Canopus - Revision history

FloraC: Text replacement - "Category:Mirkwai clan" to "Category:Canopic clan"

2026-06-06T10:30:13Z

Text replacement - "Category:Mirkwai clan" to "Category:Canopic clan"

← Older revision		Revision as of 10:30, 6 June 2026
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	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Non-octave temperaments]]		[[Category:Non-octave temperaments]]
	[[Category:~~Mirkwai~~ clan]]		[[Category:Canopic clan]]

Xenllium at 07:39, 7 March 2026

2026-03-07T07:39:46Z

← Older revision		Revision as of 07:39, 7 March 2026
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	{{~~URWTC~~}}		{{Infobox regtemp
			\| Title = Canopus
			\| Subgroups = 3.5.7
			\| Comma basis = [[16875/16807]]
			\| Edo join 1 = b13 \| Edo join 2 = b88
			\| Mapping = 1; -5 -4
			\| Generators = 7/5
			\| Generators tuning = 583.986
			\| Optimization method = CWE
			\| MOS scales = [[3L 1s (3/1-equivalent)\|3L 1s <3/1>]], [[3L 4s (3/1-equivalent)\|3L 4s <3/1>]], [[3L 7s (3/1-equivalent)\|3L 7s <3/1>]]
			\| Color name =
			\| Odd limit 1 = 3.5.7 7 \| Mistuning 1 = 1.40 \| Complexity 1 = 7
			\| Odd limit 2 = 3.5.7 49 \| Mistuning 2 = 2.80 \| Complexity 2 = 13
			}}
	'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.		'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.

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	In the below, tritave-reduced harmonics and subharmonics are indicated in '''bold'''.		In the below, tritave-reduced harmonics and subharmonics are indicated in '''bold'''.

	~~<div>~~<div style="display: inline-grid; margin-right: 25px;">		<div style="display: inline-grid; margin-right: 25px;">
	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	\|+ style="font-size: 105%;" \| Canopus		\|+ style="font-size: 105%;" \| Canopus

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:21:32Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:21, 29 April 2025
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	</div>		</div>

			{{Todo\|inline=1\|expand\|comment=add tuning spectrum}}
	[[Category:Canopus\| ]] <!-- main article -->		[[Category:Canopus\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup temperaments]]~~		[[Category:Non-octave temperaments]]
	~~[[Category:Tritave~~-~~equivalent~~ temperaments]]
	[[Category:Mirkwai clan]]		[[Category:Mirkwai clan]]
	~~{{Todo\|inline=1\|expand\|comment=add interval table, tuning spectrum, etc.}}~~

FloraC: +category

2025-04-28T13:56:05Z

+category

← Older revision		Revision as of 13:56, 28 April 2025
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	[[Category:Subgroup temperaments]]		[[Category:Subgroup temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]
			[[Category:Mirkwai clan]]
	{{~~todo~~\|add interval table, tuning spectrum, etc.~~\|inline=1~~}}		{{Todo\|inline=1\|expand\|comment=add interval table, tuning spectrum, etc.}}

FloraC: - parent category

2025-04-28T13:54:43Z

- parent category

← Older revision		Revision as of 13:54, 28 April 2025
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	{{URWTC}}		{{URWTC}}

	''~~For technical information see~~ [[No-~~twos~~ subgroup ~~temperaments#~~Canopus]]''		'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.

	~~'''Canopus''' is the~~ [[~~Rank~~-~~2 temperament\|rank two]] [[3.5.7~~ subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] ~~to 53/27~~.		For technical information see [[No-twos subgroup temperaments #Canopus]].

	== Interval table ==		== Interval table ==
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	</div>		</div>

	~~[[Category:Temperaments]]~~		[[Category:Canopus\| ]] <!-- main article -->
	[[Category:Canopus]]
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

	{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}		{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}

Lériendil at 23:01, 19 April 2025

2025-04-19T23:01:03Z

← Older revision		Revision as of 23:01, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Canopus]]		[[Category:Canopus]]
			[[Category:Rank-2 temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

	{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}		{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}

Lériendil at 18:24, 3 April 2025

2025-04-03T18:24:25Z

← Older revision		Revision as of 18:24, 3 April 2025
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			{{URWTC}}

	''For technical information see [[No-twos subgroup temperaments#Canopus]]''		''For technical information see [[No-twos subgroup temperaments#Canopus]]''

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	</div>		</div>

			[[Category:Temperaments]]
			[[Category:Canopus]]
			[[Category:Tritave-equivalent temperaments]]

	{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}		{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}

Lériendil: added intervals

2024-12-10T18:58:53Z

added intervals

← Older revision		Revision as of 18:58, 10 December 2024
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	'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.		'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.

			== Interval table ==
			In the below, tritave-reduced harmonics and subharmonics are indicated in '''bold'''.

			<div><div style="display: inline-grid; margin-right: 25px;">
			{\| class="wikitable center-1 right-2"
			\|+ style="font-size: 105%;" \| Canopus
			\|-
			! rowspan="2" \| # !! rowspan="2" \| Cents* !! colspan="1" \| Approximate Ratios
			\|-
			! 3.5.7.11/4.53 subgroup
			\|-
			\| −3 \|\| 149.9 \|\| 12/11, 49/45
			\|-
			\| −2 \|\| 733.9 \|\| 55/36, 75/49, '''81/53''', 84/55
			\|-
			\| −1 \|\| 1318.0 \|\| 15/7
			\|-
			\| 0 \|\| 0.0 \|\| 1/1
			\|-
			\| 1 \|\| 584.0 \|\| 7/5
			\|-
			\| 2 \|\| 1168.0 \|\| 49/25, '''53/27''', 55/28, 108/55
			\|-
			\| 3 \|\| 1752.0 \|\| 11/4, 135/49
			\|-
			\| 4 \|\| 434.1 \|\| '''9/7'''
			\|-
			\| 5 \|\| 1018.1 \|\| '''9/5'''
			\|-
			\| 6 \|\| 1602.1 \|\| 53/21, 63/25
			\|-
			\| 7 \|\| 284.1 \|\| 33/28, 53/45
			\|-
			\| 8 \|\| 868.1 \|\| 33/20, '''81/49'''
			\|-
			\| 9 \|\| 1452.1 \|\| '''81/35'''
			\|-
			\| 10 \|\| 134.2 \|\| '''27/25''', 53/49
			\|}
			<nowiki />* In 3.5.7-targeted [[DKW theory\|DKW]] tuning
			</div>


	{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}		{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}

Lériendil at 00:47, 9 December 2024

2024-12-09T00:47:05Z

← Older revision		Revision as of 00:47, 9 December 2024
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	''For technical information see [[No-twos subgroup temperaments#Canopus]]''		''For technical information see [[No-twos subgroup temperaments#Canopus]]''

	'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], ~~and~~ [[3L 7s (3/1-equivalent)\|3L 7s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.		'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], [[3L 7s (3/1-equivalent)\|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)\|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.

	{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}		{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}

Lériendil at 00:23, 9 December 2024

2024-12-09T00:23:07Z

← Older revision		Revision as of 00:23, 9 December 2024
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	~~{{todo\|cleanup}}~~
	''For technical information see [[No-twos subgroup temperaments#Canopus]]''		''For technical information see [[No-twos subgroup temperaments#Canopus]]''

	'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], and [[3L 7s (3/1-equivalent)\|3L 7s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.		'''Canopus''' is the [[Rank-2 temperament\|rank two]] [[3.5.7 subgroup]] temperament [[Temper out\|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5\|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)\|1L 2s]], [[3L 1s (3/1-equivalent)\|3L 1s]], [[3L 4s (3/1-equivalent)\|3L 4s]], and [[3L 7s (3/1-equivalent)\|3L 7s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.

			{{todo\|add interval table, tuning spectrum, etc.\|inline=1}}