Ploidacot/Triploid monocot - Revision history

Overthink: formatting; unify precision

2026-03-28T02:44:40Z

formatting; unify precision

← Older revision		Revision as of 02:44, 28 March 2026
Line 5:		Line 5:
	While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 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]]), so vvC# and ^Db are enharmonic.		While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 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]]), so vvC# and ^Db are enharmonic.

	{\| class="wikitable"		{\| class="wikitable center-1 right-2 right-5 right-8"
	\|+ style="font-size: 105%;" \| Triploid monocot intervals (assuming pure fifth and octave)		\|+ style="font-size: 105%;" \| Triploid monocot intervals (assuming pure fifth and octave)
	\|-		\|-
Line 90:		Line 90:
	\|-		\|-
	\| 0		\| 0
	\| 0		\| 0.00
	\| C		\| C
	\| unison		\| unison
	\| 400		\| 400.00
	\| vE		\| vE
	\| —		\| —
	\| 800		\| 800.00
	\| ^Ab		\| ^Ab
	\| —		\| —

Overthink: note range

2026-03-28T02:27:36Z

note range

← Older revision		Revision as of 02:27, 28 March 2026
Line 1:		Line 1:
	{{Breadcrumb}}{{Infobox ploidacot\|Ploids=3\|Shears=0\|Cots=1\|Pergen=[P8/3, P5]\|Forms=9, 12, 15, 27\|Title=Triploid monocot\|Wedgie=3}}		{{Breadcrumb}}{{Infobox ploidacot\|Ploids=3\|Shears=0\|Cots=1\|Pergen=[P8/3, P5]\|Forms=9, 12, 15, 27\|Title=Triploid monocot\|Wedgie=3}}
	'''Triploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is 1/3 of a [[2/1]] octave, or 400{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the [[3L 6s]] MOS structure and either [[3L 9s]] (and thus [[12L 3s]]) or [[9L 3s]] as children.		'''Triploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is 1/3 of a [[2/1]] octave, or 400{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the [[3L 6s]] MOS structure and either [[3L 9s]] (and thus [[12L 3s]]) or [[9L 3s]] (when the fifth is flatter than [[12edo\|7\12]]) as children.

	== Intervals and notation ==		== Intervals and notation ==

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

2026-01-06T09:44:29Z

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

← Older revision		Revision as of 09:44, 6 January 2026
Line 175:		Line 175:
	[[Augmented family\|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period.		[[Augmented family\|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period.

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

Xenllium at 22:19, 5 January 2026

2026-01-05T22:19:53Z

← Older revision		Revision as of 22:19, 5 January 2026
Line 175:		Line 175:
	[[Augmented family\|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period.		[[Augmented family\|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period.

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

Xenllium at 13:06, 5 January 2026

2026-01-05T13:06:06Z

Show changes

Xenllium: /* Notation */

2026-01-04T14:58:57Z

Notation

← Older revision		Revision as of 14:58, 4 January 2026
Line 5:		Line 5:
	Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" 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 triploid monocot intervals align with standard monocot intervals.		Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" 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 triploid monocot intervals align with standard monocot intervals.

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

	{\| class="wikitable"		{\| class="wikitable"

Xenllium at 03:30, 4 January 2026

2026-01-04T03:30:28Z

Show changes

Xenllium: Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15|Title=Triploid monocot|Wedgie=3}} '''Triploid monocot''' is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/3 of a 2/1 octave, or 400{{c}}. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" $\frac{2\sqrt[3]{4}}{3}$ . Triploid monocot temperaments usually generate the 3L 6..."

2026-01-04T02:39:15Z

Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15|Title=Triploid monocot|Wedgie=3}} '''Triploid monocot''' is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/3 of a 2/1 octave, or 400{{c}}. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the 3L 6..."

New page

{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15|Title=Triploid monocot|Wedgie=3}}
'''Triploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is 1/3 of a [[2/1]] octave, or 400{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the [[3L 6s]] MOS structure and either [[3L 9s]] (and thus [[12L 3s]]) or [[9L 3s]] as children.

== Notation ==
Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" 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 triploid monocot intervals align with standard monocot intervals.

{| 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
! Name
! Notation
! Cents
! Name
! Notation
! Cents
! Name
! Notation
|-
| −5
| 90.22
| minor second
| Db
| 490.22
| —
| —
| 890.22
| —
| —
|-
| −4
| 392.18
| —
| —
| 792.18
| minor sixth
| Ab
| 1192.18
| —
| —
|-
| −3
| 294.13
| minor third
| Eb
| 694.13
| —
| —
| 1094.13
| —
| —
|-
| −2
| 196.09
| —
| —
| 596.09
| —
| —
| 996.09
| minor seventh
| Bb
|-
| −1
| 98.04
| —
| —
| 498.04
| perfect fourth
| F
| 898.04
| —
| —
|-
| 0
| 0
| unison
| C
| 400
| —
| —
| 800
| —
| —
|-
| 1
| 301.96
| —
| —
| 701.96
| perfect fifth
| G
| 1101.96
| —
| —
|-
| 2
| 203.91
| major second
| D
| 603.91
| —
| —
| 1003.91
| —
| —
|-
| 3
| 105.87
| —
| —
| 505.87
| —
| —
| 905.87
| major sixth
| A
|-
| 4
| 7.82
| —
| —
| 407.82
| major third
| E
| 807.82
| —
| —
|-
| 5
| 309.78
| —
| —
| 709.78
| —
| —
| 1109.78
| major seventh
| B
|}

== Temperament interpretations ==
By definition, triploid monocot temperaments equate some interval to its octave complement.

=== Augmented ===
[[Augmented family|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit or higher prime limits: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9).

[[Category:Ploidacot]]