the interval of 6/1 into 160 equal parts of about 19.4 ¢ each. Each step represents a frequency ratio of 61/160, or the 160th root of 6.
Theory
160ed6 is related to 62edo, but with the 6th harmonic rather than the octave being just. The octave is stretched by about 2.0 cents. Like 62edo, 160ed6 is consistent to the 8-integer-limit. It provides an excellent amendment for what is left out by 80ed6, as it has very accurately tuned 13th, 17th, 19th, and 23rd harmonics.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.01 | -2.01 | +4.02 | +5.45 | +0.00 | +4.55 | +6.02 | -4.02 | +7.45 | -2.45 | +2.01 |
| Relative (%) | +10.4 | -10.4 | +20.7 | +28.1 | +0.0 | +23.5 | +31.1 | -20.7 | +38.4 | -12.7 | +10.4 | |
| Steps (reduced) |
62 (62) |
98 (98) |
124 (124) |
144 (144) |
160 (0) |
174 (14) |
186 (26) |
196 (36) |
206 (46) |
214 (54) |
222 (62) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.85 | +6.56 | +3.44 | +8.03 | +0.01 | -2.01 | +1.33 | +9.46 | +2.54 | -0.45 | +0.15 | +4.02 |
| Relative (%) | -4.4 | +33.8 | +17.7 | +41.4 | +0.1 | -10.4 | +6.8 | +48.8 | +13.1 | -2.3 | +0.8 | +20.7 | |
| Steps (reduced) |
229 (69) |
236 (76) |
242 (82) |
248 (88) |
253 (93) |
258 (98) |
263 (103) |
268 (108) |
272 (112) |
276 (116) |
280 (120) |
284 (124) | |
Subsets and supersets
Since 160 factors into primes as 25 × 5, 160ed6 has subset ed6's 2, 4, 5, 8, 10, 16, 20, 32, 40, and 80.