Ploidacot/Gamma-pentacot - Revision history

Xenllium at 23:46, 7 January 2026

2026-01-07T23:46:22Z

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

2026-01-06T09:43:16Z

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

← Older revision		Revision as of 09:43, 6 January 2026
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	An obvious interpretation for gamma-pentacot is [[amity]], 5/4 is equated to 4 octaves minus 13 generators, and 7/4 is equated to 17 generators minus 4 octaves. Other interpretations include [[sixix]], which interprets 6/5 as a generator.		An obvious interpretation for gamma-pentacot is [[amity]], 5/4 is equated to 4 octaves minus 13 generators, and 7/4 is equated to 17 generators minus 4 octaves. Other interpretations include [[sixix]], which interprets 6/5 as a generator.

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

Xenllium at 13:48, 5 January 2026

2026-01-05T13:48:35Z

← Older revision		Revision as of 13:48, 5 January 2026
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=3\|Cots=5\|Pergen=[P8, P11/5]\|Forms=7, 11, 18, 25, 32\|Title=Gamma-pentacot\|Wedgie=5}}		{{Infobox ploidacot\|Ploids=1\|Shears=3\|Cots=5\|Pergen=[P8, P11/5]\|Forms=7, 11, 18, 25, 32\|Title=Gamma-pentacot\|Wedgie=5}}
	'''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]] and [[7L 4s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.		'''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]], [[7L 4s]], and [[7L 11s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.

	Gamma-pentacot temperaments often generate ~~[[7L 11s]],~~ 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly 18L 7s, 25L 7s, 32L 7s, or 39L 7s.		Gamma-pentacot temperaments often generate 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly flat tunings 18L 7s, 25L 7s, 32L 7s, or 39L 7s.

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

Xenllium at 12:48, 5 January 2026

2026-01-05T12:48:11Z

← Older revision		Revision as of 12:48, 5 January 2026
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	{{Breadcrumb}}		{{Breadcrumb}}
	{{Infobox ploidacot\|Ploids=1\|Shears=3\|Cots=5\|Pergen=[P8, P11/5]\|Forms=7, 11, 18, 25\|Title=Gamma-pentacot\|Wedgie=5}}		{{Infobox ploidacot\|Ploids=1\|Shears=3\|Cots=5\|Pergen=[P8, P11/5]\|Forms=7, 11, 18, 25, 32\|Title=Gamma-pentacot\|Wedgie=5}}
	'''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]] and [[7L 4s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.		'''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]] and [[7L 4s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.

	Gamma-pentacot temperaments often generate [[7L 11s]], 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly ~~sharp tunings~~ 39L 7s.		Gamma-pentacot temperaments often generate [[7L 11s]], 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly 18L 7s, 25L 7s, 32L 7s, or 39L 7s.

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

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=5|Pergen=[P8, P11/5]|Forms=7, 11, 18, 25|Title=Gamma-pentacot|Wedgie=5}} '''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Gamma-pentacot temperaments typically generate the 4L 3s and 7L 4s MOS scales, and they split the chromatic semitone into five equal parts, creating..."

2026-01-04T05:15:12Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=5|Pergen=[P8, P11/5]|Forms=7, 11, 18, 25|Title=Gamma-pentacot|Wedgie=5}} '''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Gamma-pentacot temperaments typically generate the 4L 3s and 7L 4s MOS scales, and they split the chromatic semitone into five equal parts, creating..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=3|Cots=5|Pergen=[P8, P11/5]|Forms=7, 11, 18, 25|Title=Gamma-pentacot|Wedgie=5}}
'''Gamma-pentacot''' is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Gamma-pentacot temperaments typically generate the [[4L 3s]] and [[7L 4s]] MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.

Gamma-pentacot temperaments often generate [[7L 11s]], 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly sharp tunings 39L 7s.

== Intervals and notation ==
While there is no agreed-upon notation system for gamma-pentacot, the notation provided here is based on interpreting the generator as a subneutral third, and allowing for an ^ or v to stand for 1/5 of a chromatic semitone, so ^^^C and vvC# are enharmonic.

{| class="wikitable"
|+ style="font-size: 105%;" | Gamma-pentacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −30
| 611.730
| F#
| augmented fourth
|-
| −29
| 951.339
| ^^A
|
|-
| −28
| 90.948
| vC#
|
|-
| −27
| 430.557
| ^E
|
|-
| −26
| 770.166
| vvG#
|
|-
| −25
| 1109.775
| B
| major seventh
|-
| −24
| 249.384
| ^^D
|
|-
| −23
| 588.993
| vF#
|
|-
| −22
| 928.602
| ^A
|
|-
| −21
| 68.211
| vvC#
|
|-
| −20
| 407.820
| E
| major third
|-
| −19
| 747.429
| ^^G
|
|-
| −18
| 1087.038
| vB
|
|-
| −17
| 226.647
| ^D
|
|-
| −16
| 566.256
| vvF#
|
|-
| −15
| 905.865
| A
| major sixth
|-
| −14
| 45.474
| ^^C
|
|-
| −13
| 385.083
| vE
|
|-
| −12
| 724.692
| ^G
|
|-
| −11
| 1064.301
| vvB
|
|-
| −10
| 203.910
| D
| major second
|-
| −9
| 543.519
| ^^F
|
|-
| −8
| 883.128
| vA
|
|-
| −7
| 22.737
| ^C
|
|-
| −6
| 362.346
| vvE
|
|-
| −5
| 701.955
| G
| perfect fifth
|-
| −4
| 1041.564
| ^^Bb
|
|-
| −3
| 181.173
| vD
|
|-
| −2
| 520.782
| ^F
|
|-
| −1
| 860.391
| vvA
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 339.609
| ^^Eb
|
|-
| 2
| 679.218
| vG
|
|-
| 3
| 1018.827
| ^Bb
|
|-
| 4
| 158.436
| vvD
|
|-
| 5
| 498.045
| F
| perfect fourth
|-
| 6
| 837.654
| ^^Ab
|
|-
| 7
| 1177.263
| vC
|
|-
| 8
| 316.872
| ^Eb
|
|-
| 9
| 656.481
| vvG
|
|-
| 10
| 996.090
| Bb
| minor seventh
|-
| 11
| 135.699
| ^^Db
|
|-
| 12
| 475.308
| vF
|
|-
| 13
| 814.917
| ^Ab
|
|-
| 14
| 1174.526
| vvC
|
|-
| 15
| 294.135
| Eb
| minor third
|-
| 16
| 633.744
| ^^Gb
|
|-
| 17
| 973.353
| vBb
|
|-
| 18
| 112.962
| ^Db
|
|-
| 19
| 452.571
| vvF
|
|-
| 20
| 792.180
| Ab
| minor sixth
|-
| 21
| 1131.789
| ^^Cb
|
|-
| 22
| 271.398
| vEb
|
|-
| 23
| 611.007
| ^Gb
|
|-
| 24
| 950.616
| vvBb
|
|-
| 25
| 90.225
| Db
| minor second
|-
| 26
| 429.834
| ^^Fb
|
|-
| 27
| 769.443
| vAb
|
|-
| 28
| 1109.052
| ^Cb
|
|-
| 29
| 248.661
| vvEb
|
|-
| 30
| 588.270
| Gb
| diminished fifth
|}

== Temperament interpretations ==
An obvious interpretation for gamma-pentacot is [[amity]], 5/4 is equated to 4 octaves minus 13 generators, and 7/4 is equated to 17 generators minus 4 octaves. Other interpretations include [[sixix]], which interprets 6/5 as a generator.

[[Category:Ploidacot]]