834edo - Revision history

ArrowHead294 at 12:21, 21 February 2025

2025-02-21T12:21:26Z

← Older revision		Revision as of 12:21, 21 February 2025
Line 23:		Line 23:
	== 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" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)

Francium: changed EDO intro to ED intro

2025-02-21T06:18:41Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:18, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-02-12T08:35:22Z

Review

← Older revision		Revision as of 08:35, 12 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~834et~~ is ~~only~~ consistent to the [[3-odd-limit]], with three mappings possible for the [[7-limit]]:		834edo is [[enfactoring\|enfactored]] in the [[3-limit]] with the same tuning as [[417edo]] and is in[[consistent]] to the [[5-odd-limit]], with three mappings possible for the [[7-limit]]:
	* {{val\|834 1322 1936 2341}} (patent val),		* {{val\| 834 1322 1936 2341 }} ([[patent val]]),
	* {{val\|834 1322 '''1937''' 2341}} (834c),		* {{val\| 834 1322 '''1937''' 2341 }} (834c),
	* {{val\|834 1322 '''1937''' '''2342'''}} (834cd).		* {{val\| 834 1322 '''1937''' '''2342''' }} (834cd).

	Using the patent val, it ~~tempers~~ out [[1600000/1594323]] and {{monzo\|-71 -5 34}} in the 5-limit; [[2401/2400]], [[4802000/4782969]] and {{monzo\|-28 -1 20 -6}} in the 7-limit.		Using the patent val, it is enfactored in the 5-limit, tempering out [[1600000/1594323]] and {{monzo\| -71 -5 34 }} in the 5-limit. It further tempers out [[2401/2400]], [[4802000/4782969]] and {{monzo\| -28 -1 20 -6 }} in the 7-limit.

	Using the 834c val, it tempers out {{monzo\|40 7 -22}} and {{monzo\|-31 43 -16}} in the 5-limit; 823543/820125, 1959552/1953125 and [[1640558367/1638400000]] in the 7-limit.		Using the 834c val, it tempers out {{monzo\| 40 7 -22 }} and {{monzo\| -31 43 -16 }} in the 5-limit; 823543/820125, 1959552/1953125 and [[1640558367/1638400000]] in the 7-limit.

	Using the 834cd val, it tempers out {{monzo\|40 7 -22}} and {{monzo\|-31 43 -16}} in the 5-limit; [[250047/250000]], 283435200/282475249 and 102760448/102515625 in the 7-limit.		Using the 834cd val, it tempers out {{monzo\| 40 7 -22 }} and {{monzo\| -31 43 -16 }} in the 5-limit; [[250047/250000]], 283435200/282475249 and 102760448/102515625 in the 7-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	834 factors into 2 × 3 × 139, ~~with~~ subset edos {{EDOs\|2, 3, 6, 139, 278, and 417}}. [[1668edo]], which doubles it, gives a good correction to the harmonic 5.		Since 834 factors into 2 × 3 × 139, 834edo has subset edos {{EDOs\| 2, 3, 6, 139, 278, and 417 }}. [[1668edo]], which doubles it, gives a good correction to the harmonic 5.

			<!--
	== 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" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-
	~~\|2.3~~
	~~\|{{monzo\|661 -417}}~~
	~~\|{{mapping\|834 1322}}~~
	~~\| -0.0641~~
	~~\| 0.0641~~
	~~\| 4.45~~
	\|}		\|}
			-->
	== Music ==		== Music ==
	; [[JUMBLE]]		; [[JUMBLE]]

Francium: Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 834et is only consistent to the 3-odd-limit, with three mappings possible for the 7-limit: * {{val|834 1322 1936 2341}} (pat..."

2024-02-10T12:54:17Z

Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 834et is only consistent to the 3-odd-limit, with three mappings possible for the 7-limit: * {{val|834 1322 1936 2341}} (pat..."

New page

{{Infobox ET}}
{{EDO intro}}

== Theory ==
834et is only consistent to the [[3-odd-limit]], with three mappings possible for the [[7-limit]]:
* {{val|834 1322 1936 2341}} (patent val),
* {{val|834 1322 '''1937''' 2341}} (834c),
* {{val|834 1322 '''1937''' '''2342'''}} (834cd).

Using the patent val, it tempers out [[1600000/1594323]] and {{monzo|-71 -5 34}} in the 5-limit; [[2401/2400]], [[4802000/4782969]] and {{monzo|-28 -1 20 -6}} in the 7-limit.

Using the 834c val, it tempers out {{monzo|40 7 -22}} and {{monzo|-31 43 -16}} in the 5-limit; 823543/820125, 1959552/1953125 and [[1640558367/1638400000]] in the 7-limit.

Using the 834cd val, it tempers out {{monzo|40 7 -22}} and {{monzo|-31 43 -16}} in the 5-limit; [[250047/250000]], 283435200/282475249 and 102760448/102515625 in the 7-limit.

=== Prime harmonics ===
{{Harmonics in equal|834}}

=== Subsets and supersets ===
834 factors into 2 × 3 × 139, with subset edos {{EDOs|2, 3, 6, 139, 278, and 417}}. [[1668edo]], which doubles it, gives a good correction to the harmonic 5.

== 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|661 -417}}
|{{mapping|834 1322}}
| -0.0641
| 0.0641
| 4.45
|}

== Music ==
; [[JUMBLE]]
* [https://www.youtube.com/watch?v=j6aQv-s_j9Y ''Lullaby For A Dead Planet''] (2024)

[[Category:Listen]]

← Older revision		Revision as of 12:21, 21 February 2025
Line 23:		Line 23:
	== 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" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)