111edt
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Prime factorization
3 × 37
Step size
17.1347¢
Octave
70\111edt (1199.43¢)
Consistency limit
10
Distinct consistency limit
10
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← 110edt | 111edt | 112edt → |
111 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 111edt or 111ed3), is a nonoctave tuning system that divides the interval of 3/1 into 111 equal parts of about 17.1 ¢ each. Each step represents a frequency ratio of 31/111, or the 111th root of 3.
Intervals
Steps | Cents | Hekts | ExpandApproximate ratios |
---|
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -0.57 | +0.00 | -1.14 | +6.65 | -0.57 | +6.72 | -1.71 | +0.00 | +6.08 | -4.71 | -1.14 |
Relative (%) | -3.3 | +0.0 | -6.6 | +38.8 | -3.3 | +39.2 | -10.0 | +0.0 | +35.5 | -27.5 | -6.6 | |
Steps (reduced) |
70 (70) |
111 (0) |
140 (29) |
163 (52) |
181 (70) |
197 (86) |
210 (99) |
222 (0) |
233 (11) |
242 (20) |
251 (29) |