Ploidacot/Pentacot - Revision history

Xenllium at 23:18, 7 January 2026

2026-01-07T23:18:09Z

← Older revision		Revision as of 23:18, 7 January 2026
Line 3:		Line 3:
	'''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Pentacot temperaments typically generate the [[8L 1s]], [[9L 8s]], and [[17L 9s]] MOS scales.		'''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Pentacot temperaments typically generate the [[8L 1s]], [[9L 8s]], and [[17L 9s]] MOS scales.

	== ~~Notation~~ ==		== Intervals and notation ==
	There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).		There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

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	An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are some extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).		An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are some extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Pentacot]]

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

2026-01-06T09:43:32Z

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

← Older revision		Revision as of 09:43, 6 January 2026
Line 223:		Line 223:
	An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are some extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).		An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are some extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).

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

Xenllium at 15:17, 4 January 2026

2026-01-04T15:17:28Z

← Older revision		Revision as of 15:17, 4 January 2026
Line 4:		Line 4:

	== Notation ==		== Notation ==
	There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).		There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

	{\| class="wikitable"		{\| class="wikitable"
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	== Temperament interpretations ==		== Temperament interpretations ==
	An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are ~~many~~ extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).		An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are some extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).

	[[Category:Ploidacot]]		[[Category:Ploidacot]]

Xenllium: /* Notation */

2026-01-04T14:52:41Z

Notation

← Older revision		Revision as of 14:52, 4 January 2026
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	== Notation ==		== Notation ==
	There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather ~~their sum~~. Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).		There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

	{\| class="wikitable"		{\| class="wikitable"

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=0|Cots=5|Pergen=[P8, P5/5]|Forms=8, 9, 17, 26|Title=Pentacot|Wedgie=5}} '''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Pentacot temperaments typically generate the 8L 1s, 9L 8s, and 17L 9s MOS scales. == Notation == There is no agreed-upon notation for..."

2026-01-04T13:24:36Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=0|Cots=5|Pergen=[P8, P5/5]|Forms=8, 9, 17, 26|Title=Pentacot|Wedgie=5}} '''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Pentacot temperaments typically generate the 8L 1s, 9L 8s, and 17L 9s MOS scales. == Notation == There is no agreed-upon notation for..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=0|Cots=5|Pergen=[P8, P5/5]|Forms=8, 9, 17, 26|Title=Pentacot|Wedgie=5}}
'''Pentacot''' is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Pentacot temperaments typically generate the [[8L 1s]], [[9L 8s]], and [[17L 9s]] MOS scales.

== Notation ==
There is no agreed-upon notation for pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather their sum. Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

{| class="wikitable"
|+ style="font-size: 105%;" | Pentacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −20
| 792.180
| Ab
| minor sixth
|-
| −19
| 932.571
|
|
|-
| −18
| 1072.962
|
|
|-
| −17
| 13.353
|
|
|-
| −16
| 153.744
|
|
|-
| −15
| 294.135
| Eb
| minor third
|-
| −14
| 434.526
|
|
|-
| −13
| 574.917
|
|
|-
| −12
| 715.308
|
|
|-
| −11
| 845.699
|
|
|-
| −10
| 996.090
| Bb
| minor seventh
|-
| −9
| 1136.481
|
|
|-
| −8
| 76.872
|
|
|-
| −7
| 217.263
|
|
|-
| −6
| 357.654
|
|
|-
| −5
| 498.045
| F
| perfect fourth
|-
| −4
| 638.436
|
|
|-
| −3
| 778.827
|
|
|-
| −2
| 919.218
|
|
|-
| −1
| 1059.609
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 140.391
|
|
|-
| 2
| 280.782
|
|
|-
| 3
| 421.173
|
|
|-
| 4
| 561.564
|
|
|-
| 5
| 701.955
| G
| perfect fifth
|-
| 6
| 842.346
|
|
|-
| 7
| 982.737
|
|
|-
| 8
| 1123.128
|
|
|-
| 9
| 63.519
|
|
|-
| 10
| 203.910
| D
| major second
|-
| 11
| 344.301
|
|
|-
| 12
| 484.692
|
|
|-
| 13
| 625.083
|
|
|-
| 14
| 765.474
|
|
|-
| 15
| 905.865
| A
| major sixth
|-
| 16
| 1046.256
|
|
|-
| 17
| 1186.647
|
|
|-
| 18
| 127.038
|
|
|-
| 19
| 267.429
|
|
|-
| 20
| 407.820
| E
| major third
|}

== Temperament interpretations ==
An obvious interpretation for pentacot is [[glacier]], a 2.3.13 subgroup temperament, where the generator is [[13/12]] and five of them make a perfect fifth. There are many extensions for full 13-limit: [[jerome]] (26 & 43), [[tsaharuk]] (77 & 94), and [[quanic]] (94 & 111).

[[Category:Ploidacot]]