117edt
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Prime factorization
32 × 13
Step size
16.256¢
Octave
74\117edt (1202.95¢)
Consistency limit
4
Distinct consistency limit
4
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← 116edt | 117edt | 118edt → |
117 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 117edt or 117ed3), is a nonoctave tuning system that divides the interval of 3/1 into 117 equal parts of about 16.3 ¢ each. Each step represents a frequency ratio of 31/117, or the 117th root of 3.
Intervals
Steps | Cents | Hekts | ExpandApproximate ratios |
---|
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +2.95 | +0.00 | +5.89 | -6.53 | +2.95 | -3.83 | -7.42 | +0.00 | -3.59 | -6.03 | +5.89 |
Relative (%) | +18.1 | +0.0 | +36.2 | -40.2 | +18.1 | -23.6 | -45.6 | +0.0 | -22.1 | -37.1 | +36.2 | |
Steps (reduced) |
74 (74) |
117 (0) |
148 (31) |
171 (54) |
191 (74) |
207 (90) |
221 (104) |
234 (0) |
245 (11) |
255 (21) |
265 (31) |