Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3217edo is only consistent to the 5-limit. The errors of the lower harmonics are high, except for its 11th harmonic with a relative error of only 0.8 percent. === Odd harmonics === {{Harmonics in equal|3217}} === Subsets and supersets === 3217edo is the 455th prime edo. 16085edo, which quintuples it, gives a good correction to its harmonic 7. == Regular temperament properties == {| class="w..."

2026-08-14T18:15:59Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3217edo is only consistent to the 5-limit. The errors of the lower harmonics are high, except for its 11th harmonic with a relative error of only 0.8 percent. === Odd harmonics === {{Harmonics in equal|3217}} === Subsets and supersets === 3217edo is the 455th prime edo. 16085edo, which quintuples it, gives a good correction to its harmonic 7. == Regular temperament properties == {| class="w..."

New page

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

== Theory ==
3217edo is only [[consistent]] to the [[5-limit]]. The errors of the lower [[harmonic]]s are high, except for its [[11/1|11]]th harmonic with a relative error of only 0.8 percent.

=== Odd harmonics ===
{{Harmonics in equal|3217}}

=== Subsets and supersets ===
3217edo is the 455th [[prime edo]]. [[16085edo]], which quintuples it, gives a good correction to its harmonic [[7/1|7]].

== 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|5099 -3217}}
| {{mapping|3217 5099}}
| −0.0207
| 0.0207
| 5.55
|-
| 2.3.5
| {{monzo|77 -31 -12}}, {{monzo|5 95 -67}}
| {{mapping|3217 5099 7470}}
| −0.0329
| 0.0242
| 6.49
|}

User:Francium/3217edo - Revision history