Ploidacot/Diploid tricot - Revision history

Xenllium at 12:58, 7 January 2026

2026-01-07T12:58:07Z

← Older revision		Revision as of 12:58, 7 January 2026
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			\|+ style="font-size: 105%;" \| Diploid tricot intervals (assuming pure fifth and octave)
	\|-		\|-
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	Here, there is one obvious temperament, [[baladic]], which is useful for the 2.3.7.13.17 subgroup. It tempers out [[169/168]], which splits [[7/6]] in half (13/12~14/13) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]].		Here, there is one obvious temperament, [[baladic]], which is useful for the 2.3.7.13.17 subgroup. It tempers out [[169/168]], which splits [[7/6]] in half (13/12~14/13) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]].

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Diploid tricot]]

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

2026-01-06T09:44:15Z

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

← Older revision		Revision as of 09:44, 6 January 2026
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	Here, there is one obvious temperament, [[baladic]], which is useful for the 2.3.7.13.17 subgroup. It tempers out [[169/168]], which splits [[7/6]] in half (13/12~14/13) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]].		Here, there is one obvious temperament, [[baladic]], which is useful for the 2.3.7.13.17 subgroup. It tempers out [[169/168]], which splits [[7/6]] in half (13/12~14/13) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]].

	[[Category:~~Ploidacot~~]]		[[Category:Ploidacots]]

Xenllium at 09:11, 4 January 2026

2026-01-04T09:11:22Z

← Older revision		Revision as of 09:11, 4 January 2026
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	== Intervals and notation ==		== Intervals and notation ==
	Diploid tricot 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. Note and interval names are provided where diploid ~~dicot~~ intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).		Diploid tricot 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. Note and interval names are provided where diploid tricot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

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			A notable feature of diploid tricot is encountering the following small intervals:
			* 1/3 of a [[diatonic semitone]] (encountered after 5 steps)
			* half of an ''inversed'' diminished second (encountered after 18 steps, representing a half of [[Pythagorean comma]])

	== Temperament interpretations ==		== Temperament interpretations ==

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=2|Shears=0|Cots=3|Pergen=[P8/2, P5/3]|Forms=10, 16, 26, 36|Title=Diploid tricot|Wedgie=6}} '''Diploid tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a perfect fifth (233.98{{c}}). Diploid tricot temperaments usually generate the 4L 2s, 6L 4s, and 10L 6s MOS structures. == Intervals and notation == Diploid tricot notation is complicated a..."

2026-01-04T08:10:12Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=2|Shears=0|Cots=3|Pergen=[P8/2, P5/3]|Forms=10, 16, 26, 36|Title=Diploid tricot|Wedgie=6}} '''Diploid tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a perfect fifth (233.98{{c}}). Diploid tricot temperaments usually generate the 4L 2s, 6L 4s, and 10L 6s MOS structures. == Intervals and notation == Diploid tricot notation is complicated a..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=2|Shears=0|Cots=3|Pergen=[P8/2, P5/3]|Forms=10, 16, 26, 36|Title=Diploid tricot|Wedgie=6}}

'''Diploid tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a perfect fifth (233.98{{c}}).

Diploid tricot temperaments usually generate the [[4L 2s]], [[6L 4s]], and [[10L 6s]] MOS structures.

== Intervals and notation ==
Diploid tricot 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. Note and interval names are provided where diploid dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

{| class="wikitable"
|-
! rowspan="2" | #
! colspan="3" | Ploid 1
! colspan="3" | Ploid 2
|-
! Cents
! Notation
! Name
! Cents
! Notation
! Name
|-
| -13
| 558.195
|
|
| 1158.195
|
|
|-
| -12
| 192.180
|
|
| 792.180
| Ab
| minor sixth
|-
| -11
| 426.165
|
|
| 1026.165
|
|
|-
| -10
| 60.150
|
|
| 660.150
|
|
|-
| -9
| 294.135
| Eb
| minor third
| 894.135
|
|
|-
| -8
| 528.120
|
|
| 1128.120
|
|
|-
| -7
| 162.105
|
|
| 762.105
|
|
|-
| -6
| 396.090
|
|
| 996.090
| Bb
| minor seventh
|-
| -5
| 30.075
|
|
| 630.075
|
|
|-
| -4
| 264.060
|
|
| 864.060
|
|
|-
| -3
| 498.045
| F
| perfect fourth
| 1098.045
|
|
|-
| -2
| 132.030
|
|
| 732.030
|
|
|-
| -1
| 366.015
|
|
| 966.015
|
|
|-
| 0
| 0
| C
| perfect unison
| 600
|
|
|-
| 1
| 233.985
|
|
| 833.985
|
|
|-
| 2
| 467.970
|
|
| 1067.970
|
|
|-
| 3
| 101.955
|
|
| 701.955
| G
| perfect fifth
|-
| 4
| 335.940
|
|
| 935.940
|
|
|-
| 5
| 569.925
|
|
| 1169.925
|
|
|-
| 6
| 203.910
| D
| major second
| 803.910
|
|
|-
| 7
| 437.895
|
|
| 1037.895
|
|
|-
| 8
| 71.880
|
|
| 671.880
|
|
|-
| 9
| 305.865
|
|
| 905.865
| A
| major sixth
|-
| 10
| 539.850
|
|
| 1139.850
|
|
|-
| 11
| 173.835
|
|
| 773.835
|
|
|-
| 12
| 407.820
| E
| major third
| 1007.820
|
|
|-
| 13
| 41.805
|
|
| 641.805
|
|
|}

== Temperament interpretations ==
Here, there is one obvious temperament, [[baladic]], which is useful for the 2.3.7.13.17 subgroup. It tempers out [[169/168]], which splits [[7/6]] in half (13/12~14/13) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]].

[[Category:Ploidacot]]