Xenllium at 11:32, 6 January 2026

2026-01-06T11:32:02Z

← Older revision		Revision as of 11:32, 6 January 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|+ style="font-size: 105%;" \| Triploid ~~monocot~~ intervals (assuming pure fifth and octave)		\|+ style="font-size: 105%;" \| Triploid dicot intervals (assuming pure fifth and octave)
	\|-		\|-
	! rowspan="2" \| #		! rowspan="2" \| #
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for triploid dicot is [[hemiaug]]. The period is [[5/4]][[~]][[14/11]] and the generator is [[36/35]]~[[40/39]]~[[45/44]], so that [[3/2]] is two periods down two generators, [[7/4]] at one octave down five generators, [[11/8]] at two periods down five generators, and [[13/8]] at two periods up one generator.		An obvious interpretation for triploid dicot is [[hemiaug]], a weak extension of [[augmented]]. The period is [[5/4]][[~]][[14/11]] and the generator is [[36/35]]~[[40/39]]~[[45/44]], so that [[3/2]] is two periods down two generators, [[7/4]] at one octave down five generators, [[11/8]] at two periods down five generators, and [[13/8]] at two periods up one generator.

	[[Category:Ploidacots\|Triploid dicot]]		[[Category:Ploidacots\|Triploid dicot]]

Xenllium: /* Temperament interpretations */

2026-01-06T11:12:18Z

Temperament interpretations

← Older revision		Revision as of 11:12, 6 January 2026
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	An obvious interpretation for triploid dicot is [[hemiaug]]. The period is [[5/4]][[~]][[14/11]] and the generator is [[36/35]]~[[40/39]]~[[45/44]], so that [[3/2]] is two periods down two generators, [[7/4]] at one octave down five generators, [[11/8]] at two periods down five generators, and [[13/8]] at two periods up one generator.		An obvious interpretation for triploid dicot is [[hemiaug]]. The period is [[5/4]][[~]][[14/11]] and the generator is [[36/35]]~[[40/39]]~[[45/44]], so that [[3/2]] is two periods down two generators, [[7/4]] at one octave down five generators, [[11/8]] at two periods down five generators, and [[13/8]] at two periods up one generator.

	[[Category:~~Ploidacot~~\|Triploid dicot]]		[[Category:Ploidacots\|Triploid dicot]]

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=3|Shears=0|Cots=2|Pergen=[P8/3, P5/2]|Forms=18, 21, 24|Title=Triploid dicot|Wedgie=6}} '''Triploid dicot''' is a temperament archetype with a 1/3-octave period, and a generator of a neutral third. In a pure tuning, the generator is exactly a half of 3/2. But the alternative generator, a quartertone, with size around 49¢ is rather easier to grasp. Triploid dicot temperaments usually generate the 3L 12s, 3L 15s, and..."

2026-01-06T11:04:11Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=3|Shears=0|Cots=2|Pergen=[P8/3, P5/2]|Forms=18, 21, 24|Title=Triploid dicot|Wedgie=6}} '''Triploid dicot''' is a temperament archetype with a 1/3-octave period, and a generator of a neutral third. In a pure tuning, the generator is exactly a half of 3/2. But the alternative generator, a quartertone, with size around 49¢ is rather easier to grasp. Triploid dicot temperaments usually generate the 3L 12s, 3L 15s, and..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=3|Shears=0|Cots=2|Pergen=[P8/3, P5/2]|Forms=18, 21, 24|Title=Triploid dicot|Wedgie=6}}

'''Triploid dicot''' is a temperament archetype with a 1/3-octave period, and a generator of a neutral third. In a pure tuning, the generator is exactly a half of [[3/2]]. But the alternative generator, a quartertone, with size around 49¢ is rather easier to grasp.

Triploid dicot temperaments usually generate the [[3L 12s]], [[3L 15s]], and [[3L 18s]] MOS structures.

== Intervals and notation ==
While there is no agreed-upon notation system for triploid dicot, the following is based on interpreting the generator as a quartertone (1/6 of a minor third), allowing for an ^ or v to stand for 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), along with [[neutral chain-of-fifths notation]], so vvC# and ^Db are enharmonic.

{| class="wikitable"
|+ style="font-size: 105%;" | Triploid monocot intervals (assuming pure fifth and octave)
|-
! rowspan="2" | #
! colspan="3" | Ploid 1
! colspan="3" | Ploid 2
! colspan="3" | Ploid 3
|-
! Cents
! Notation
! Name
! Cents
! Notation
! Name
! Cents
! Notation
! Name
|-
| −12
| 211.73
| ^D
| —
| 611.73
| F#
| augmented fourth
| 1011.73
| vA#
| —
|-
| −11
| 260.75
| Dt
| semiaugmented second
| 660.75
| vFt#
| —
| 1060.75
| ^Bd
| —
|-
| −10
| 309.78
| vD#
| —
| 709.78
| ^G
| —
| 1109.78
| B
| major seventh
|-
| −9
| 358.80
| ^Ed
| —
| 758.80
| Gt
| semiaugmented fifth
| 1158.80
| vBt
| —
|-
| −8
| 7.82
| ^C
| —
| 407.82
| E
| major third
| 807.82
| vG#
| —
|-
| −7
| 56.84
| Ct
| semiaugmented unison
| 456.84
| vEt
| —
| 856.84
| ^Ad
| —
|-
| −6
| 105.87
| vC#
| —
| 505.87
| ^F
| —
| 905.87
| A
| major sixth
|-
| −5
| 154.89
| ^Dd
| —
| 554.89
| Ft
| semiaugmented fourth
| 954.89
| vAt
| —
|-
| −4
| 203.91
| D
| major second
| 603.91
| vF#
| —
| 1003.91
| ^Bb
| —
|-
| −3
| 252.93
| vDt
| —
| 652.93
| ^Gd
| —
| 1052.93
| Bd
| neutral seventh
|-
| −2
| 301.96
| ^Eb
| —
| 701.96
| G
| perfect fifth
| 1101.96
| vB
| —
|-
| −1
| 350.98
| Ed
| neutral third
| 750.98
| vGt
| —
| 1150.98
| ^Cd
| —
|-
| 0
| 0
| C
| unison
| 400
| vE
| —
| 800
| ^Ab
| —
|-
| 1
| 49.02
| vCt
| —
| 449.02
| ^Fd
| —
| 849.02
| Ad
| neutral sixth
|-
| 2
| 98.04
| ^Db
| —
| 498.04
| F
| perfect fourth
| 898.04
| vA
| —
|-
| 3
| 147.07
| Dd
| neutral second
| 547.07
| vFt
| —
| 947.07
| ^Bdb
| —
|-
| 4
| 196.09
| vD
| —
| 596.09
| ^Gb
| —
| 996.09
| Bb
| minor seventh
|-
| 5
| 245.11
| ^Edb
| —
| 645.11
| Gd
| semidiminished fifth
| 1045.11
| vBd
| —
|-
| 6
| 294.13
| Eb
| minor third
| 694.13
| vG
| —
| 1094.13
| ^Cb
| —
|-
| 7
| 343.16
| vEd
| —
| 743.16
| ^Adb
| —
| 1143.16
| Cd
| semidiminished octave
|-
| 8
| 392.18
| ^Fb
| —
| 792.18
| Ab
| minor sixth
| 1192.18
| vC
| —
|-
| 9
| 41.20
| ^Ddb
| —
| 441.20
| Fd
| semidiminished fourth
| 841.20
| vAd
| —
|-
| 10
| 90.22
| Db
| minor second
| 490.22
| vF
| —
| 890.22
| ^Bbb
| —
|-
| 11
| 139.25
| vDd
| —
| 539.25
| ^Gdb
| —
| 939.25
| Bdb
| semidiminished seventh
|-
| 12
| 188.27
| ^Ebb
| —
| 588.27
| Gb
| diminished fifth
| 988.27
| vBb
| —
|}

== Temperament interpretations ==
An obvious interpretation for triploid dicot is [[hemiaug]]. The period is [[5/4]][[~]][[14/11]] and the generator is [[36/35]]~[[40/39]]~[[45/44]], so that [[3/2]] is two periods down two generators, [[7/4]] at one octave down five generators, [[11/8]] at two periods down five generators, and [[13/8]] at two periods up one generator.

[[Category:Ploidacot|Triploid dicot]]

Ploidacot/Triploid dicot - Revision history

Xenllium at 11:32, 6 January 2026

Xenllium: /* Temperament interpretations */