97/84 - Revision history

Godtone: missing words

2026-06-12T14:13:01Z

missing words

← Older revision		Revision as of 14:13, 12 June 2026
Line 3:		Line 3:
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
	'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a very semifourth, as it is also a convergent of the square root of 4/3. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[S-expression\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.		'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a very exact [[JI]] semifourth, as it is also a convergent of the square root of 4/3. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[S-expression\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.

	{{Todo\|improve synopsis}}		{{Todo\|improve synopsis}}

2026-06-10T20:06:55Z

note that it's a convergent

← Older revision		Revision as of 20:06, 10 June 2026
Line 3:		Line 3:
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
	'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[S-expression\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.		'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a very semifourth, as it is also a convergent of the square root of 4/3. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[S-expression\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.

	{{Todo\|improve synopsis}}		{{Todo\|improve synopsis}}

2025-05-21T15:54:49Z

Text replacement - "[[Square superparticular|S" to "[[S-expression|S"

← Older revision		Revision as of 15:54, 21 May 2025
Line 3:		Line 3:
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
	'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[~~Square superparticular~~\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.		'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[S-expression\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.

	{{Todo\|improve synopsis}}		{{Todo\|improve synopsis}}

2025-01-18T08:51:57Z

Bold lemma; -stub (looks good to me)

← Older revision		Revision as of 08:51, 18 January 2025
Line 3:		Line 3:
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
	97/84 is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[Square superparticular\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.		'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[Square superparticular\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.

	{{~~stub}}~~		{{Todo\|improve synopsis}}
	~~{{todo~~\|improve synopsis}}

2025-01-17T21:44:34Z

← Older revision		Revision as of 21:44, 17 January 2025
Line 3:		Line 3:
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
	~~This interval~~ is ~~very near~~ 5\24.		97/84 is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a semifourth. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[Square superparticular\|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo\|5\24]] or [[53edo\|11\53]]. It is closely related to [[97/56]], a semitritave.


	{{stub}}		{{stub}}
	{{todo\|improve synopsis}}		{{todo\|improve synopsis}}

2024-12-15T01:13:55Z

Todo

← Older revision		Revision as of 01:13, 15 December 2024
Line 1:		Line 1:
	~~{{stub}}~~
	{{Infobox Interval		{{Infobox Interval
	\| Name = nonacesimoseptimal semifourth, homothetic semifourth		\| Name = nonacesimoseptimal semifourth, homothetic semifourth
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
	~~{{todo\|expand}}~~
	This interval is very near 5\24.		This interval is very near 5\24.


			{{stub}}
			{{todo\|improve synopsis}}

2024-12-14T14:04:29Z

2024-01-30T07:22:53Z

move stub to start, +todo:expand

← Older revision		Revision as of 07:22, 30 January 2024
Line 1:		Line 1:
			{{stub}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = nonacesimoseptimal semifourth, homothetic semifourth		\| Name = nonacesimoseptimal semifourth, homothetic semifourth
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}
			{{todo\|expand}}

	{{~~Stub~~}}

2024-01-11T20:53:18Z

← Older revision		Revision as of 20:53, 11 January 2024
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = homothetic semifourth		\| Name = nonacesimoseptimal semifourth, homothetic semifourth
	\| Color name = 97or2		\| Color name = 97or2
	}}		}}

2024-01-11T20:02:22Z

Mark as stub