Ploidacot/Beta-hexacot - Revision history

ArrowHead294 at 12:29, 26 January 2026

2026-01-26T12:29:38Z

← Older revision		Revision as of 12:29, 26 January 2026
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	{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=6\|Pergen=[P8, ccP5/6]\|Forms=16, 23, 30, 37\|Title=Beta-hexacot\|Wedgie=6}}		{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=6\|Pergen=[P8, ccP5/6]\|Forms=16, 23, 30, 37\|Title=Beta-hexacot\|Wedgie=6}}
	'''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about ~~516–518¢~~, six of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth), and the period is a [[2/1]] octave. Beta-hexacot temperaments also include all [[Ploidacot/Dicot\|dicot]] and [[Ploidacot/Omega-tricot\|omega-tricot]] intervals. Beta-hexacot temperaments typically generate the [[7L 2s]], [[7L 9s]], and [[7L 16s]] MOS scales.		'''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about 516–518{{c}}, six of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth), and the period is a [[2/1]] octave. Beta-hexacot temperaments also include all [[Ploidacot/Dicot\|dicot]] and [[Ploidacot/Omega-tricot\|omega-tricot]] intervals. Beta-hexacot temperaments typically generate the [[7L 2s]], [[7L 9s]], and [[7L 16s]] MOS scales.

	== Intervals and notation ==		== Intervals and notation ==
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], two of which make [[20/11]], three make [[11/9]]~[[27/22]] above an octave, and six make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo (65d & 72), zarvo (65 & 72), and gravid (58 & 65).		An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], two of which make [[20/11]], three make {{nowrap\|[[11/9]]~[[27/22]]}} above an octave, and six make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo ({{nowrap\|65d & 72}}), zarvo ({{nowrap\|65 & 72}}), and gravid ({{nowrap\|58 & 65}}).

	[[Category:Ploidacots\|Beta-hexacot]]		[[Category:Ploidacots\|Beta-hexacot]]

Xenllium at 07:55, 26 January 2026

2026-01-26T07:55:08Z

Show changes

Xenllium: /* Temperament interpretations */

2026-01-10T07:01:32Z

Temperament interpretations

← Older revision		Revision as of 07:01, 10 January 2026
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], three ~~of them~~ make [[11/9]] above an octave, and six ~~of them~~ make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo (65d & 72), zarvo (65 & 72), and gravid (58 & 65).		An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], two of which make [[20/11]], three make [[11/9]]~[[27/22]] above an octave, and six make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo (65d & 72), zarvo (65 & 72), and gravid (58 & 65).

	[[Category:Ploidacots\|Beta-hexacot]]		[[Category:Ploidacots\|Beta-hexacot]]

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=6|Pergen=[P8, ccP5/6]|Forms=16, 23, 30, 37|Title=Beta-hexacot|Wedgie=6}} '''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about 516–518¢, six of which make 6/1 (sixth harmonic, two octaves above a perfect fifth), and the period is a 2/1 octave. Beta-hexacot temperaments also include all dicot and omega-tricot intervals..."

2026-01-10T03:55:02Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=6|Pergen=[P8, ccP5/6]|Forms=16, 23, 30, 37|Title=Beta-hexacot|Wedgie=6}} '''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about 516–518¢, six of which make 6/1 (sixth harmonic, two octaves above a perfect fifth), and the period is a 2/1 octave. Beta-hexacot temperaments also include all dicot and omega-tricot intervals..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=2|Cots=6|Pergen=[P8, ccP5/6]|Forms=16, 23, 30, 37|Title=Beta-hexacot|Wedgie=6}}
'''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about 516–518¢, six of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth), and the period is a [[2/1]] octave. Beta-hexacot temperaments also include all [[Ploidacot/Dicot|dicot]] and [[Ploidacot/Omega-tricot|omega-tricot]] intervals. Beta-hexacot temperaments typically generate the [[7L 2s]], [[7L 9s]], and [[7L 16s]] MOS scales.

== Intervals and notation ==
Due to dividing the sixth harmonic into so many steps, standard notation becomes almost useless for beta-hexacot. Regardless, notation has been provided for where beta-hexacot intervals align with standard dicot intervals (which use [[neutral chain-of-fifths notation]]).

{| class="wikitable"
|+ style="font-size: 105%;" | Beta-hexacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −24
| 792.180
| Ab
| minor sixth
|-
| −23
| 109.172
|
|
|-
| −22
| 626.165
|
|
|-
| −21
| 1143.157
| Cd
| semidiminished octave
|-
| −20
| 460.150
|
|
|-
| −19
| 977.142
|
|
|-
| −18
| 294.135
| Eb
| minor third
|-
| −17
| 811.127
|
|
|-
| −16
| 128.120
|
|
|-
| −15
| 645.112
| Gd
| semidiminished fifth
|-
| −14
| 1162.105
|
|
|-
| −13
| 479.097
|
|
|-
| −12
| 996.090
| Bb
| minor seventh
|-
| −11
| 313.082
|
|
|-
| −10
| 830.075
|
|
|-
| −9
| 147.067
| Dd
| neutral second
|-
| −8
| 664.060
|
|
|-
| −7
| 1181.052
|
|
|-
| −6
| 498.045
| F
| perfect fourth
|-
| −5
| 1015.037
|
|
|-
| −4
| 332.030
|
|
|-
| −3
| 849.022
| Ad
| neutral sixth
|-
| −2
| 166.015
|
|
|-
| −1
| 683.007
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 516.993
|
|
|-
| 2
| 1033.985
|
|
|-
| 3
| 350.978
| Ed
| neutral third
|-
| 4
| 867.970
|
|
|-
| 5
| 184.963
|
|
|-
| 6
| 701.955
| G
| perfect fifth
|-
| 7
| 18.948
|
|
|-
| 8
| 535.940
|
|
|-
| 9
| 1052.933
| Bd
| neutral seventh
|-
| 10
| 369.925
|
|
|-
| 11
| 886.918
|
|
|-
| 12
| 203.910
| D
| major second
|-
| 13
| 720.903
|
|
|-
| 14
| 37.895
|
|
|-
| 15
| 554.888
| Ft
| semiaugmented fourth
|-
| 16
| 1071.880
|
|
|-
| 17
| 388.873
|
|
|-
| 18
| 905.865
| A
| major sixth
|-
| 19
| 222.858
|
|
|-
| 20
| 739.850
|
|
|-
| 21
| 56.843
| Ct
| semiaugmented unison
|-
| 22
| 573.835
|
|
|-
| 23
| 1090.828
|
|
|-
| 24
| 407.820
| E
| major third
|}

== Temperament interpretations ==
An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], three of them make [[11/9]] above an octave, and six of them make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo (65d & 72), zarvo (65 & 72), and gravid (58 & 65).

[[Category:Ploidacots|Beta-hexacot]]