659edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|659}} == Theory == 659edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.11...." |
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| {{monzo|2089 -659}} | | {{monzo|2089 -659}} | ||
| {{mapping 659 2089}} | | {{mapping|659 2089}} | ||
| -0.0056 | | -0.0056 | ||
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| 2.9.5 | | 2.9.5 | ||
| {{monzo|10 -20 23}}, {{monzo|-83 13 18}} | | {{monzo|10 -20 23}}, {{monzo|-83 13 18}} | ||
| {{mapping 659 2089 1530}} | | {{mapping|659 2089 1530}} | ||
| +0.0357 | | +0.0357 | ||
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| 2.9.5.7 | | 2.9.5.7 | ||
| 420175/419904, 703125/702464, {{monzo|44 -14 5 -4}} | | 420175/419904, 703125/702464, {{monzo|44 -14 5 -4}} | ||
| {{mapping 659 2089 1530 1850}} | | {{mapping|659 2089 1530 1850}} | ||
| +0.0343 | | +0.0343 | ||
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| 2.9.5.7.11 | | 2.9.5.7.11 | ||
| 496125/495616, 420175/419904, 151263/151250, 2097152/2096325 | | 496125/495616, 420175/419904, 151263/151250, 2097152/2096325 | ||
| {{mapping 659 2089 1530 1850 2280}} | | {{mapping|659 2089 1530 1850 2280}} | ||
| +0.0028 | | +0.0028 | ||
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| 2.9.5.7.11.13 | | 2.9.5.7.11.13 | ||
| 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539 | | 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539 | ||
| {{mapping 659 2089 1530 1850 2280 2439}} | | {{mapping|659 2089 1530 1850 2280 2439}} | ||
| -0.0313 | | -0.0313 | ||
| 0.1042 | | 0.1042 | ||
| 18.97 | | 18.97 | ||
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Revision as of 13:39, 13 August 2024
| ← 658edo | 659edo | 660edo → |
Theory
659edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.11.17.23.31 subgroup, it tempers out 1225/1224, 2025/2024, 5832/5831, 3520/3519, 3969/3968, 790625/790272 and 1740800/1740123. It supports counterultrakleismic.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.893 | -0.274 | -0.085 | +0.035 | +0.427 | +0.747 | +0.654 | +0.659 | -0.700 | +0.843 | -0.050 |
| Relative (%) | -49.0 | -15.1 | -4.7 | +1.9 | +23.5 | +41.0 | +35.9 | +36.2 | -38.4 | +46.3 | -2.7 | |
| Steps (reduced) |
1044 (385) |
1530 (212) |
1850 (532) |
2089 (112) |
2280 (303) |
2439 (462) |
2575 (598) |
2694 (58) |
2799 (163) |
2895 (259) |
2981 (345) | |
Subsets and supersets
659edo is the 120th prime EDO. 1318edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [2089 -659⟩ | [⟨659 2089]] | -0.0056 | 0.0056 | 1.02 |
| 2.9.5 | [10 -20 23⟩, [-83 13 18⟩ | [⟨659 2089 1530]] | +0.0357 | 0.0585 | 10.65 |
| 2.9.5.7 | 420175/419904, 703125/702464, [44 -14 5 -4⟩ | [⟨659 2089 1530 1850]] | +0.0343 | 0.0507 | 9.23 |
| 2.9.5.7.11 | 496125/495616, 420175/419904, 151263/151250, 2097152/2096325 | [⟨659 2089 1530 1850 2280]] | +0.0028 | 0.0777 | 14.15 |
| 2.9.5.7.11.13 | 1575/1573, 4096/4095, 86625/86528, 31250/31213, 650000/649539 | [⟨659 2089 1530 1850 2280 2439]] | -0.0313 | 0.1042 | 18.97 |