14348edo: Difference between revisions
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41- and higher-limit notability |
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{{EDO intro|14348}} | {{EDO intro|14348}} | ||
14348edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit relative error than any lower | 14348edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit [[relative error]] than any lower equal temperaments aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that, it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]], which has to do with its higher limit capability – it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|14348}} | {{Harmonics in equal|14348|columns=15}} | ||
=== Subsets and supersets === | |||
It factors as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all divisors. | |||
Revision as of 14:22, 20 February 2023
| ← 14347edo | 14348edo | 14349edo → |
14348edo is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from 7033. It is also distinctly consistent in the 29-odd-limit, and has a lower 23-limit relative error than any lower equal temperaments aside from 2460, 8269, 8539 and 11664. Besides all that, it is a zeta peak, integral and gap edo, which has to do with its higher limit capability – it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0035 | -0.0020 | +0.0060 | +0.0063 | +0.0076 | +0.0070 | -0.0221 | -0.0056 | -0.0260 | +0.0160 | -0.0198 | -0.0131 | -0.0039 | -0.0201 |
| Relative (%) | +0.0 | -4.2 | -2.4 | +7.2 | +7.5 | +9.1 | +8.3 | -26.4 | -6.7 | -31.1 | +19.1 | -23.7 | -15.6 | -4.7 | -24.1 | |
| Steps (reduced) |
14348 (0) |
22741 (8393) |
33315 (4619) |
40280 (11584) |
49636 (6592) |
53094 (10050) |
58647 (1255) |
60949 (3557) |
64904 (7512) |
69702 (12310) |
71083 (13691) |
74745 (3005) |
76870 (5130) |
77856 (6116) |
79697 (7957) | |
Subsets and supersets
It factors as 22 × 17 × 211, so 17, 34, 68 and 422 are all divisors.