600edo - 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"

2026-03-13T13:38:11Z

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 13:38, 13 March 2026
Line 54:		Line 54:
	\| [[Minutes]] (600e)		\| [[Minutes]] (600e)
	\|}		\|}
	<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]]		; [[Francium]]
	* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning		* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning

Tristanbay: Corrected representation of 600e val

2025-06-05T05:15:30Z

Corrected representation of 600e val

← Older revision		Revision as of 05:15, 5 June 2025
Line 5:		Line 5:
	600edo has good approximations to [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[23/1\|23]], on top of which we may consider adding [[7/1\|7]] or [[19/1\|19]]. The equal temperament [[tempering out\|tempers out]] the [[alphatricot comma]], {{monzo\| 39 -29 3 }}, and the [[mutt comma]], {{monzo\| -44 -3 21 }} in the [[5-limit]], [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the [[7-limit]], [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]].		600edo has good approximations to [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[23/1\|23]], on top of which we may consider adding [[7/1\|7]] or [[19/1\|19]]. The equal temperament [[tempering out\|tempers out]] the [[alphatricot comma]], {{monzo\| 39 -29 3 }}, and the [[mutt comma]], {{monzo\| -44 -3 21 }} in the [[5-limit]], [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the [[7-limit]], [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]].

	In the 11-limit, the 600e [[val]], {{val\| 600 951 1393 ~~684~~ '''~~2076~~''' }}, is better tuned than the patent val. 600e is a tuning for atomic in the 11-limit as well as for the 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.		In the 11-limit, the 600e [[val]], {{val\| 600 951 1393 1684 '''2075''' }}, is better tuned than the patent val. 600e is a tuning for atomic in the 11-limit as well as for the 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.

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

FloraC: Cleanup and update

2025-03-16T14:20:50Z

Cleanup and update

← Older revision		Revision as of 14:20, 16 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	600edo has good approximations to [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[23/1\|23]], on top of which we may consider adding [[7/1\|7]] or [[19/1\|19]]. The equal temperament [[tempering out\|tempers out]] the [[~~tricot~~ comma]], {{monzo\| 39 -29 3 }}, and the [[mutt comma]], {{monzo\| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]].		600edo has good approximations to [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[23/1\|23]], on top of which we may consider adding [[7/1\|7]] or [[19/1\|19]]. The equal temperament [[tempering out\|tempers out]] the [[alphatricot comma]], {{monzo\| 39 -29 3 }}, and the [[mutt comma]], {{monzo\| -44 -3 21 }} in the [[5-limit]], [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the [[7-limit]], [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]].

	In the 11-limit, the 600e [[val]], {{~~Val~~\|600 951 1393 684 '''2076'''}}, is better tuned than the patent val. 600e is a tuning for atomic in the 11-limit as well as for the 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.		In the 11-limit, the 600e [[val]], {{val\| 600 951 1393 684 '''2076''' }}, is better tuned than the patent val. 600e is a tuning for atomic in the 11-limit as well as for the 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 600 factors into {{~~factorization~~\|~~600~~}}, 600edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since {{nowrap\|600 {{=}} 6 × 100}}, one step of 600edo is named a ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.		Since 600 factors into primes as {{nowrap\| 2<sup>3</sup> × 3 × 5<sup>2</sup> }}, 600edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since {{nowrap\|600 {{=}} 6 × 100}}, one step of 600edo is named a ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 18:		Line 18:
	\|+ 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 28:		Line 28:
	\| 566.00		\| 566.00
	\| 81920/59049		\| 81920/59049
	\| [[~~Tricot~~]]		\| [[Alphatricot]]
	\|-		\|-
	\| 3		\| 3
	\| 193\600<br />(7\600)		\| 193\600<br>(7\600)
	\| 386.00<br />(14.00)		\| 386.00<br>(14.00)
	\| 5/4<br />(126/125)		\| 5/4<br>(126/125)
	\| [[Mutt]]		\| [[Mutt]]
	\|-		\|-
	\| 12		\| 12
	\| 249\600<br />(1\600)		\| 249\600<br>(1\600)
	\| 498.00<br />(2.00)		\| 498.00<br>(2.00)
	\| 4/3<br />(32805/32768)		\| 4/3<br>(32805/32768)
	\| [[Atomic]] (600e)		\| [[Atomic]] (600e)
	\|-		\|-
	\| 20		\| 20
	\| 283\600<br />(13\600)		\| 283\600<br>(13\600)
	\| 566.00<br />(26.00)		\| 566.00<br>(26.00)
	\| 238/165<br />(?)		\| 238/165<br>(?)
	\| [[Soviet ferris wheel]] (600e)		\| [[Soviet ferris wheel]] (600e)
	\|-		\|-
	\| 60		\| 60
	\| 249\600<br />(1\600)		\| 249\600<br>(1\600)
	\| 498.00<br />(2.00)		\| 498.00<br>(2.00)
	\| 4/3<br />(32805/32768)		\| 4/3<br>(32805/32768)
	\| [[Minutes]] (600e)		\| [[Minutes]] (600e)
	\|}		\|}
	<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

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning		* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning

Francium: changed EDO intro to ED intro

2025-02-21T06:12:50Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:12, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|600~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:08, 15 January 2025

2025-01-15T18:08:41Z

← Older revision		Revision as of 18:08, 15 January 2025
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 600 factors into {{factorization\|600}}, 600edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since 600 = 6 × 100, one step of 600edo is named a ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.		Since 600 factors into {{factorization\|600}}, 600edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. Since {{nowrap\|600 {{=}} 6 × 100}}, one step of 600edo is named a ''centitone'', being a relative cent of [[6edo]], otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 54:		Line 54:
	\| [[Minutes]] (600e)		\| [[Minutes]] (600e)
	\|}		\|}
	<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]]
	* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) ~~–~~ [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] ~~–~~ tricot in 600edo tuning		* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning

Eliora: /* Theory */ clarify 600e's significance

2025-01-06T10:56:07Z

Theory: clarify 600e's significance

← Older revision		Revision as of 10:56, 6 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	600edo has good approximations to [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[23/1\|23]], on top of which we may consider adding [[7/1\|7]] or [[19/1\|19]]. The equal temperament [[tempering out\|tempers out]] the [[tricot comma]], {{monzo\| 39 -29 3 }}, and the [[mutt comma]], {{monzo\| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]], ~~whereas~~ the 600e [[val]] is a tuning for atomic in the 11-limit~~. In addition, 600e val is a tuning~~ for 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.		600edo has good approximations to [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[23/1\|23]], on top of which we may consider adding [[7/1\|7]] or [[19/1\|19]]. The equal temperament [[tempering out\|tempers out]] the [[tricot comma]], {{monzo\| 39 -29 3 }}, and the [[mutt comma]], {{monzo\| -44 -3 21 }} in the 5-limit, [[65625/65536]], [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, [[support]]ing septimal [[mutt]]. The [[patent val]] is also a tuning for [[atomic]].

			In the 11-limit, the 600e [[val]], {{Val\|600 951 1393 684 '''2076'''}}, is better tuned than the patent val. 600e is a tuning for atomic in the 11-limit as well as for the 20th-octave temperament [[soviet ferris wheel]] as high as the 19-limit.

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

ArrowHead294: Partial undo

2024-11-16T13:07:54Z

Partial undo

← Older revision		Revision as of 13:07, 16 November 2024
Line 13:		Line 13:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== 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 44:		Line 51:
	\| 4/3<br />(32805/32768)		\| 4/3<br />(32805/32768)
	\| [[Minutes]] (600e)		\| [[Minutes]] (600e)
	~~{{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 ==
	; [[Francium]]		; [[Francium]]
	* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning		* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning

ArrowHead294 at 02:31, 16 November 2024

2024-11-16T02:31:02Z

← Older revision		Revision as of 02:31, 16 November 2024
Line 13:		Line 13:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== 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 28:		Line 22:
	\|-		\|-
	\| 3		\| 3
	\| 193\600<br>(7\600)		\| 193\600<br />(7\600)
	\| 386.00<br>(14.00)		\| 386.00<br />(14.00)
	\| 5/4<br>(126/125)		\| 5/4<br />(126/125)
	\| [[Mutt]]		\| [[Mutt]]
	\|-		\|-
	\| 12		\| 12
	\| 249\600<br>(1\600)		\| 249\600<br />(1\600)
	\| 498.00<br>(2.00)		\| 498.00<br />(2.00)
	\| 4/3<br>(32805/32768)		\| 4/3<br />(32805/32768)
	\| [[Atomic]] (600e)		\| [[Atomic]] (600e)
	\|-		\|-
	\| 20		\| 20
	\| 283\600<br>(13\600)		\| 283\600<br />(13\600)
	\| 566.00<br>(26.00)		\| 566.00<br />(26.00)
	\| 238/165<br>(?)		\| 238/165<br />(?)
	\| [[Soviet ferris wheel]] (600e)		\| [[Soviet ferris wheel]] (600e)
	\|-		\|-
	\| 60		\| 60
	\| 249\600<br>(1\600)		\| 249\600<br />(1\600)
	\| 498.00<br>(2.00)		\| 498.00<br />(2.00)
	\| 4/3<br>(32805/32768)		\| 4/3<br />(32805/32768)
	\| [[Minutes]] (600e)		\| [[Minutes]] (600e)
	\|}		{{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]]
	* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning		* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning

Francium: /* Music */ +links

2024-09-29T12:07:08Z

Music: +links

← Older revision		Revision as of 12:07, 29 September 2024
Line 55:		Line 55:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=cRHgCe_xdGI ~~''So Thankful For You''~~] ~~(2024)~~ – tricot in 600edo tuning		* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] \| [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] \| [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning

Francium: /* Music */

2024-08-10T12:17:10Z

Music

← Older revision		Revision as of 12:17, 10 August 2024
Line 55:		Line 55:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=cRHgCe_xdGI ''So Thankful For You''] (2024)		* [https://www.youtube.com/watch?v=cRHgCe_xdGI ''So Thankful For You''] (2024) – tricot in 600edo tuning