Ploidacot/Tetraploid monocot - Revision history

FilterNashi: /* Bidia */

2026-01-31T03:21:35Z

Bidia

← Older revision		Revision as of 03:21, 31 January 2026
Line 221:		Line 221:

	=== Bidia ===		=== Bidia ===
	Bidia is a weak [[extension]] for diaschismic temperament and splits the period again into 1/4 octave. It has very clear extensions through 23-limit. It behaves very well by tempering two [[17/12]]'s or four [[19/16]]'s into one octave in the 17- and 19-limit. It sets ~[[25/21]] also ~[[19/16]] as a period.		Bidia is a weak [[extension]] for diaschismic temperament and splits the period again into 1/4 octave. It has very clear extensions through 23-limit. It behaves very well by tempering two [[17/12]]<nowiki/>s or four [[19/16]]<nowiki/>s into one octave in the 17- and 19-limit. It sets ~[[25/21]] also ~[[19/16]] as a period.

	See [[Diaschismic family #Bidia]] for details.		See [[Diaschismic family #Bidia]] for details.

	=== Undim ===		=== Undim ===

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

2026-01-06T09:44:28Z

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

← Older revision		Revision as of 09:44, 6 January 2026
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	See [[Undim family #Undim]] for details.		See [[Undim family #Undim]] for details.

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

FloraC: /* Temperament interpretations */ cleanup

2026-01-06T09:39:57Z

Temperament interpretations: cleanup

← Older revision		Revision as of 09:39, 6 January 2026
Line 216:		Line 216:

	=== Diminished ===		=== Diminished ===
			{{Main\| Diminished (temperament) }}

	Diminished temperament sets [[6/5]]~[[7/6]] as a period, and uses a fifth as a free generator.		Diminished temperament sets [[6/5]]~[[7/6]] as a period, and uses a fifth as a free generator.

	~~main article: [[Diminished_(temperament)\|Diminished]]~~

	=== Bidia ===		=== Bidia ===
	Bidia is a weak [[extension]] for diaschismic temperament~~, split~~ the period again into 1/4 octave. It has very clear extensions through 23-limit. It behaves very well by tempering two [[17/12]]s or four [[19/16]]s into one octave in the 17- and 19-limit. It sets ~[[25/21]] also ~[[19/16]] as a period.		Bidia is a weak [[extension]] for diaschismic temperament and splits the period again into 1/4 octave. It has very clear extensions through 23-limit. It behaves very well by tempering two [[17/12]]'s or four [[19/16]]'s into one octave in the 17- and 19-limit. It sets ~[[25/21]] also ~[[19/16]] as a period.

	See [[~~Diaschismic_family~~ #Bidia]] for ~~technical data~~.		See [[Diaschismic family #Bidia]] for details.

	=== Undim ===		=== Undim ===
	Undim was named for it is some sort of opposite to diminished~~<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>~~, and sets ~1215/1024 as a period.		Undim was named for it is some sort of opposite to diminished, and sets ~1215/1024 as a period.

	~~main article:~~ [[Undim family]]		See [[Undim family #Undim]] for details.

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

FilterNashi: /* Temperament interpretations */add more info about diminished, bidia and undim temperament

2026-01-06T09:35:16Z

Temperament interpretations: add more info about diminished, bidia and undim temperament

@@ Line 217: / Line 217: @@
 === Diminished ===
 Diminished temperament sets [[6/5]]~[[7/6]] as a period, and uses a fifth as a free generator.
 [[Category:Ploidacot|Tetraploid monocot]]

Xenllium: Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=4|Shears=0|Cots=1|Pergen=[P8/4, P5]|Forms=8, 12, 20, 32|Title=Tetraploid monocot|Wedgie=4}} '''Tetraploid monocot''' is a temperament archetype where the generator is a 3/2 perfect fifth and the period is a quarter of a 2/1 octave, or 300{{c}}. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" $\frac{3}{2\sqrt{2}}$ . Tetraploid monocot temperaments usually generate th..."

2026-01-05T23:09:10Z

Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=4|Shears=0|Cots=1|Pergen=[P8/4, P5]|Forms=8, 12, 20, 32|Title=Tetraploid monocot|Wedgie=4}} '''Tetraploid monocot''' is a temperament archetype where the generator is a 3/2 perfect fifth and the period is a quarter of a 2/1 octave, or 300{{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>. Tetraploid monocot temperaments usually generate th..."

New page

{{Breadcrumb}}{{Infobox ploidacot|Ploids=4|Shears=0|Cots=1|Pergen=[P8/4, P5]|Forms=8, 12, 20, 32|Title=Tetraploid monocot|Wedgie=4}}
'''Tetraploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is a quarter of a [[2/1]] octave, or 300{{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>. Tetraploid monocot temperaments usually generate the [[4L 4s]] MOS structure and either [[4L 8s]] (and thus [[12L 4s]]) or [[8L 4s]] as children.

== Intervals and notation ==
While there is no agreed-upon notation system for tetraploid monocot, the following is based on interpreting the generator as a semitone (half a whole tone), allowing for an ^ or v to stand for a quarter 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"
|+ style="font-size: 105%;" | Tetraploid monocot intervals (assuming pure fifth and octave)
|-
! rowspan="2" | #
! colspan="3" | Ploid 1
! colspan="3" | Ploid 2
! colspan="3" | Ploid 3
! colspan="3" | Ploid 4
|-
! Cents
! Notation
! Name
! Cents
! Notation
! Name
! Cents
! Notation
! Name
! Cents
! Notation
! Name
|-
| −6
| 288.27
| vEb
| —
| 588.27
| Gb
| diminished fifth
| 888.27
| ^Bbb
| —
| 1188.27
| vvC/^^Dbb
| —
|-
| −5
| 90.22
| Db
| minor second
| 390.22
| ^Fb
| —
| 690.22
| vvG/^^Abb
| —
| 990.22
| vBb
| —
|-
| −4
| 192.18
| vvD/^^Ebb
| —
| 492.18
| vF
| —
| 792.18
| Ab
| minor sixth
| 1092.18
| ^Cb
| —
|-
| −3
| 294.13
| Eb
| minor third
| 594.13
| ^Gb
| —
| 894.13
| vvA/^^Bbb
| —
| 1194.13
| vC
| —
|-
| −2
| 96.09
| ^Db
| —
| 396.09
| vvE/^^Fb
| —
| 696.09
| vG
| —
| 996.09
| Bb
| minor seventh
|-
| −1
| 198.04
| vD
| —
| 498.04
| F
| perfect fourth
| 798.04
| ^Ab
| —
| 1098.04
| vvB/^^Cb
| —
|-
| 0
| 0
| C
| unison
| 300
| ^Eb
| —
| 600
| vvF#/^^Gb
| —
| 900
| vA
| —
|-
| 1
| 101.96
| vvC#/^^Db
| —
| 401.96
| vE
| —
| 701.96
| G
| perfect fifth
| 1001.96
| ^Bb
| —
|-
| 2
| 203.91
| D
| major second
| 503.91
| ^F
| —
| 803.91
| vvG#/^^Ab
| —
| 1103.91
| vB
| —
|-
| 3
| 5.87
| ^C
| —
| 305.87
| vvD#/^^Eb
| —
| 605.87
| vF#
| —
| 905.87
| A
| major sixth
|-
| 4
| 107.82
| vC#
| —
| 407.82
| E
| major third
| 707.82
| ^G
| —
| 1007.82
| vvA#/^^Bb
| —
|-
| 5
| 209.78
| ^D
| —
| 509.78
| vvE#/^^F
| —
| 809.78
| vG#
| —
| 1109.78
| B
| major seventh
|-
| 6
| 11.73
| vvB#/^^C
| —
| 311.73
| vD#
| —
| 611.73
| F#
| augmented fourth
| 911.73
| ^A
| —
|}

A notable feature of tetraploid monocot is the small comma, encountered after 3 steps, which represents a quarter of a Pythagorean comma (or its equivalence, ''inversed'' diminished second). This makes tetraploid monocot scales cluster around 12edo.

== Temperament interpretations ==
By definition, tetraploid monocot temperaments split the octave in four.

=== Diminished ===
Diminished temperament sets [[6/5]]~[[7/6]] as a period, and uses a fifth as a free generator.

[[Category:Ploidacot|Tetraploid monocot]]