Ploidacot/Beta-tetracot - Revision history

Fredg999 category edits: Removing from Category:Ploidacots using Cat-a-lot

2026-07-16T06:38:46Z

Removing from Category:Ploidacots using Cat-a-lot

← Older revision		Revision as of 06:38, 16 July 2026
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is {{nowrap\|[[9/7]]~[[14/11]]}} and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares ({{nowrap\|14c & 17c}}) and [[Smate family\|smate]] ({{nowrap\|14 & 17c}}).		An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is {{nowrap\|[[9/7]]~[[14/11]]}} and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares ({{nowrap\|14c & 17c}}) and [[Smate family\|smate]] ({{nowrap\|14 & 17c}}).

	~~[[Category:Ploidacots\|Beta-tetracot]]~~

ArrowHead294 at 02:25, 29 January 2026

2026-01-29T02:25:32Z

← Older revision		Revision as of 02:25, 29 January 2026
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=4\|Pergen=[P8, P11/4]\|Forms=11, 14, 17, 31\|Title=Beta-tetracot\|Wedgie=4}}		{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=4\|Pergen=[P8, P11/4]\|Forms=11, 14, 17, 31\|Title=Beta-tetracot\|Wedgie=4}}
	'''Beta-tetracot''' is a temperament archetype where the generator is a supermajor third of about ~~424–426¢~~, four of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Beta-tetracot temperaments typically generate the [[3L 5s]], [[3L 8s]], and [[3L 11s]] MOS scales, and containing all [[Ploidacot/Dicot\|dicot]] intervals.		'''Beta-tetracot''' is a temperament archetype where the generator is a supermajor third of about 424–426{{c}}, four of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Beta-tetracot temperaments typically generate the [[3L 5s]], [[3L 8s]], and [[3L 11s]] MOS scales, and containing all [[Ploidacot/Dicot\|dicot]] intervals.

	Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]].		Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]].

	== Intervals and notation ==		== Intervals and notation ==
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c) and [[Smate family\|smate]] (14 & 17c).		An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is {{nowrap\|[[9/7]]~[[14/11]]}} and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares ({{nowrap\|14c & 17c}}) and [[Smate family\|smate]] ({{nowrap\|14 & 17c}}).

	[[Category:Ploidacots\|Beta-tetracot]]		[[Category:Ploidacots\|Beta-tetracot]]

Xenllium at 21:30, 28 January 2026

2026-01-28T21:30:56Z

← Older revision		Revision as of 21:30, 28 January 2026
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	== Temperament interpretations ==		== Temperament interpretations ==
	~~=== Squares ===~~
	An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c) and [[Smate family\|smate]] (14 & 17c).		An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c) and [[Smate family\|smate]] (14 & 17c).

	[[Category:Ploidacots\|Beta-tetracot]]		[[Category:Ploidacots\|Beta-tetracot]]

Xenllium at 21:30, 28 January 2026

2026-01-28T21:30:22Z

← Older revision		Revision as of 21:30, 28 January 2026
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c).		=== Squares ===
			An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c) and [[Smate family\|smate]] (14 & 17c).

	[[Category:Ploidacots\|Beta-tetracot]]		[[Category:Ploidacots\|Beta-tetracot]]

Xenllium at 22:31, 7 January 2026

2026-01-07T22:31:47Z

← Older revision		Revision as of 22:31, 7 January 2026
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=4\|Pergen=[P8, P11/4]\|Forms=11, 14, 17, 31\|Title=Beta-tetracot\|Wedgie=4}}		{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=4\|Pergen=[P8, P11/4]\|Forms=11, 14, 17, 31\|Title=Beta-tetracot\|Wedgie=4}}
	'''Beta-tetracot''' is a temperament archetype where the generator is a ~~wide semitone~~, four of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Beta-tetracot temperaments typically generate the [[3L 5s]], [[3L 8s]], and [[3L 11s]] MOS scales, and containing all [[Ploidacot/Dicot\|dicot]] intervals.		'''Beta-tetracot''' is a temperament archetype where the generator is a supermajor third of about 424–426¢, four of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Beta-tetracot temperaments typically generate the [[3L 5s]], [[3L 8s]], and [[3L 11s]] MOS scales, and containing all [[Ploidacot/Dicot\|dicot]] intervals.

	Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]].		Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]].
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	An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c).		An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c).

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Beta-tetracot]]

FloraC: Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

2026-01-06T09:44:02Z

Text replacement - "[[Category:Ploidacot" to "[[Category:Ploidacots"

← Older revision		Revision as of 09:44, 6 January 2026
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	An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c).		An obvious interpretation for beta-tetracot is [[Squares\|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c).

	[[Category:~~Ploidacot~~]]		[[Category:Ploidacots]]

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=4|Pergen=[P8, P11/4]|Forms=11, 14, 17, 31|Title=Beta-tetracot|Wedgie=4}} '''Beta-tetracot''' is a temperament archetype where the generator is a wide semitone, four of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Beta-tetracot temperaments typically generate the 3L 5s, 3L 8s, and 3L 11s MOS scales, and containing all dicot intervals...."

2026-01-05T12:37:32Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=4|Pergen=[P8, P11/4]|Forms=11, 14, 17, 31|Title=Beta-tetracot|Wedgie=4}} '''Beta-tetracot''' is a temperament archetype where the generator is a wide semitone, four of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Beta-tetracot temperaments typically generate the 3L 5s, 3L 8s, and 3L 11s MOS scales, and containing all dicot intervals...."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=2|Cots=4|Pergen=[P8, P11/4]|Forms=11, 14, 17, 31|Title=Beta-tetracot|Wedgie=4}}
'''Beta-tetracot''' is a temperament archetype where the generator is a wide semitone, four of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Beta-tetracot temperaments typically generate the [[3L 5s]], [[3L 8s]], and [[3L 11s]] MOS scales, and containing all [[Ploidacot/Dicot|dicot]] intervals.

Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]].

== Intervals and notation ==
There is no agreed-upon notation for beta-tetracot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where beta-tetracot intervals align with standard dicot intervals (which use [[neutral chain-of-fifths notation]]).

{| class="wikitable"
|+ style="font-size: 105%;" | Beta-tetracot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −12
| 905.87
| A
| major sixth
|-
| −11
| 130.38
|
|
|-
| −10
| 554.89
| Ft
| semiaugmented fourth
|-
| −9
| 979.40
|
|
|-
| −8
| 203.91
| D
| major second
|-
| −7
| 628.42
|
|
|-
| −6
| 1052.93
| Bd
| neutral seventh
|-
| −5
| 277.44
|
|
|-
| −4
| 701.96
| G
| perfect fifth
|-
| −3
| 1126.47
|
|
|-
| −2
| 350.98
| Ed
| neutral third
|-
| −1
| 775.49
|
|
|-
| 0
| 0.00
| C
| perfect unison
|-
| 1
| 424.51
|
|
|-
| 2
| 849.02
| Ad
| neutral sixth
|-
| 3
| 73.53
|
|
|-
| 4
| 498.04
| F
| perfect fourth
|-
| 5
| 922.56
|
|
|-
| 6
| 147.07
| Dd
| neutral second
|-
| 7
| 571.58
|
|
|-
| 8
| 996.09
| Bb
| minor seventh
|-
| 9
| 220.60
|
|
|-
| 10
| 645.11
| Gd
| semidiminished fifth
|-
| 11
| 1069.62
|
|
|-
| 12
| 294.13
| Eb
| minor third
|}

== Temperament interpretations ==
An obvious interpretation for beta-tetracot is [[Squares|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c).

[[Category:Ploidacot]]