Ploidacot/Hexacot - Revision history

Squib: /* Temperament interpretations */

2026-03-06T21:06:31Z

Temperament interpretations

← Older revision		Revision as of 21:06, 6 March 2026
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for hexacot is [[miracle]], where the generator is [[16/15]]~[[15/14]], three of them make [[11/9]], and six of them make a perfect fifth. ~~There are some~~ extensions for ~~the 13-limit: miraculous (31 & 41), benediction (31 & 72), and manna (41 & 72)~~.		An obvious interpretation for hexacot is [[miracle]], where the generator is [[16/15]]~[[15/14]], three of them make [[11/9]], and six of them make a perfect fifth. See [[miracle extensions]] for extensions.

	[[Category:Ploidacots\|Hexacot]]		[[Category:Ploidacots\|Hexacot]]

Xenllium at 22:58, 8 January 2026

2026-01-08T22:58:16Z

← Older revision		Revision as of 22:58, 8 January 2026
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	{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=6\|Pergen=[P8, P5/6]\|Forms=10, 11, 21, 31\|Title=Hexacot\|Wedgie=6}}		{{Infobox ploidacot\|Ploids=1\|Shears=0\|Cots=6\|Pergen=[P8, P5/6]\|Forms=10, 11, 21, 31\|Title=Hexacot\|Wedgie=6}}
	'''Hexacot''' is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Hexacot temperaments also include all [[Ploidacot/Dicot\|dicot]] and [[Ploidacot/Tricot\|tricot]] intervals, as the dicot generator is split further into three, or the tricot generator is split further into two. Hexacot temperaments typically generate the [[1L 9s]] and [[10L 1s]] MOS scales, .		'''Hexacot''' is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Hexacot temperaments also include all [[Ploidacot/Dicot\|dicot]] and [[Ploidacot/Tricot\|tricot]] intervals, as the dicot generator is split further into three, or the tricot generator is split further into two. Hexacot temperaments typically generate the [[1L 9s]] and [[10L 1s]] MOS scales.

	== Intervals and notation ==		== Intervals and notation ==
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	\| major third		\| major third
	\|}		\|}

			A notable feature of hexacot is the small diesis, known as the [[quark]], encountered after 10 steps, which represents one-third of a diatonic semitone. This makes hexacot scales cluster around [[10edo]].

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

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=0|Cots=6|Pergen=[P8, P5/6]|Forms=10, 11, 21, 31|Title=Hexacot|Wedgie=6}} '''Hexacot''' is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Hexacot temperaments also include all dicot and tricot intervals, as the dicot generator is split further into three, or the tricot..."

2026-01-08T22:56:30Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=0|Cots=6|Pergen=[P8, P5/6]|Forms=10, 11, 21, 31|Title=Hexacot|Wedgie=6}} '''Hexacot''' is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Hexacot temperaments also include all dicot and tricot intervals, as the dicot generator is split further into three, or the tricot..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=0|Cots=6|Pergen=[P8, P5/6]|Forms=10, 11, 21, 31|Title=Hexacot|Wedgie=6}}
'''Hexacot''' is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Hexacot temperaments also include all [[Ploidacot/Dicot|dicot]] and [[Ploidacot/Tricot|tricot]] intervals, as the dicot generator is split further into three, or the tricot generator is split further into two. Hexacot temperaments typically generate the [[1L 9s]] and [[10L 1s]] MOS scales, .

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

{| class="wikitable"
|+ style="font-size: 105%;" | Hexacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −24
| 792.180
| Ab
| minor sixth
|-
| −23
| 909.172
|
|
|-
| −22
| 1026.165
|
|
|-
| −21
| 1143.157
| Cd
| semidiminished octave
|-
| −20
| 60.150
|
|
|-
| −19
| 177.142
|
|
|-
| −18
| 294.135
| Eb
| minor third
|-
| −17
| 411.127
|
|
|-
| −16
| 528.120
|
|
|-
| −15
| 645.112
| Gd
| semidiminished fifth
|-
| −14
| 762.105
|
|
|-
| −13
| 879.097
|
|
|-
| −12
| 996.090
| Bb
| minor seventh
|-
| −11
| 1113.082
|
|
|-
| −10
| 30.075
|
|
|-
| −9
| 147.067
| Dd
| neutral second
|-
| −8
| 264.060
|
|
|-
| −7
| 381.052
|
|
|-
| −6
| 498.045
| F
| perfect fourth
|-
| −5
| 615.037
|
|
|-
| −4
| 732.030
|
|
|-
| −3
| 849.022
| Ad
| neutral sixth
|-
| −2
| 966.015
|
|
|-
| −1
| 1083.007
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 116.993
|
|
|-
| 2
| 233.985
|
|
|-
| 3
| 350.978
| Ed
| neutral third
|-
| 4
| 467.970
|
|
|-
| 5
| 584.963
|
|
|-
| 6
| 701.955
| G
| perfect fifth
|-
| 7
| 818.948
|
|
|-
| 8
| 935.940
|
|
|-
| 9
| 1052.933
| Bd
| neutral seventh
|-
| 10
| 1169.925
|
|
|-
| 11
| 86.918
|
|
|-
| 12
| 203.910
| D
| major second
|-
| 13
| 320.903
|
|
|-
| 14
| 437.895
|
|
|-
| 15
| 554.888
| Ft
| semiaugmented fourth
|-
| 16
| 671.880
|
|
|-
| 17
| 788.873
|
|
|-
| 18
| 905.865
| A
| major sixth
|-
| 19
| 1022.858
|
|
|-
| 20
| 1139.850
|
|
|-
| 21
| 56.843
| Ct
| semiaugmented unison
|-
| 22
| 173.835
|
|
|-
| 23
| 290.828
|
|
|-
| 24
| 407.820
| E
| major third
|}

== Temperament interpretations ==
An obvious interpretation for hexacot is [[miracle]], where the generator is [[16/15]]~[[15/14]], three of them make [[11/9]], and six of them make a perfect fifth. There are some extensions for the 13-limit: miraculous (31 & 41), benediction (31 & 72), and manna (41 & 72).

[[Category:Ploidacots|Hexacot]]