500edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|500}} == Theory == 500et is only consistent to the 3-odd-limit and the error of the harmonic 3 is very large. It can be used in the..." |
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== Theory == | == Theory == | ||
500edo is in[[consistent]] to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is very large. It can be used in the 2.9.5.7.11.13.17.19.23.29.31.37.41.43 [[subgroup]], [[tempering out]] [[936/935]], [[4096/4095]], [[12376/12375]], [[2025/2024]], 3328/3325, [[9801/9800]], 35750/35721, 46592/46575, 5104/5103, 12555/12544, 1296/1295, 1376/1375 and 6273/6272. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
500 factors into | Since 500 factors into {{factorization|500}}, 500edo has subset edos {{EDOs| 2, 4, 5, 10, 20, 25, 50, 100, 125, and 250 }}. [[1000edo]], which doubles it, gives a good correction to the harmonic 3. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.9 | | 2.9 | ||
|{{monzo|317 -100}} | | {{monzo| 317 -100 }} | ||
|{{mapping|500 1585}} | | {{mapping| 500 1585 }} | ||
| -0.0142 | | -0.0142 | ||
| 0.0142 | | 0.0142 | ||
| 0.59 | | 0.59 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|{{monzo|38 -1 -15}}, {{monzo|55 -32 20}} | | {{monzo| 38 -1 -15 }}, {{monzo| 55 -32 20 }} | ||
|{{mapping|500 1585 1161}} | | {{mapping| 500 1585 1161 }} | ||
| -0.0219 | | -0.0219 | ||
| 0.0159 | | 0.0159 | ||
| 0.66 | | 0.66 | ||
|- | |- | ||
|2.9.5.7 | | 2.9.5.7 | ||
|703125/702464 | | 589824/588245, 703125/702464, 31381059609/31360000000 | ||
|{{mapping|500 1585 1161 1404}} | | {{mapping| 500 1585 1161 1404 }} | ||
| -0.0853 | | -0.0853 | ||
| 0.1108 | | 0.1108 | ||
| 4.62 | | 4.62 | ||
|- | |- | ||
|2.9.5.7.11 | | 2.9.5.7.11 | ||
|9801/9800, 46656/46585, 2252800/2250423, 703125/702464 | | 9801/9800, 46656/46585, 2252800/2250423, 703125/702464 | ||
|{{mapping|500 1585 1161 1404 1730}} | | {{mapping| 500 1585 1161 1404 1730 }} | ||
| -0.1077 | | -0.1077 | ||
| 0.1087 | | 0.1087 | ||
| 4.53 | | 4.53 | ||
|- | |- | ||
|2.9.5.7.11.13 | | 2.9.5.7.11.13 | ||
|4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091 | | 4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091 | ||
|{{mapping|500 1585 1161 1404 1730 1850}} | | {{mapping| 500 1585 1161 1404 1730 1850 }} | ||
| -0.0660 | | -0.0660 | ||
| 0.1362 | | 0.1362 | ||
| 5.68 | | 5.68 | ||
|- | |- | ||
|2.9.5.7.11.13.17 | | 2.9.5.7.11.13.17 | ||
|936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011 | | 936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011 | ||
|{{mapping|500 1585 1161 1404 1730 1850 2044}} | | {{mapping| 500 1585 1161 1404 1730 1850 2044 }} | ||
| -0.0791 | | -0.0791 | ||
| 0.1301 | | 0.1301 | ||