148418edo: Difference between revisions
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148418edo is a | 148418edo is a very strong higher-limit tuning, distinctly [[consistent]] through the [[39-odd-limit]], and is a [[zeta peak edo]]. It marks the first equal temperament with lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]s after [[16808edo|16808]] in the [[23-limit|23-]], [[29-limit|29-]], and [[31-limit]], the first after 83096 in the [[37-limit]], and the first after 95524 in the [[41-limit]]. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760. | ||
=== Prime harmonics === | === Prime harmonics === | ||
Latest revision as of 14:17, 30 July 2025
| ← 148417edo | 148418edo | 148419edo → |
148418 equal divisions of the octave (abbreviated 148418edo or 148418ed2), also called 148418-tone equal temperament (148418tet) or 148418 equal temperament (148418et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 148418 equal parts of about 0.00809 ¢ each. Each step represents a frequency ratio of 21/148418, or the 148418th root of 2.
148418edo is a very strong higher-limit tuning, distinctly consistent through the 39-odd-limit, and is a zeta peak edo. It marks the first equal temperament with lower relative errors after 16808 in the 23-, 29-, and 31-limit, the first after 83096 in the 37-limit, and the first after 95524 in the 41-limit. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00029 | +0.00061 | -0.00002 | +0.00063 | +0.00112 | -0.00048 | +0.00076 | -0.00015 |
| Relative (%) | +0.0 | +3.6 | +7.6 | -0.3 | +7.8 | +13.8 | -6.0 | +9.4 | -1.8 | |
| Steps (reduced) |
148418 (0) |
235237 (86819) |
344616 (47780) |
416662 (119826) |
513442 (68188) |
549212 (103958) |
606653 (12981) |
630469 (36797) |
671378 (77706) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00143 | +0.00074 | +0.00283 | -0.00124 | -0.00293 | +0.00026 | -0.00403 | -0.00094 | -0.00141 |
| Relative (%) | +17.7 | +9.2 | +35.0 | -15.3 | -36.2 | +3.2 | -49.8 | -11.6 | -17.4 | |
| Steps (reduced) |
721012 (127340) |
735292 (141620) |
773177 (31087) |
795157 (53067) |
805355 (63265) |
824401 (82311) |
850126 (108036) |
873090 (131000) |
880228 (138138) | |
Subsets and supersets
Since 148418 factors into primes as 2 × 74209, 148418edo has subset edos 2 and 74209.