Ploidacot/Alpha-dicot - Revision history

Overthink: /* Bug */ this feels better

2026-03-20T03:35:10Z

Bug: this feels better

← Older revision		Revision as of 03:35, 20 March 2026
Line 116:		Line 116:

	=== Bug ===		=== Bug ===
	[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the simplest ~~reasonable~~ (arguably) 5-limit interpretation of this ploidacot.		[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the simplest (arguably) reasonable 5-limit interpretation of this ploidacot.

	The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].		The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].

Overthink: /* Bug */ don't use "best"

2026-03-20T03:34:32Z

Bug: don't use "best"

← Older revision		Revision as of 03:34, 20 March 2026
Line 116:		Line 116:

	=== Bug ===		=== Bug ===
	[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the ~~best~~ 5-limit interpretation of this ploidacot.		[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the simplest reasonable (arguably) 5-limit interpretation of this ploidacot.

	The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].		The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].

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

2026-01-06T09:44:37Z

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

← Older revision		Revision as of 09:44, 6 January 2026
Line 130:		Line 130:
	As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.		As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.

	[[Category:~~Ploidacot~~\|Alpha-dicot]]		[[Category:Ploidacots\|Alpha-dicot]]

Xenllium at 23:47, 5 January 2026

2026-01-05T23:47:20Z

← Older revision		Revision as of 23:47, 5 January 2026
Line 130:		Line 130:
	As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.		As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.

	[[Category:Ploidacot]]		[[Category:Ploidacot\|Alpha-dicot]]

Xenllium: /* Intervals and notation */

2026-01-04T07:24:07Z

Intervals and notation

← Older revision		Revision as of 07:24, 4 January 2026
Line 4:		Line 4:

	== Intervals and notation ==		== Intervals and notation ==
	Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[~~Chain~~-of-fifths notation]]).		Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

	{\| class="wikitable"		{\| class="wikitable"
Line 30:		Line 30:
	\|-		\|-
	\| −6		\| −6
	\| 294.14		\| 294.13
	\| Eb		\| Eb
	\| minor third		\| minor third
Line 50:		Line 50:
	\|-		\|-
	\| −2		\| −2
	\| 498.05		\| 498.04
	\| F		\| F
	\| perfect fourth		\| perfect fourth
Line 105:		Line 105:
	\|-		\|-
	\| 9		\| 9
	\| 158.8		\| 158.80
	\|		\|
	\|		\|

Xenllium at 02:05, 4 January 2026

2026-01-04T02:05:01Z

← Older revision		Revision as of 02:05, 4 January 2026
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha~~-dicot; omega~~-dicot\|Wedgie=2}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha-dicot\|Wedgie=2}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.

	Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.		Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.
Line 130:		Line 130:
	As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.		As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.

	~~{{Todo\| unify precision }}~~		[[Category:Ploidacot]]

VectorGraphics at 23:28, 25 October 2025

2025-10-25T23:28:16Z

← Older revision		Revision as of 23:28, 25 October 2025
Line 1:		Line 1:
	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha-dicot; omega-dicot\|Wedgie=2}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.

	Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.		Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.

ArrowHead294 at 15:53, 9 September 2025

2025-09-09T15:53:19Z

← Older revision		Revision as of 15:53, 9 September 2025
Line 1:		Line 1:
	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.

	Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.		Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.

	== Intervals and notation ==		== Intervals and notation ==
	Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[Chain-of-fifths notation]]).		Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[Chain-of-fifths notation]]).

	{\| class="wikitable"		{\| class="wikitable"
	\|+Alpha-dicot intervals (assuming pure octave and fifth)		\|+ style="font-size: 105%;" \| Alpha-dicot intervals (assuming pure octave and fifth)
	!#		\|-
	!Cents		! #
	!Notation		! Cents
	!Name		! Notation
			! Name
	\|-		\|-
	\| -9		\| −9
	\|1041.20		\| 1041.20
	\|		\|
	\|		\|
	\|-		\|-
	\| -8		\| −8
	\|792.18		\| 792.18
	\|Ab		\| Ab
	\|minor sixth		\| minor sixth
	\|-		\|-
	\| -7		\| −7
	\|543.16		\| 543.16
	\|		\|
	\|		\|
	\|-		\|-
	\| -6		\| −6
	\|294.14		\| 294.14
	\|Eb		\| Eb
	\|minor third		\| minor third
	\|-		\|-
	\| -5		\| −5
	\|45.11		\| 45.11
	\|		\|
	\|		\|
	\|-		\|-
	\| -4		\| −4
	\|996.09		\| 996.09
	\|Bb		\| Bb
	\|minor seventh		\| minor seventh
	\|-		\|-
	\| -3		\| −3
	\|747.07		\| 747.07
	\|		\|
	\|		\|
	\|-		\|-
	\| -2		\| −2
	\|498.05		\| 498.05
	\|F		\| F
	\|perfect fourth		\| perfect fourth
	\|-		\|-
	\| -1		\| −1
	\|249.02		\| 249.02
	\|		\|
	\|		\|
	\|-		\|-
	\|0		\| 0
	\|0		\| 0
	\|C		\| C
	\|perfect unison		\| perfect unison
	\|-		\|-
	\|1		\| 1
	\|950.98		\| 950.98
	\|		\|
	\|		\|
	\|-		\|-
	\|2		\| 2
	\|701.96		\| 701.96
	\|G		\| G
	\|perfect fifth		\| perfect fifth
	\|-		\|-
	\|3		\| 3
	\|452.93		\| 452.93
	\|		\|
	\|		\|
	\|-		\|-
	\|4		\| 4
	\|203.91		\| 203.91
	\|D		\| D
	\|major second		\| major second
	\|-		\|-
	\|5		\| 5
	\|1154.89		\| 1154.89
	\|		\|
	\|		\|
	\|-		\|-
	\|6		\| 6
	\|905.87		\| 905.87
	\|A		\| A
	\|major sixth		\| major sixth
	\|-		\|-
	\|7		\| 7
	\|656.84		\| 656.84
	\|		\|
	\|		\|
	\|-		\|-
	\|8		\| 8
	\|407.82		\| 407.82
	\|E		\| E
	\|major third		\| major third
	\|-		\|-
	\|9		\| 9
	\|158.8		\| 158.8
	\|		\|
	\|		\|
	\|}		\|}

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	=== Barbados ===		=== Barbados ===
	Here, the generator actually is 26/15, equated with [[45/26]]. This is an accurate temperament, tempering out the unnoticeable comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The semifourth here is [[15/13]][[~]][[52/45]].		Here, the generator actually is 26/15, equated with [[45/26]]. This is an accurate temperament, tempering out the unnoticeable comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The semifourth here is {{nowrap\|[[15/13]][[~]][[52/45]]}}.

	As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.		As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.

	{{Todo\| unify precision }}		{{Todo\| unify precision }}

Lériendil at 18:29, 8 September 2025

2025-09-08T18:29:44Z

← Older revision		Revision as of 18:29, 8 September 2025
Line 1:		Line 1:
	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14, 19\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.

	Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.		Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.

Jerdle at 12:43, 2 September 2025

2025-09-02T12:43:59Z

← Older revision		Revision as of 12:43, 2 September 2025
Line 1:		Line 1:
	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' ~~means~~ the same thing. However, the preferred term is alpha-dicot.		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=1\|Cots=2\|Pergen=[P8, P4/2]\|Forms=5, 9, 14\|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval\|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.

	Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.		Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.