413edo - Revision history

ArrowHead294 at 12:55, 21 February 2025

2025-02-21T12:55:21Z

← Older revision		Revision as of 12:55, 21 February 2025
Line 13:		Line 13:
	== 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" \|[[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		! rowspan="2" \| [[Subgroup]]
	\|{{monzo\|187 -59}}		! rowspan="2" \| [[Comma list]]
	\|{{mapping\|413 1309}}		! rowspan="2" \| [[Mapping]]
	\| 0.0820		! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
			\|-
			\| 2.9
			\| {{monzo\|187 -59}}
			\| {{mapping\|413 1309}}
			\| +0.0820
	\| 0.0821		\| 0.0821
	\| 2.83		\| 2.83
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|32805/32768, {{monzo\|8 7 -13}}		\| 32805/32768, {{monzo\|8 7 -13}}
	\|{{mapping\|413 1309 959}}		\| {{mapping\|413 1309 959}}
	\| 0.0365		\| +0.0365
	\| 0.0930		\| 0.0930
	\| 3.20		\| 3.20
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T05:53:53Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:53, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|413~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: Created page with "{{Infobox ET}} {{EDO intro|413}} == Theory == 413et is only consistent to the 5-limit. Omitting the harmonics 3 and 7, it can be used until the 31-limit. === Odd harmonics =..."

2023-12-04T19:19:19Z

Created page with "{{Infobox ET}} {{EDO intro|413}} == Theory == 413et is only consistent to the 5-limit. Omitting the harmonics 3 and 7, it can be used until the 31-limit. === Odd harmonics =..."

New page

{{Infobox ET}}
{{EDO intro|413}}

== Theory ==
413et is only consistent to the 5-limit. Omitting the harmonics 3 and 7, it can be used until the 31-limit.

=== Odd harmonics ===
{{Harmonics in equal|413}}

=== Subsets and supersets ===
413 factors into 7 × 59, with [[7edo]] and [[59edo]] as its subset edos. [[826edo]], which doubles it, gives a good correction to the harmonics 3 and 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]] (%)
|-
|2.9
|{{monzo|187 -59}}
|{{mapping|413 1309}}
| 0.0820
| 0.0821
| 2.83
|-
|2.9.5
|32805/32768, {{monzo|8 7 -13}}
|{{mapping|413 1309 959}}
| 0.0365
| 0.0930
| 3.20
|}