User:Francium/5113edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} == Theory == 5113edo is consistent to the 11-limit, tempering out 21437500/21434787, 47265625/47258883, 184549376/184528125 and 246071287/246037500 in the 11-limit; 123201/123200, 196625/196608, 1664000/1663893, 5175625/5174928 and 1063348/1063125 in the 13-limit; and 12376/12375, 123201/123200, 221221/221184, 4685824/4685625, 1664000/1663893 and 7109375/7108992 in the 17-limit. {{Harmonics in equal|5113}}" |
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== Theory == | == Theory == | ||
5113edo is [[consistent]] to the [[11-limit]], [[tempering out]] 21437500/21434787, 47265625/47258883, 184549376/184528125 and 246071287/246037500 in the 11-limit; [[123201/123200]], 196625/196608, 1664000/1663893, 5175625/5174928 and 1063348/1063125 in the [[13-limit]]; and [[12376/12375]], 123201/123200, 221221/221184, 4685824/4685625, 1664000/1663893 and 7109375/7108992 in the [[17-limit]]. | 5113edo is [[consistent]] to the [[11-limit]], [[tempering out]] 21437500/21434787, 47265625/47258883, 184549376/184528125 and 246071287/246037500 in the 11-limit; [[123201/123200]], 196625/196608, 1664000/1663893, 5175625/5174928 and 1063348/1063125 in the [[13-limit]]; and [[12376/12375]], 123201/123200, 221221/221184, 4685824/4685625, 1664000/1663893 and 7109375/7108992 in the [[17-limit]]. It is strong in the 2.3.5.7.11.17.23.29.31 [[subgroup]], tempering out 21505/21504, 126225/126224, 30625/30624, 150920/150903, 15625/15624, 53361/53360, 750200/750141 and 69632/69629. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|5113}} | {{Harmonics in equal|5113}} | ||
=== Subsets and supersets === | |||
5113edo is the 684th [[prime edo]]. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo|8104 -5113}} | |||
| {{mapping|5113 8104}} | |||
| −0.0064 | |||
| 0.0064 | |||
| 2.73 | |||
|- | |||
| 2.3.5 | |||
| {{monzo|56 -91 38}}, {{monzo|144 -22 -47}} | |||
| {{mapping|5113 8104 11872}} | |||
| −0.0037 | |||
| 0.0065 | |||
| 2.77 | |||
|- | |||
| 2.3.5.7 | |||
| 24414062500/24407490807, 13841287201/13839609375, 281484423828125/281474976710656 | |||
| {{mapping|5113 8104 11872 14354}} | |||
| −0.0026 | |||
| 0.0059 | |||
| 2.51 | |||
|- | |||
| 2.3.5.7.11 | |||
| 21437500/21434787, 47265625/47258883, 184549376/184528125, 246071287/246037500 | |||
| {{mapping|5113 8104 11872 14354 17688}} | |||
| −0.0011 | |||
| 0.0061 | |||
| 2.60 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 123201/123200, 196625/196608, 1664000/1663893, 5175625/5174928, 1063348/1063125 | |||
| {{mapping|5113 8104 11872 14354 17688 18920}} | |||
| +0.0028 | |||
| 0.0103 | |||
| 4.39 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 12376/12375, 123201/123200, 221221/221184, 4685824/4685625, 1664000/1663893, 7109375/7108992 | |||
| {{mapping|5113 8104 11872 14354 17688 18920 20899}} | |||
| +0.0040 | |||
| 0.0100 | |||
| 4.26 | |||
|} | |||