Ploidacot/Diploid monocot - Revision history

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
Line 135:		Line 135:
	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.

Line 18:		Line 18:
	! Notation		! Notation
	! Name		! Name
			\|-
			\| −6
			\| 588.27
			\| Gb
			\| diminished fifth
			\| 1188.27
			\| —
			\| —
	\|-		\|-
	\| −5		\| −5
Line 106:		Line 114:
	\| 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 ===

VectorGraphics at 00:17, 2 September 2025

2025-09-02T00:17:40Z

← Older revision		Revision as of 00:17, 2 September 2025
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	{{Breadcrumb}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=2\|Shears=0\|Cots=1\|Pergen=[P8/2, P5]\|Forms=10, 12\|Title=Diploid monocot}}'''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 cents. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" 3/(2*sqrt2). 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 cents. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" 3/(2*sqrt2). Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children.

	== Notation ==		== Notation ==

FloraC: Todo

2025-09-01T09:32:05Z

Todo

← Older revision		Revision as of 09:32, 1 September 2025
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	=== Injera ===		=== Injera ===
	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-cent tritone representing 7/5.		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-cent tritone representing 7/5.

			{{Todo\| unify precision }}