8019/8000 - Revision history

Fitzgerald Lee: quick fix

2025-01-24T11:08:23Z

quick fix

← Older revision		Revision as of 11:08, 24 January 2025
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	== Temperaments ==		== Temperaments ==
	In the full 11-limit, tempering it out leads to the rank-4 ~~'''trimitone temperament''' (→~~ [[Rank-4 temperament #Trimitone]]). Due to the factorization above, it extends neatly to the 13-limit.		In the full 11-limit, tempering it out leads to the rank-4 [[Rank-4 temperament #Trimitone (8019/8000)\|trimitone temperament]]. Due to the factorization above, it extends neatly to the 13-limit.

	In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512\|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 (or equivalently 12&53) temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). This temperament is therefore great for 8:9:10:11:12 chords. If extended to the full [[11-limit\|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic\|bischismic]], which also tempers [[3136/3125]].		In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512\|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 (or equivalently 12&53) temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). This temperament is therefore great for 8:9:10:11:12 chords. If extended to the full [[11-limit\|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic\|bischismic]], which also tempers [[3136/3125]].

	== See also ==		==See also==
	* [[Small comma]]		*[[Small comma]]

	[[Category:Trimitone]]		[[Category:Trimitone]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]

BudjarnLambeth at 03:19, 4 November 2024

2024-11-04T03:19:00Z

← Older revision		Revision as of 03:19, 4 November 2024
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	[[Category:Trimitone]]		[[Category:Trimitone]]
	[[Category:Commas named for ~~other reasons~~]]		[[Category:Commas named for the intervals they stack]]

BudjarnLambeth at 13:24, 3 November 2024

2024-11-03T13:24:57Z

← Older revision		Revision as of 13:24, 3 November 2024
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	[[Category:Trimitone]]		[[Category:Trimitone]]
			[[Category:Commas named for other reasons]]

Godtone at 18:29, 10 October 2024

2024-10-10T18:29:07Z

← Older revision		Revision as of 18:29, 10 October 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 11-limit (also 2.3.5.11 [[subgroup]]) by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>. ~~Furthermore, it~~ is also the interval separating the [[syntonic comma]] and the [[ptolemisma]].		'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 11-limit (also 2.3.5.11 [[subgroup]]) by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>. It is also the interval separating the [[syntonic comma]] and the [[ptolemisma]] because of being an [[ultraparticular]].

	In the 13-limit, it factors neatly into ([[729/728]])([[1001/1000]]).		In the 13-limit, it factors neatly into ([[729/728]])([[1001/1000]]).

FloraC: Note the 13-limit extension

2024-04-08T15:09:46Z

Note the 13-limit extension

← Older revision		Revision as of 15:09, 8 April 2024
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 2.3.5.11 subgroup by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>. Furthermore, it is also the interval separating the [[syntonic comma]] and the [[ptolemisma]].		'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 11-limit (also 2.3.5.11 [[subgroup]]) by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>. Furthermore, it is also the interval separating the [[syntonic comma]] and the [[ptolemisma]].

			In the 13-limit, it factors neatly into ([[729/728]])([[1001/1000]]).

	== Temperaments ==		== Temperaments ==
	In the full 11-limit, tempering it out leads to the rank-4 '''trimitone temperament''' (→ [[Rank-4 temperament #Trimitone]]).		In the full 11-limit, tempering it out leads to the rank-4 '''trimitone temperament''' (→ [[Rank-4 temperament #Trimitone]]). Due to the factorization above, it extends neatly to the 13-limit.

	In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512\|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 (or equivalently 12&53) temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). This temperament is therefore great for 8:9:10:11:12 chords. If extended to the full [[11-limit\|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic\|bischismic]], which also tempers [[3136/3125]].		In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512\|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 (or equivalently 12&53) temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). This temperament is therefore great for 8:9:10:11:12 chords. If extended to the full [[11-limit\|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic\|bischismic]], which also tempers [[3136/3125]].

	== See also ==		== See also ==

TallKite at 07:27, 14 January 2023

2023-01-14T07:27:29Z

← Older revision		Revision as of 07:27, 14 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = trimitone comma		\| Name = trimitone comma
	\| Color name = L1og<sup>3</sup>1, Lalotrigu comma		\| Color name = L1og<sup>3</sup>1, lalotrigu 1sn,<br>Lalotrigu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

TallKite: added color name

2022-12-29T02:55:01Z

added color name

← Older revision		Revision as of 02:55, 29 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = trimitone comma		\| Name = trimitone comma
			\| Color name = L1og<sup>3</sup>1, Lalotrigu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:00:59Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:00, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	~~\| Ratio = 8019/8000~~
	~~\| Monzo = -6 6 -3 0 1~~
	~~\| Cents = 4.1068~~
	\| Name = trimitone comma		\| Name = trimitone comma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name =~~
	~~\| Sound~~ =
	}}		}}
	'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 2.3.5.11 subgroup by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>. Furthermore, it is also the interval separating the [[syntonic comma]] and the [[ptolemisma]].		'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 2.3.5.11 subgroup by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>. Furthermore, it is also the interval separating the [[syntonic comma]] and the [[ptolemisma]].
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	* [[Small comma]]		* [[Small comma]]

	* [[Category:11-limit]]		[[Category:Trimitone]]
	* [[Category:Small commas]]
	* [[Category:Trimitone]]

Fredg999 category edits: Moving from Category:Small comma to Category:Small commas using Cat-a-lot

2022-03-20T21:59:57Z

Moving from Category:Small comma to Category:Small commas using Cat-a-lot

← Older revision		Revision as of 21:59, 20 March 2022
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	* [[Category:11-limit]]		* [[Category:11-limit]]
	* [[Category:Small ~~comma~~]]		* [[Category:Small commas]]
	* [[Category:Trimitone]]		* [[Category:Trimitone]]

FloraC: Improve category

2022-01-12T00:12:45Z

Improve category

← Older revision		Revision as of 00:12, 12 January 2022
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	* [[Category:11-limit]]		* [[Category:11-limit]]
	* [[Category:Small comma]]		* [[Category:Small comma]]
	* [[Category:~~Ratio~~]]		* [[Category:Trimitone]]