User:BudjarnLambeth/Table of stretched 42edo tunings: Difference between revisions
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[[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch|stretches]] or [[Octave shrinking|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions. | [[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch|stretches]] or [[Octave shrinking|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions. | ||
Latest revision as of 00:13, 2 August 2025
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42edo has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one stretches or compresses the octave, either way it will improve 42edo’s approximations of JI, but in opposite directions.
This table provides a detailed comparison of three stretched- and three compressed-octave tunings for 42edo.
| Tuning | 42ed257/128 | APS720jot | 189zpi | 42edo | APS715jot | 191zpi | 42ed255/128 |
|---|---|---|---|---|---|---|---|
| Steps / octave | ~41.77 | ~41.81 | ~41.83 | 42.00 | ~42.10 | ~42.19 | ~42.24 |
| Step size | ~28.73¢ | ~28.70¢ | ~28.69¢ | ~28.57¢ | ~28.50¢ | ~28.44¢ | ~28.41¢ |
| Overview | ex: 5 gd: 2, 3, 7 ok: ba: 11, 13 |
ex: 5 gd: 2, 3 ok: 7, 11, 13 ba: |
ex: 5 gd: 2, 13 ok: 3, 11 ba: 7 |
ex: 2, 7 gd: ok: 11 ba: 3, 5, 13 |
ex: 2 gd: 5, 7, 13 ok: 3, 11 ba: |
ex: 5, 11, 13 gd: 2, 3 ok: ba: 7 |
ex: 3, 5, 11 gd: 2 ok: 13 ba: 7 |
| 2/1 error | +23.5% (6.7¢) |
+19.0% (5.5¢) |
+17.2% (4.9¢) |
0.0% (0.0¢) |
-10.2% (2.9¢) |
−18.8% (5.3¢) |
−23.9% (6.8¢) |
| 3/1 error | −19.6% (5.6¢) |
−26.7% (7.7¢) |
−29.6% (8.5¢) |
+43.2% (12.3¢) |
+27.0% (7.7¢) |
+13.4% (3.8¢) |
+5.4% (1.5¢) |
| 5/1 error | +2.4% (0.7¢) |
−7.9% (2.3¢) |
−12.2% (3.5¢) |
+47.9% (13.7¢) |
+24.2% (6.9¢) |
+4.3% (1.2¢) |
−7.5% (2.1¢) |
| 7/1 error | −24.9% (7.2¢) |
−37.5% (10.8¢) |
−42.6% (12.2¢) |
+9.1% (2.6¢) |
-19.6% (5.6¢) |
−43.6% (12.4¢) |
+42.2% (12.0¢) |
| 11/1 error | −48.3% (13.9¢) |
+36.2% (10.4¢) |
+29.8% (8.6¢) |
−29.6% (8.5¢) |
+35.1% (10.0¢) |
+5.5% (1.6¢) |
−12.1% (3.4¢) |
| 13/1 error | +45.1% (13.0¢) |
+28.6% (8.2¢) |
+21.7% (6.2¢) |
−41.8% (12.0¢) |
+20.4% (5.8¢) |
−11.3% (3.2¢) |
−30.1% (8.6¢) |
| 17/1 error | +28.7% (8.2¢) |
+10.4% (3.0¢) |
+2.9% (0.8¢) |
+32.7% (9.3¢) |
-9.1% (2.5¢) |
-44.0% (12.5¢) |
+35.2% (10.0¢) |
| 2/1 val (& reduced) |
42 (0) |
42 (0) |
42 (0) |
42 (0) |
42 (0) |
42 (0) |
42 (0) |
| 3/1 val | 66 (24) |
66 (24) |
66 (24) |
67 (25) |
67 (25) |
67 (25) |
67 (25) |
| 5/1 val | 97 (13) |
97 (13) |
97 (13) |
98 (14) |
98 (14) |
98 (14) |
98 (14) |
| 7/1 val | 117 (33) |
117 (33) |
117 (33) |
118 (34) |
118 (34) |
118 (34) |
118 (34) |
| 11/1 val | 144 (18) |
145 (19) |
145 (19) |
145 (19) |
146 (20) |
146 (20) |
146 (20) |
| 13/1 val | 155 (29) |
155 (29) |
155 (29) |
155 (29) |
156 (30) |
156 (30) |
156 (30) |
| 17/1 val | 171 (3) |
171 (3) |
171 (3) |
172 (4) |
172 (4) |
172 (4) |
173 (5) |
ex = “excellent”, 0-13% relative error • gd = “good”, 13-27% • ok = “okay”, 27-40% • bd = “bad”, 40-50%
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