Ploidacot/Dicot - Revision history

Eufalesio: Expansion and slight rewriting following Monocot

2026-07-22T22:16:46Z

Expansion and slight rewriting following Monocot

← Older revision		Revision as of 22:16, 22 July 2026
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10, 17\|Title=Dicot\|Wedgie=2}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10, 17\|Title=Dicot\|Wedgie=2}}

	'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments ~~tend to~~ involve "neutral" intervals, ~~which~~ are ~~in-~~between ~~conventional diatonic intervals~~.		'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments involve "neutral" intervals - right in the middle of typical diatonic intervals. More precisely, they are ''interchromatic'', as the neutrals are found between [[Apotome\|apotomes]] (chromatic semitones).

	== Intervals and notation ==		== Intervals and notation ==
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	== Temperament interpretations ==		== Temperament interpretations ==
	By definition, dicot temperaments ~~equate some interval~~ to ~~its fifth complement~~.		By definition, dicot temperaments map a pair of intervals to the neutral third, equating them.

	=== ~~Dicot~~ ===		=== Low accuracy ===
	The temperament named "[[dicot]]" is an exotemperament, equating the neutral third to 5/4. This means that 6/5 is the same interval, and the neutral sixth represents both 5/3 and 8/5. It is best tuned with either a sharpened generator of around 360{{c}} (optimizing for the tuning of 5/4) or a flattened generator of around 340{{c}} (optimizing for the tuning of 5/3).

	=== ~~Neutral~~ ===		==== Dicot ====
	[[~~Neutral (temperament)\|Neutral~~]] is ~~the temperament equating [[11~~/~~9]]~~ with ~~[[27~~/~~22]]. This makes 11~~/~~9 the neutral third and [[11~~/~~8]]~~ the ~~semiaugmented fourth. [[Namo]] extends neutral so that [[16~~/~~13]] is found at~~ the ~~same neutral third. Namo is often used as an 11- and 13-limit extension~~ of ~~other temperaments~~.		The temperament named "[[dicot]]" is an exotemperament that equates 5/4 with 6/5, as well as 5/3 with 8/5 with It is well tuned either way with a sharpened generator of around 360{{c}} (optimizing for the tuning of 5/4) or a flattened generator of around 340{{c}} (optimizing for the tuning of 5/3).

	~~=== Mohajira ===~~		Despite its noticeable innacuracy, it is the first "usable" dicot temperament, as the one before it would be the extreme temperament that "equates" 9/8 and 4/3.
	~~When neutral~~ is ~~combined with [[meantone]] (which sets~~ the ~~major third equal to [[5/4]])~~, the ~~result is [[mohajira]], which tunes~~ the ~~generator of ~11~~/~~9 to about 348{{c}}~~ and ~~extends to the full 11-limit by setting 7~~/~~4 equal to the semidiminished seventh~~.

	=== Hemififths ===		=== Medium accuracy ===
	~~Fittingly to~~ its name, [[hemififths]] ~~divides the fifth evenly into two {{nowrap\|~~[[49/40]]~[[60/49]]~~<nowiki/>s}}~~. 7/4 ~~is the~~ semiaugmented sixth, and consequently 5/4 ~~is the~~ sesqui-augmented (one-and-a-half augmented) second.
			==== Neutral ====
			[[Neutral (temperament)\|Neutral]] (AKA the 2.3.11 restriction of [[rastmic]]) is the temperament equating [[11/9]] with [[27/22]]. This maps 11/9 to the neutral third and [[11/8]] to the semiaugmented fourth. [[Namo]] extends neutral so that [[16/13]] is mapped at the same neutral third. Namo is often used as an 11- and 13-limit extension of other temperaments.

			==== Mohajira ====
			When neutral is combined with [[meantone]] (which maps the major third to [[5/4]]), the result is [[mohajira]], which tunes the generator of ~11/9 to about 348{{c}} and extends to the full 11-limit by setting 7/4 equal to the semidiminished seventh.

			==== Hemififths ====
			As its name implies, [[hemififths]] has hemififths as generators, equating [[49/40]] with [[60/49]]. 7/4 maps to a semiaugmented sixth, and consequently 5/4 maps to a sesqui-augmented (one-and-a-half augmented) second.

			=== High accuracy ===

			==== Newt ====
			Much like hemififths, [[newt]] equates 49/40 with 60/49, but primes are found much deeper in the dicot chain, albeit its accuracy is astounding, solidifying it as a [[microtemperament]]. It maps, with incredible exactitude: 7/4 to a subminor seventh (doubly diminished octave), 11/8 to a hyperfourth (3x-augmented second), 5/4 at -28.5 hemififths, 13/8 at 40.5 fifths, 19/16 at -23.5 fifths.

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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	=== Hemififths ===		=== Hemififths ===
	Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.		Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.

	~~[[Category:Ploidacots\|Dicot]]~~

Hotcrystal0: fix link

2026-04-30T20:19:55Z

fix link

← Older revision		Revision as of 20:19, 30 April 2026
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	=== Neutral ===		=== Neutral ===
	[[Neutral]] is the temperament equating [[11/9]] with [[27/22]]. This makes 11/9 the neutral third and [[11/8]] the semiaugmented fourth. [[Namo]] extends neutral so that [[16/13]] is found at the same neutral third. Namo is often used as an 11- and 13-limit extension of other temperaments.		[[Neutral (temperament)\|Neutral]] is the temperament equating [[11/9]] with [[27/22]]. This makes 11/9 the neutral third and [[11/8]] the semiaugmented fourth. [[Namo]] extends neutral so that [[16/13]] is found at the same neutral third. Namo is often used as an 11- and 13-limit extension of other temperaments.

	=== Mohajira ===		=== Mohajira ===

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

2026-01-06T09:43:46Z

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

← Older revision		Revision as of 09:43, 6 January 2026
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	Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.		Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.

	[[Category:~~Ploidacot~~\|Dicot]]		[[Category:Ploidacots\|Dicot]]

Xenllium at 23:43, 5 January 2026

2026-01-05T23:43:56Z

← Older revision		Revision as of 23:43, 5 January 2026
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	== Intervals and notation ==		== Intervals and notation ==
	Dicot temperaments can be notated using [[Neutral chain-of-fifths notation\|neutral chain-of-fifths notation.]]		Dicot temperaments can be notated using [[Neutral chain-of-fifths notation\|neutral chain-of-fifths notation]].

	{\| class="wikitable"		{\| class="wikitable"
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	\|-		\|-
	\| −7		\| −7
	\| ~~1,143~~.16		\| 1143.16
	\| Cd		\| Cd
	\| semidiminished octave		\| semidiminished octave
	\|-		\|-
	\| −6		\| −6
	\| 294.14		\| 294.13
	\| Eb		\| Eb
	\| minor third		\| minor third
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	\|-		\|-
	\| −2		\| −2
	\| 498.05		\| 498.04
	\| F		\| F
	\| perfect fourth		\| perfect fourth
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	\| 0		\| 0
	\| C		\| C
	\| perfect unison~~/perfect octave~~		\| perfect unison
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 3		\| 3
	\| ~~1,052~~.93		\| 1052.93
	\| Bd		\| Bd
	\| neutral seventh		\| neutral seventh
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	\|-		\|-
	\| 10		\| 10
	\| ~~1,109~~.78		\| 1109.78
	\| B		\| B
	\| major seventh		\| major seventh
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	Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.		Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.

	[[Category:Ploidacot]]		[[Category:Ploidacot\|Dicot]]

Xenllium: /* Temperament interpretations */

2026-01-04T02:02:06Z

Temperament interpretations

← Older revision		Revision as of 02:02, 4 January 2026
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	Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.		Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap\|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.

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

VectorGraphics at 23:26, 25 October 2025

2025-10-25T23:26:30Z

← Older revision		Revision as of 23:26, 25 October 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10, 17\|Title=Dicot}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10, 17\|Title=Dicot\|Wedgie=2}}

	'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.		'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.

ArrowHead294 at 15:50, 9 September 2025

2025-09-09T15:50:42Z

Show changes

Lériendil at 18:31, 8 September 2025

2025-09-08T18:31:50Z

← Older revision		Revision as of 18:31, 8 September 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10\|Title=Dicot}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10, 17\|Title=Dicot}}

	'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.		'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.

VectorGraphics at 00:15, 2 September 2025

2025-09-02T00:15:52Z

← Older revision		Revision as of 00:15, 2 September 2025
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	{{Breadcrumb}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=2\|Pergen=[P8, P5/2]\|Forms=7, 10\|Title=Dicot}}

	'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.		'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)\|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.