80ed6
| ← 79ed6 | 80ed6 | 81ed6 → |
80 equal divisions of the 6th harmonic (abbreviated 80ed6) is a nonoctave tuning system that divides the interval of 6/1 into 80 equal parts of about 38.8 ¢ each. Each step represents a frequency ratio of 61/80, or the 80th root of 6.
Theory
80ed6 is related to 31edo, but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 2 cents. Like 31edo, 80ed6 is consistent to the 12-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.0 | -2.0 | +4.0 | +5.4 | +0.0 | +4.6 | +6.0 | -4.0 | +7.5 | -2.5 | +2.0 |
| Relative (%) | +5.2 | -5.2 | +10.4 | +14.0 | +0.0 | +11.7 | +15.5 | -10.4 | +19.2 | -6.3 | +5.2 | |
| Steps (reduced) |
31 (31) |
49 (49) |
62 (62) |
72 (72) |
80 (0) |
87 (7) |
93 (13) |
98 (18) |
103 (23) |
107 (27) |
111 (31) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +18.5 | +6.6 | +3.4 | +8.0 | -19.4 | -2.0 | -18.1 | +9.5 | +2.5 | -0.4 | +0.1 | +4.0 |
| Relative (%) | +47.8 | +16.9 | +8.9 | +20.7 | -50.0 | -5.2 | -46.6 | +24.4 | +6.6 | -1.1 | +0.4 | +10.4 | |
| Steps (reduced) |
115 (35) |
118 (38) |
121 (41) |
124 (44) |
126 (46) |
129 (49) |
131 (51) |
134 (54) |
136 (56) |
138 (58) |
140 (60) |
142 (62) | |
Subsets and supersets
Since 80 factors into primes as 24 × 5, 80ed6 has subset ed6's 2, 4, 5, 8, 10, 16, 20, and 40.