1429edo - 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"

2026-03-13T13:33:08Z

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 13:33, 13 March 2026
Line 90:		Line 90:
	\| [[Alphatrillium]]		\| [[Alphatrillium]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==

FloraC: Cleanup and update

2025-03-16T15:16:40Z

Cleanup and update

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

	== Theory ==		== Theory ==
	1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.		1429edo has a reasonable approximation of the full [[17-limit]]. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.

	As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It ~~supports~~ the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[~~trillium~~]] temperament.		As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It [[support]]s the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[alphatrillium]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 19:		Line 19:
	! rowspan="2" \| [[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
	\|-		\|-
Line 26:		Line 26:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 2265 -1429 }}		\| {{Monzo\| 2265 -1429 }}
	\| {{~~mapping~~\| 1429 2265 }}		\| {{Mapping\| 1429 2265 }}
	\| −0.0235		\| −0.0235
	\| 0.0234		\| 0.0234
Line 33:		Line 33:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 39 -29 3 }}, {{monzo\| -66 -36 53 }}		\| {{Monzo\| 39 -29 3 }}, {{monzo\| -66 -36 53 }}
	\| {{~~mapping~~\| 1429 2265 3318 }}		\| {{Mapping\| 1429 2265 3318 }}
	\| −0.0114		\| −0.0114
	\| 0.0257		\| 0.0257
Line 41:		Line 41:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, {{monzo\| 26 4 -3 -14 }}, {{monzo\| 40 -22 -1 -1 }}		\| 4375/4374, {{monzo\| 26 4 -3 -14 }}, {{monzo\| 40 -22 -1 -1 }}
	\| {{~~mapping~~\| 1429 2265 3318 4012 }}		\| {{Mapping\| 1429 2265 3318 4012 }}
	\| −0.0302		\| −0.0302
	\| 0.0395		\| 0.0395
Line 48:		Line 48:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172		\| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172
	\| {{~~mapping~~\| 1429 2265 3318 4012 4944 }}		\| {{Mapping\| 1429 2265 3318 4012 4944 }}
	\| −0.0471		\| −0.0471
	\| 0.0488		\| 0.0488
Line 55:		Line 55:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172		\| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172
	\| {{~~mapping~~\| 1429 2265 3318 4012 4944 5288 }}		\| {{Mapping\| 1429 2265 3318 4012 4944 5288 }}
	\| −0.0420		\| −0.0420
	\| 0.0460		\| 0.0460
Line 62:		Line 62:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045		\| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045
	\| {{~~mapping~~\| 1429 2265 3318 4012 4944 5288 5841 }}		\| {{Mapping\| 1429 2265 3318 4012 4944 5288 5841 }}
	\| −0.0364		\| −0.0364
	\| 0.0447		\| 0.0447
Line 72:		Line 72:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 87:		Line 87:
	\| 674\1429		\| 674\1429
	\| 565.990		\| 565.990
	\| 25/18		\| 104/75
	\| [[~~Trillium~~]]		\| [[Alphatrillium]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==
Line 97:		Line 97:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M~~?si=Puvjpvzud8yQ2TAj~~ YouTube] – gross in 1429edo tuning		* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M YouTube] – gross in 1429edo tuning

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

Francium: changed EDO intro to ED intro

2025-02-21T06:19:49Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:19, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1429~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:42:48Z

Theory: cleanup

← Older revision		Revision as of 16:42, 17 January 2025
Line 5:		Line 5:
	1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.		1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.

	It [[tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.		As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===

ArrowHead294 at 19:32, 15 January 2025

2025-01-15T19:32:17Z

← Older revision		Revision as of 19:32, 15 January 2025
Line 5:		Line 5:
	1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.		1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.

	~~The equal temperament~~ [[~~Tempering out\|~~tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.		It [[tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 28:		Line 28:
	\| {{monzo\| 2265 -1429 }}		\| {{monzo\| 2265 -1429 }}
	\| {{mapping\| 1429 2265 }}		\| {{mapping\| 1429 2265 }}
	\| ~~−0~~.0235		\| −0.0235
	\| 0.0234		\| 0.0234
	\| 2.80		\| 2.80
Line 35:		Line 35:
	\| {{monzo\| 39 -29 3 }}, {{monzo\| -66 -36 53 }}		\| {{monzo\| 39 -29 3 }}, {{monzo\| -66 -36 53 }}
	\| {{mapping\| 1429 2265 3318 }}		\| {{mapping\| 1429 2265 3318 }}
	\| ~~−0~~.0114		\| −0.0114
	\| 0.0257		\| 0.0257
	\| 3.06		\| 3.06
Line 42:		Line 42:
	\| 4375/4374, {{monzo\| 26 4 -3 -14 }}, {{monzo\| 40 -22 -1 -1 }}		\| 4375/4374, {{monzo\| 26 4 -3 -14 }}, {{monzo\| 40 -22 -1 -1 }}
	\| {{mapping\| 1429 2265 3318 4012 }}		\| {{mapping\| 1429 2265 3318 4012 }}
	\| ~~−0~~.0302		\| −0.0302
	\| 0.0395		\| 0.0395
	\| 4.70		\| 4.70
Line 49:		Line 49:
	\| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172		\| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172
	\| {{mapping\| 1429 2265 3318 4012 4944 }}		\| {{mapping\| 1429 2265 3318 4012 4944 }}
	\| ~~−0~~.0471		\| −0.0471
	\| 0.0488		\| 0.0488
	\| 5.81		\| 5.81
Line 56:		Line 56:
	\| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172		\| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172
	\| {{mapping\| 1429 2265 3318 4012 4944 5288 }}		\| {{mapping\| 1429 2265 3318 4012 4944 5288 }}
	\| ~~−0~~.0420		\| −0.0420
	\| 0.0460		\| 0.0460
	\| 5.48		\| 5.48
Line 63:		Line 63:
	\| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045		\| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045
	\| {{mapping\| 1429 2265 3318 4012 4944 5288 5841 }}		\| {{mapping\| 1429 2265 3318 4012 4944 5288 5841 }}
	\| ~~−0~~.0364		\| −0.0364
	\| 0.0447		\| 0.0447
	\| 5.32		\| 5.32
Line 90:		Line 90:
	\| [[Trillium]]		\| [[Trillium]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==
Line 97:		Line 97:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] ~~–~~ gross in 1429edo tuning		* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning

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

ArrowHead294: Partial undo

2024-11-16T12:43:57Z

Partial undo

← Older revision		Revision as of 12:43, 16 November 2024
Line 14:		Line 14:

	== 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 57:		Line 66:
	\| 0.0447		\| 0.0447
	\| 5.32		\| 5.32
	~~{{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 73:		Line 89:
	\| 25/18		\| 25/18
	\| [[Trillium]]		\| [[Trillium]]
	~~{{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

	== Scales ==		== Scales ==

ArrowHead294 at 04:02, 16 November 2024

2024-11-16T04:02:55Z

← Older revision		Revision as of 04:02, 16 November 2024
Line 14:		Line 14:

	== 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
	\| {{monzo\| 2265 -1429 }}		\| {{monzo\| 2265 -1429 }}
	\| {{mapping\| 1429 2265 }}		\| {{mapping\| 1429 2265 }}
	\| -0.0235		\| −0.0235
	\| 0.0234		\| 0.0234
	\| 2.80		\| 2.80
Line 34:		Line 26:
	\| {{monzo\| 39 -29 3 }}, {{monzo\| -66 -36 53 }}		\| {{monzo\| 39 -29 3 }}, {{monzo\| -66 -36 53 }}
	\| {{mapping\| 1429 2265 3318 }}		\| {{mapping\| 1429 2265 3318 }}
	\| -0.0114		\| −0.0114
	\| 0.0257		\| 0.0257
	\| 3.06		\| 3.06
Line 41:		Line 33:
	\| 4375/4374, {{monzo\| 26 4 -3 -14 }}, {{monzo\| 40 -22 -1 -1 }}		\| 4375/4374, {{monzo\| 26 4 -3 -14 }}, {{monzo\| 40 -22 -1 -1 }}
	\| {{mapping\| 1429 2265 3318 4012 }}		\| {{mapping\| 1429 2265 3318 4012 }}
	\| -0.0302		\| −0.0302
	\| 0.0395		\| 0.0395
	\| 4.70		\| 4.70
Line 48:		Line 40:
	\| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172		\| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172
	\| {{mapping\| 1429 2265 3318 4012 4944 }}		\| {{mapping\| 1429 2265 3318 4012 4944 }}
	\| -0.0471		\| −0.0471
	\| 0.0488		\| 0.0488
	\| 5.81		\| 5.81
Line 55:		Line 47:
	\| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172		\| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172
	\| {{mapping\| 1429 2265 3318 4012 4944 5288 }}		\| {{mapping\| 1429 2265 3318 4012 4944 5288 }}
	\| -0.0420		\| −0.0420
	\| 0.0460		\| 0.0460
	\| 5.48		\| 5.48
Line 62:		Line 54:
	\| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045		\| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045
	\| {{mapping\| 1429 2265 3318 4012 4944 5288 5841 }}		\| {{mapping\| 1429 2265 3318 4012 4944 5288 5841 }}
	\| -0.0364		\| −0.0364
	\| 0.0447		\| 0.0447
	\| 5.32		\| 5.32
	\|}		{{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 87:		Line 73:
	\| 25/18		\| 25/18
	\| [[Trillium]]		\| [[Trillium]]
	\|}		{{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}}

	== Scales ==		== Scales ==
Line 95:		Line 81:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning		* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning

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

Francium: +categories

2024-02-13T18:27:06Z

+categories

← Older revision		Revision as of 18:27, 13 February 2024
Line 94:		Line 94:

	== Music ==		== Music ==
	; [[~~User:Francium\|~~Francium]]		; [[Francium]]
	* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning		* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning

			[[Category:Listen]]

FloraC: /* Music */ links to spotify and bandcamp

2023-10-21T11:33:33Z

Music: links to spotify and bandcamp

← Older revision		Revision as of 11:33, 21 October 2023
Line 95:		Line 95:
	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* [https://~~www~~.~~youtube~~.com/~~watch~~?v=~~ttQVdzSy96M ''Gross Pattern''~~] ~~(2023)~~		* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] \| [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] \| [https://youtu.be/ttQVdzSy96M?si=Puvjpvzud8yQ2TAj YouTube] – gross in 1429edo tuning

FloraC: Expand theory, on its consistency w/ or w/out octave compression

2023-10-17T12:52:45Z

Expand theory, on its consistency w/ or w/out octave compression

← Older revision		Revision as of 12:52, 17 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~1429et~~ tempers out [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.		1429edo has a reasonable approximation of the full 17-limit. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning\|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.

			The equal temperament [[Tempering out\|tempers out]] [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===