Francium at 11:41, 29 August 2025

2025-08-29T11:41:13Z

← Older revision		Revision as of 11:41, 29 August 2025
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	== Theory ==		== Theory ==
	3389edo is [[consistent]] to the [[7-limit]], and its [[harmonic]] [[3/1\|3]] is about halfway its steps. As an equal temperament, it [[tempers out]] [[2460375/2458624]], [[1640558367/1638400000]] and {{monzo\|63 29 -30 -14}} in the 7-limit. 3389edo is strong in the 2.5.7.11 [[subgroup]], tempering out 214375000/214358881, {{monzo\|49 -17 4 -6}} and {{monzo\|-30 -8 21 -3}}.		3389edo is [[consistent]] to the [[7-limit]], and its [[harmonic]] [[3/1\|3]] is about halfway its steps. As an equal temperament, it [[tempering out\|tempers out]] [[2460375/2458624]], [[1640558367/1638400000]] and {{monzo\|63 29 -30 -14}} in the 7-limit. 3389edo is strong in the 2.5.7.11 [[subgroup]], tempering out 214375000/214358881, {{monzo\|49 -17 4 -6}} and {{monzo\|-30 -8 21 -3}}.

	=== Odd harmonics ===		=== Odd harmonics ===

Francium: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3389edo is consistent to the 7-limit, and its harmonic 3 is about halfway its steps. As an equal temperament, it tempers out 2460375/2458624, 1640558367/1638400000 and {{monzo|63 29 -30 -14}} in the 7-limit. 3389edo is strong in the 2.5.7.11 subgroup, tempering out 214375000/214358881, {{monzo|49 -17 4 -6}} and {{monzo|-30 -8 21 -3}}. === Odd harmonics === {{Harmonics in equal|3389}} === Subs..."

2025-08-29T11:40:45Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 3389edo is consistent to the 7-limit, and its harmonic 3 is about halfway its steps. As an equal temperament, it tempers out 2460375/2458624, 1640558367/1638400000 and {{monzo|63 29 -30 -14}} in the 7-limit. 3389edo is strong in the 2.5.7.11 subgroup, tempering out 214375000/214358881, {{monzo|49 -17 4 -6}} and {{monzo|-30 -8 21 -3}}. === Odd harmonics === {{Harmonics in equal|3389}} === Subs..."

New page

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

== Theory ==
3389edo is [[consistent]] to the [[7-limit]], and its [[harmonic]] [[3/1|3]] is about halfway its steps. As an equal temperament, it [[tempers out]] [[2460375/2458624]], [[1640558367/1638400000]] and {{monzo|63 29 -30 -14}} in the 7-limit. 3389edo is strong in the 2.5.7.11 [[subgroup]], tempering out 214375000/214358881, {{monzo|49 -17 4 -6}} and {{monzo|-30 -8 21 -3}}.

=== Odd harmonics ===
{{Harmonics in equal|3389}}

=== Subsets and supersets ===
3389edo is the 477th [[prime edo]]. [[6778edo]], 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|10743 -3389}}
| {{mapping|3389 10743}}
| −0.0069
| 0.0069
| 1.95
|-
| 2.9.5
| {{monzo|144 -11 -47}}, {{monzo|57 -59 56}}
| {{mapping|3389 10743 7869}}
| −0.0039
| 0.0071
| 2.01
|-
| 2.9.5.7
| 24414062500/24407490807, 33232930569601/33215062500000, {{monzo|47 -9 -14 5}}
| {{mapping|3389 10743 7869 9514}}
| +0.0010
| 0.0105
| 2.97
|-
| 2.9.5.7.11
| 151263/151250, 184549376/184528125, 1722499009/1721868840, 46894531250/46877879169
| {{mapping|3389 10743 7869 9514 11724}}
| +0.0011
| 0.0094
| 2.65
|-
| 2.9.5.7.11.13
| 10648/10647, 1146880/1146717, 105644/105625, 140625/140608, 1377751375/1377495072
| {{mapping|3389 10743 7869 9514 11724 12541}}
| −0.0024
| 0.0117
| 3.30
|}

User:Francium/3389edo - Revision history

Francium at 11:41, 29 August 2025