349edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:50Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
Line 68:		Line 68:
	\| [[Orson]]		\| [[Orson]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Francium: changed EDO intro to ED intro

2025-02-21T06:02:53Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:02, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|349~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:59, 15 January 2025

2025-01-15T16:59:04Z

← Older revision		Revision as of 16:59, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	349edo is only [[consistent]] to the [[5-odd-limit]]. Omitting the [[harmonic]] [[7/1\|7]], it is consistent to the [[13-odd-limit]] with a flat tendency. In the 2.3.5.11.13 [[subgroup]], the equal temperament [[tempering out\|tempers out]] [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072 and 166375/165888.		349edo is only [[consistent]] to the [[5-odd-limit]]. Omitting the [[harmonic]] [[7/1\|7]], it is consistent to the [[13-odd-limit]] with a flat tendency. In the 2.3.5.11.13 [[subgroup]], the equal temperament [[tempering out\|tempers out]] [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072, and 166375/165888.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 26:		Line 26:
	\| {{monzo\| -553 349 }}		\| {{monzo\| -553 349 }}
	\| {{mapping\| 349 553 }}		\| {{mapping\| 349 553 }}
	\| 0.1648		\| +0.1648
	\| 0.1648		\| 0.1648
	\| 4.79		\| 4.79
Line 33:		Line 33:
	\| 2109375/2097152, {{monzo\| -31 43 -16 }}		\| 2109375/2097152, {{monzo\| -31 43 -16 }}
	\| {{mapping\| 349 553 810 }}		\| {{mapping\| 349 553 810 }}
	\| 0.2841		\| +0.2841
	\| 0.2158		\| 0.2158
	\| 6.28		\| 6.28
Line 40:		Line 40:
	\| 166375/165888, 1366875/1362944, 1953125/1948617		\| 166375/165888, 1366875/1362944, 1953125/1948617
	\| {{mapping\| 349 553 810 1207 }}		\| {{mapping\| 349 553 810 1207 }}
	\| 0.2980		\| +0.2980
	\| 0.1884		\| 0.1884
	\| 5.48		\| 5.48
Line 47:		Line 47:
	\| 625/624, 17303/17280, 41067/40960, 216513/216320		\| 625/624, 17303/17280, 41067/40960, 216513/216320
	\| {{mapping\| 349 553 810 1207 1291 }}		\| {{mapping\| 349 553 810 1207 1291 }}
	\| 0.3227		\| +0.3227
	\| 0.1756		\| 0.1756
	\| 5.11		\| 5.11
Line 68:		Line 68:
	\| [[Orson]]		\| [[Orson]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) ~~–~~ [https://open.spotify.com/track/3p2RNlmQieZA2fh3ZwQzVw Spotify] \| [https://francium223.bandcamp.com/track/chill-futuristic-lounge Bandcamp] \| [https://www.youtube.com/watch?v=B_P7zp5Zmio YouTube]		* "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/3p2RNlmQieZA2fh3ZwQzVw Spotify] \| [https://francium223.bandcamp.com/track/chill-futuristic-lounge Bandcamp] \| [https://www.youtube.com/watch?v=B_P7zp5Zmio YouTube]

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T13:11:45Z

Partial undo

← Older revision		Revision as of 13:11, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 41:		Line 50:
	\| 0.1756		\| 0.1756
	\| 5.11		\| 5.11
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 51:		Line 67:
	\| 75/64		\| 75/64
	\| [[Orson]]		\| [[Orson]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==

ArrowHead294 at 01:59, 16 November 2024

2024-11-16T01:59:33Z

← Older revision		Revision as of 01:59, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! 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		\| 2.3
Line 49:		Line 41:
	\| 0.1756		\| 0.1756
	\| 5.11		\| 5.11
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 65:		Line 51:
	\| 75/64		\| 75/64
	\| [[Orson]]		\| [[Orson]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/3p2RNlmQieZA2fh3ZwQzVw Spotify] \| [https://francium223.bandcamp.com/track/chill-futuristic-lounge Bandcamp] \| [https://www.youtube.com/watch?v=B_P7zp5Zmio YouTube]		* "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/3p2RNlmQieZA2fh3ZwQzVw Spotify] \| [https://francium223.bandcamp.com/track/chill-futuristic-lounge Bandcamp] \| [https://www.youtube.com/watch?v=B_P7zp5Zmio YouTube]

	[[Category:Listen]]		[[Category:Listen]]

Francium: +music

2024-02-20T11:48:46Z

+music

← Older revision		Revision as of 11:48, 20 February 2024
Line 67:		Line 67:
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Music ==
			; [[Francium]]
			* "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/3p2RNlmQieZA2fh3ZwQzVw Spotify] \| [https://francium223.bandcamp.com/track/chill-futuristic-lounge Bandcamp] \| [https://www.youtube.com/watch?v=B_P7zp5Zmio YouTube]

			[[Category:Listen]]

FloraC: Review

2024-01-11T18:50:39Z

Review

← Older revision		Revision as of 18:50, 11 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	349edo is only consistent to the 5-limit. Omitting the harmonic 7, it is consistent to the 13-limit; tempering out [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072 and 166375/165888.		349edo is only [[consistent]] to the [[5-odd-limit]]. Omitting the [[harmonic]] [[7/1\|7]], it is consistent to the [[13-odd-limit]] with a flat tendency. In the 2.3.5.11.13 [[subgroup]], the equal temperament [[tempering out\|tempers out]] [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072 and 166375/165888.

	===Odd harmonics===		=== Odd harmonics ===
	{{Harmonics in equal\|349}}		{{Harmonics in equal\|349}}

	===Subsets and supersets===		=== Subsets and supersets ===
	349edo is the 70th [[prime edo]]. [[1047edo]], which triples it, gives a good correction to the harmonic 7.		349edo is the 70th [[prime edo]]. [[1047edo]], which triples it, gives a good correction to the harmonic 7.

	== 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		\| 2.3
	\|{{monzo\|-553 349}}		\| {{monzo\| -553 349 }}
	\|{{mapping\|349 553}}		\| {{mapping\| 349 553 }}
	\| 0.1648		\| 0.1648
	\| 0.1648		\| 0.1648
	\| 4.79		\| 4.79
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|2109375/2097152, {{monzo\|-31 43 -16}}		\| 2109375/2097152, {{monzo\| -31 43 -16 }}
	\|{{mapping\|349 553 810}}		\| {{mapping\| 349 553 810 }}
	\| 0.2841		\| 0.2841
	\| 0.2158		\| 0.2158
	\| 6.28		\| 6.28
	\|-		\|-
	\|2.3.5.11		\| 2.3.5.11
	\|166375/165888, 1366875/1362944, 1953125/1948617		\| 166375/165888, 1366875/1362944, 1953125/1948617
	\|{{mapping\|349 553 810 1207}}		\| {{mapping\| 349 553 810 1207 }}
	\| 0.2980		\| 0.2980
	\| 0.1884		\| 0.1884
	\| 5.48		\| 5.48
	\|-		\|-
	\|2.3.5.11.13		\| 2.3.5.11.13
	\|625/624, 17303/17280, 41067/40960, 216513/216320		\| 625/624, 17303/17280, 41067/40960, 216513/216320
	\|{{mapping\|349 553 810 1207 1291}}		\| {{mapping\| 349 553 810 1207 1291 }}
	\| 0.3227		\| 0.3227
	\| 0.1756		\| 0.1756
	\|5.11		\| 5.11
	\|}		\|}

Line 55:		Line 55:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~*		! Generator*
	! Cents~~<br>(reduced)~~*		! Cents*
	! Associated<br>Ratio*		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|79\349		\| 79\349
	\|271.63		\| 271.63
	\|75/64		\| 75/64
	\|[[Orson]]		\| [[Orson]]
	\|}		\|}

	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|349}} == Theory == 349edo is only consistent to the 5-limit. Omitting the harmonic 7, it is consistent to the 13-limit; tempering out 625/624,..."

2023-12-29T20:22:28Z

Created page with "{{Infobox ET}} {{EDO intro|349}} == Theory == 349edo is only consistent to the 5-limit. Omitting the harmonic 7, it is consistent to the 13-limit; tempering out 625/624,..."

New page

{{Infobox ET}}
{{EDO intro|349}}

== Theory ==
349edo is only consistent to the 5-limit. Omitting the harmonic 7, it is consistent to the 13-limit; tempering out [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072 and 166375/165888.

===Odd harmonics===
{{Harmonics in equal|349}}

===Subsets and supersets===
349edo is the 70th [[prime edo]]. [[1047edo]], which triples it, gives a good correction to the harmonic 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 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-553 349}}
|{{mapping|349 553}}
| 0.1648
| 0.1648
| 4.79
|-
|2.3.5
|2109375/2097152, {{monzo|-31 43 -16}}
|{{mapping|349 553 810}}
| 0.2841
| 0.2158
| 6.28
|-
|2.3.5.11
|166375/165888, 1366875/1362944, 1953125/1948617
|{{mapping|349 553 810 1207}}
| 0.2980
| 0.1884
| 5.48
|-
|2.3.5.11.13
|625/624, 17303/17280, 41067/40960, 216513/216320
|{{mapping|349 553 810 1207 1291}}
| 0.3227
| 0.1756
|5.11
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)*
! Cents (reduced)*
! Associated Ratio*
! Temperaments
|-
|1
|79\349
|271.63
|75/64
|[[Orson]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct