97ed9
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Theory
97ed9 is an equal-step tuning system created by dividing the interval of 9/1 into 97 equal parts.
This system can be approximated as 30.6001 EDO, meaning each step of 97ed9 corresponds closely to five steps of 153edo.
This non-octave, non-tritave scale features a well-balanced harmonic series segment from 4 to 9 and another from 39 to 50. It performs well across all prime harmonics from 5 to 19, with the exception of 13, which is slightly flat.
97ed9 sets a height record on the Riemann zeta function with primes 2 and 3 removed, approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.
Additionally, 97ed9 is close to 125zpi.
Harmonic series
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +15.7 | +19.6 | -7.9 | -2.0 | -3.9 | +3.7 | +7.8 | +0.0 | +13.7 | +5.5 | +11.8 | -9.2 | +19.4 | +17.6 | -15.7 |
| Relative (%) | +40.0 | +50.0 | -20.0 | -5.1 | -10.0 | +9.5 | +20.0 | +0.0 | +34.9 | +14.1 | +30.0 | -23.4 | +49.5 | +44.9 | -40.0 | |
| Steps (reduced) |
31 (31) |
49 (49) |
61 (61) |
71 (71) |
79 (79) |
86 (86) |
92 (92) |
97 (0) |
102 (5) |
106 (9) |
110 (13) |
113 (16) |
117 (20) |
120 (23) |
122 (25) | |
| Harmonic | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.0 | +15.7 | +0.5 | -9.9 | -15.9 | -18.0 | -16.5 | -11.8 | -4.0 | +6.5 | +19.6 | -4.1 | +13.5 | -5.9 | +15.7 | -0.0 |
| Relative (%) | -7.7 | +40.0 | +1.3 | -25.1 | -40.5 | -45.9 | -42.1 | -30.0 | -10.2 | +16.6 | +50.0 | -10.6 | +34.5 | -15.1 | +40.1 | -0.0 | |
| Steps (reduced) |
125 (28) |
128 (31) |
130 (33) |
132 (35) |
134 (37) |
136 (39) |
138 (41) |
140 (43) |
142 (45) |
144 (47) |
146 (49) |
147 (50) |
149 (52) |
150 (53) |
152 (55) |
153 (56) | |
| Harmonic | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -14.1 | +12.7 | +1.7 | -7.9 | -16.1 | +16.2 | +10.4 | +5.8 | +2.3 | -0.2 | -1.7 | -2.3 | -2.0 | -0.8 | +1.1 | +3.9 | +7.4 | +11.7 |
| Relative (%) | -35.9 | +32.3 | +4.3 | -20.0 | -41.0 | +41.3 | +26.6 | +14.9 | +5.8 | -0.5 | -4.4 | -5.9 | -5.1 | -2.2 | +2.9 | +10.0 | +18.9 | +29.7 | |
| Steps (reduced) |
154 (57) |
156 (59) |
157 (60) |
158 (61) |
159 (62) |
161 (64) |
162 (65) |
163 (66) |
164 (67) |
165 (68) |
166 (69) |
167 (70) |
168 (71) |
169 (72) |
170 (73) |
171 (74) |
172 (75) |
173 (76) | |