Ploidacot/Diploid monocot - Revision history

Eufalesio: Expansion and slight rewriting following Monocot (Also rewrote Kalismic because Kalismic doesn't belong in ploidacot - it has a 7-limit basis!)

2026-07-22T23:13:44Z

Expansion and slight rewriting following Monocot (Also rewrote Kalismic because Kalismic doesn't belong in ploidacot - it has a 7-limit basis!)

← Older revision		Revision as of 23:13, 22 July 2026
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	== Intervals and notation ==		== Intervals and notation ==
	Diploid monocot 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 diploid monocot intervals align with standard monocot intervals.		Diploid monocot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" nominals, the use of scales other than the standard diatonic scale, or the use of halved pythagorean commas. As such, there is no universally accepted convention. Note and interval names are provided where diploid monocot intervals align with standard monocot intervals.

	{\| class="wikitable"		{\| class="wikitable"
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	== Temperament interpretations ==		== Temperament interpretations ==
	By definition, diploid monocot temperaments equate ~~some interval~~ to ~~its octave complement~~.		By definition, diploid monocot temperaments equate a pair of intervals, mapping them both to the semioctave.

	=== ~~Diaschismic~~ ===		=== Medium accuracy ===
	Diaschismic sets [[3/2]] equal to [[16/15]] plus a semioctave, setting the semioctave equal to {{nowrap\|[[45/32]]~[[64/45]]}}, and mapping [[5/4]] to 2 generators down. Diaschismic naturally extends to prime 17 by setting the flat 16/15 generator also equal to [[17/16]]. Diaschismic is tuned best with fifths slightly sharp of just.

	~~To extend to the 7-limit~~, ~~a simple mapping (~~[[~~pajara~~]]~~) sets 7/5~~ equal to ~~the semioctave, meaning 7~~/~~4 is~~ a semioctave ~~above~~ 5/4. ~~This suggests tuning~~ the generator ~~to about 709{{c}} (or equivalently 109{{c}})~~. ~~With a~~ slightly ~~less~~ sharp ~~fifth, septimal diaschismic maps 7/4 to 8 generators down~~.		==== Diaschismic ====
			Diaschismic equates [[45/32]] with [[64/45]], setting [[3/2]] equal to [[16/15]] plus a semioctave and mapping [[5/4]] to 2 generators down - a minor seventh minus a semioctave, or equivalently half of a minor sixth. Diaschismic naturally extends to prime 17 by equating the flat 16/15 generator with [[17/16]]. Diaschismic is tuned best with fifths slightly sharp of just.

	~~=== Injera ===~~		To extend to the 7-limit, [[pajara]] equates 7/5 with 10/7 (as per [[jubilismic]]), meaning 7/4 simply maps to a semioctave above 5/4. This suggests tuning the generator to about 709{{c}} (or equivalently 109{{c}}).
	~~Injera extends~~ [[~~meantone~~]] ~~by setting~~ 7/5 ~~equal to~~ 10/7~~, so that both~~ [[~~5/4~~]] ~~and [[~~7/4~~]] are found at~~ 4 ~~generators up, offset by a 600~~{{c}} ~~tritone representing both 7/5 and 10/7~~.

	=== ~~Kalismic~~ ===		[[Septimal diaschismic]] instead maps 7/4 to a semioctave 8 fifths down with more accuracy, and the [[pythagorean comma]] is tuned sharp enough so that its half can be used as a [[septimal comma]] or [[syntonic comma]] accidental. [[Srutal]] is the most accurate of diaschismic extensions, though the most complex, at +15 fifths.
	~~Kalismic sets the~~ semioctave to [[99/70]]~[[140/99]], so that [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. The tone is split into two [[35/33]] semitones, and the [[Pythagorean comma]] into two [[2835/2816\|fwiwismas]].
			==== Injera ====
			Injera extends [[meantone]] by equating 7/5 with 10/7 (as per jubilismic), so that both maps of [[5/4]] and [[7/4]] are found at 4 generators up, offset by a semioctave. Either sharper fifths (as in 12edo) or flatter fifths (as in 26edo) can work.

			=== High accuracy ===

			==== Gariwizmic ====
			[[Gariwizmic]] equates [[99/70]] with [[140/99]] (as per [[kalismic]]), so that maps of [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]; The tone is split into two [[35/33]] semitones, and the Pythagorean comma into two [[2835/2816\|fwiwismas]]. Gariwizmic combines this with combining the haploid chain of fifths of [[gary]] for primes 7 and 11, with new diploid mappings for primes 5, 13, 17 and 19.

			It is incredibly accurate, qualifying as a [[microtemperament]]. Despite its great accuracy, it finds other primes deep in the diploid chain, with 5/4 at +39 fifths minus a semioctave, 13/8 at -27 fifths plus a semioctave, and 17/16 as +48 fifths (4 gary commas), and 19/16 as +44 fifths minus a semioctave.

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

2026-07-16T06:38:47Z

Removing from Category:Ploidacots using Cat-a-lot

← Older revision		Revision as of 06:38, 16 July 2026
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	=== Kalismic ===		=== Kalismic ===
	Kalismic sets the semioctave to [[99/70]]~[[140/99]], so that [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. The tone is split into two [[35/33]] semitones, and the [[Pythagorean comma]] into two [[2835/2816\|fwiwismas]].		Kalismic sets the semioctave to [[99/70]]~[[140/99]], so that [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. The tone is split into two [[35/33]] semitones, and the [[Pythagorean comma]] into two [[2835/2816\|fwiwismas]].
	~~[[Category:Ploidacots\|Diploid monocot]]~~

Eufalesio: Kalismic interpretation

2026-05-05T09:29:26Z

Kalismic interpretation

← Older revision		Revision as of 09:29, 5 May 2026
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	Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.		Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.

			=== Kalismic ===
			Kalismic sets the semioctave to [[99/70]]~[[140/99]], so that [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. The tone is split into two [[35/33]] semitones, and the [[Pythagorean comma]] into two [[2835/2816\|fwiwismas]].
	[[Category:Ploidacots\|Diploid monocot]]		[[Category:Ploidacots\|Diploid monocot]]

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

2026-01-06T09:43:48Z

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

← Older revision		Revision as of 09:43, 6 January 2026
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	Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.		Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.

	[[Category:~~Ploidacot~~\|Diploid monocot]]		[[Category:Ploidacots\|Diploid monocot]]

Xenllium at 22:23, 5 January 2026

2026-01-05T22:23:47Z

← Older revision		Revision as of 22:23, 5 January 2026
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=8, 10, 12\|Title=Diploid monocot\|Wedgie=2}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=10, 12, 22\|Title=Diploid monocot\|Wedgie=2}}
	'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.		'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.

	== ~~Notation~~ ==		== Intervals and notation ==
	Diploid monocot 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 diploid monocot intervals align with standard monocot intervals.		Diploid monocot 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 diploid monocot intervals align with standard monocot intervals.

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	! Notation		! Notation
	! Name		! Name
			\|-
			\| −6
			\| 588.27
			\| Gb
			\| diminished fifth
			\| 1188.27
			\| —
			\| —
	\|-		\|-
	\| −5		\| −5
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	\| B		\| B
	\| major seventh		\| major seventh
			\|-
			\| 6
			\| 11.73
			\| —
			\| —
			\| 611.73
			\| F#
			\| augmented fourth
	\|}		\|}

Xenllium at 22:15, 5 January 2026

2026-01-05T22:15:26Z

← Older revision		Revision as of 22:15, 5 January 2026
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=10, 12\|Title=Diploid monocot\|Wedgie=2}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=8, 10, 12\|Title=Diploid monocot\|Wedgie=2}}
	'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.		'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.

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	\|+ style="font-size: 105%;" \| Diploid monocot intervals (assuming pure fifth and octave)		\|+ style="font-size: 105%;" \| Diploid monocot intervals (assuming pure fifth and octave)
	\|-		\|-
	! colspan="4" \| Ploid 1		! rowspan="2" \| #
	! colspan="4" \| Ploid 2		! colspan="3" \| Ploid 1
			! colspan="3" \| Ploid 2
	\|-		\|-
	~~! #~~
	! Cents		! Cents
			! Notation
	! Name		! Name
			! Cents
	! Notation		! Notation
	~~! #~~
	~~! Cents~~
	! Name		! Name
	~~! Notation~~
	\|-		\|-
	\| −5		\| −5
	\| 90.23		\| 90.22
			\| Db
	\| minor second		\| minor second
	~~\| Db~~		\| 690.22
	~~\| −5~~
	\| 690.23
	\| —		\| —
	\| —		\| —
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	\| —		\| —
	\| —		\| —
	~~\| −4~~
	\| 792.18		\| 792.18
			\| Ab
	\| minor sixth		\| minor sixth
	~~\| Ab~~
	\|-		\|-
	\| −3		\| −3
	\| 294.14		\| 294.13
			\| Eb
	\| minor third		\| minor third
	~~\| Eb~~		\| 894.13
	~~\| −3~~
	\| 894.14
	\| —		\| —
	\| —		\| —
	\|-		\|-
	\| −2		\| −2
	\|396.09		\| 396.09
	\| —		\| —
	\| —		\| —
	~~\| −2~~
	\| 996.09		\| 996.09
			\| Bb
	\| minor seventh		\| minor seventh
	~~\| Bb~~
	\|-		\|-
	\| −1		\| −1
	\| 498.05		\| 498.04
			\| F
	\| perfect fourth		\| perfect fourth
	\| F		\| 1098.04
	~~\| −1~~
	~~\| 1,098~~.05
	\| —		\| —
	\| —		\| —
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	\| 0		\| 0
	\| 0		\| 0
			\| C
	\| unison		\| unison
	~~\| C~~
	~~\| 0~~
	\| 600		\| 600
	\| —		\| —
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	\| —		\| —
	\| —		\| —
	~~\| 1~~
	\| 701.96		\| 701.96
			\| G
	\| perfect fifth		\| perfect fifth
	~~\| G~~
	\|-		\|-
	\| 2		\| 2
	\| 203.91		\| 203.91
			\| D
	\| major second		\| major second
	~~\| D~~
	~~\| 2~~
	\| 803.91		\| 803.91
	\| —		\| —
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	\| —		\| —
	\| —		\| —
	~~\| 3~~
	\| 905.87		\| 905.87
			\| A
	\| major sixth		\| major sixth
	~~\| A~~
	\|-		\|-
	\| 4		\| 4
	\| 407.82		\| 407.82
			\| E
	\| major third		\| major third
	\| E		\| 1007.82
	~~\| 4~~
	~~\| 1,007~~.82
	\| —		\| —
	\| —		\| —
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	\| —		\| —
	\| —		\| —
	\| 5		\| 1109.78
	\| ~~1,109.78~~		\| B
	\| major seventh		\| major seventh
	~~\| B~~
	\|}		\|}

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	Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.		Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.

	[[Category:Ploidacot]]		[[Category:Ploidacot\|Diploid monocot]]

Xenllium: /* Temperament interpretations */

2026-01-04T01:59:58Z

Temperament interpretations

← Older revision		Revision as of 01:59, 4 January 2026
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	Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.		Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7.

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

VectorGraphics at 23:26, 25 October 2025

2025-10-25T23:26:19Z

← Older revision		Revision as of 23:26, 25 October 2025
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	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=10, 12\|Title=Diploid monocot}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=10, 12\|Title=Diploid monocot\|Wedgie=2}}
	'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.		'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.

ArrowHead294 at 15:48, 9 September 2025

2025-09-09T15:48:00Z

Show changes

Lériendil: /* Diaschismic */

2025-09-08T18:26:07Z

Diaschismic

← Older revision		Revision as of 18:26, 8 September 2025
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	Diaschismic sets [[3/2]] equal to [[16/15]] plus a semioctave, setting the semioctave equal to [[45/32]]~[[64/45]], and mapping [[5/4]] to 2 generators down. Diaschismic naturally extends to prime 17 by setting the flat 16/15 generator also equal to [[17/16]]. Diaschismic is tuned best with fifths slightly sharp of just.		Diaschismic sets [[3/2]] equal to [[16/15]] plus a semioctave, setting the semioctave equal to [[45/32]]~[[64/45]], and mapping [[5/4]] to 2 generators down. Diaschismic naturally extends to prime 17 by setting the flat 16/15 generator also equal to [[17/16]]. Diaschismic is tuned best with fifths slightly sharp of just.

	To extend to the 7-limit, 7/5 ~~can be set~~ equal to the semioctave, meaning 7/4 is a semioctave above 5/4. This suggests tuning the generator to about 709 cents (or equivalently 109 cents).		To extend to the 7-limit, a simple mapping ([[pajara]]) sets 7/5 equal to the semioctave, meaning 7/4 is a semioctave above 5/4. This suggests tuning the generator to about 709 cents (or equivalently 109 cents). With a slightly less sharp fifth, septimal diaschismic maps 7/4 to 8 generators down.

	=== Injera ===		=== Injera ===