Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3709edo is consistent to the 5-limit and the error of its harmonic 3 is very high. It is strong in the 2.5.21.11.13.23.31 subgroup, tempering out 213003/212992. 1024023/1024000, 5767168/5767125, 78375843/78369280, 44925111/44921875 and 4178302734375/4177455546368. === Odd harmonics === {{Harmonics in equal|3709}} === Subsets and supersets === 3709edo is the 518th prime edo. 7418edo, which dou..."

2025-10-29T14:49:17Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3709edo is consistent to the 5-limit and the error of its harmonic 3 is very high. It is strong in the 2.5.21.11.13.23.31 subgroup, tempering out 213003/212992. 1024023/1024000, 5767168/5767125, 78375843/78369280, 44925111/44921875 and 4178302734375/4177455546368. === Odd harmonics === {{Harmonics in equal|3709}} === Subsets and supersets === 3709edo is the 518th prime edo. 7418edo, which dou..."

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{{Infobox ET}}
{{ED intro}}

== Theory ==
3709edo is [[consistent]] to the [[5-limit]] and the error of its [[harmonic]] [[3/1|3]] is very high. It is strong in the 2.5.21.11.13.23.31 [[subgroup]], [[tempering out]] 213003/212992. 1024023/1024000, 5767168/5767125, 78375843/78369280, 44925111/44921875 and 4178302734375/4177455546368.

=== Odd harmonics ===
{{Harmonics in equal|3709}}

=== Subsets and supersets ===
3709edo is the 518th [[prime edo]]. [[7418edo]], which doubles it, gives a good correction to its harmonic 3.

== 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]] (%)
|-
| 2.9
| {{monzo|-11757 3709}}
| {{mapping|3709 11757}}
| 0.0129
| 0.0129
| 3.99
|-
| 2.9.5
| {{monzo|-53 5 16}}, {{monzo|-175 179 -169}}
| {{mapping|3709 11757 8612}}
| 0.0100
| 0.0112
| 3.46
|}

User:Francium/3709edo - Revision history