Ploidacot/Alpha-pentacot - Revision history

Xenllium at 23:19, 7 January 2026

2026-01-07T23:19:31Z

← Older revision		Revision as of 23:19, 7 January 2026
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	'''Alpha-pentacot''' is a temperament archetype where the generator is a submajor third of about 379–381¢, five of which make a perfect twelfth of [[3/1]] (third harmonic, also known as "tritave"), and the period is a [[2/1]] octave. Alpha-pentacot temperaments typically generate the [[3L 4s]], [[3L 7s]], [[3L 10s]], and [[3L 13s]] MOS scales, and either [[3L 16s]] (and thus [[19L 3s]]) or [[16L 3s]] as children.		'''Alpha-pentacot''' is a temperament archetype where the generator is a submajor third of about 379–381¢, five of which make a perfect twelfth of [[3/1]] (third harmonic, also known as "tritave"), and the period is a [[2/1]] octave. Alpha-pentacot temperaments typically generate the [[3L 4s]], [[3L 7s]], [[3L 10s]], and [[3L 13s]] MOS scales, and either [[3L 16s]] (and thus [[19L 3s]]) or [[16L 3s]] as children.

	== ~~Notation~~ ==		== Intervals and notation ==
	There is no agreed-upon notation for alpha-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 minor third. Note and interval names are provided where alpha-pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).		There is no agreed-upon notation for alpha-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 minor third. Note and interval names are provided where alpha-pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

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	* ''[https://youtube.com/watch?v=5iBXKRWE-_U Magical life]'' (2023) by [[User:Xenllium\|Xenllium]] – in 19-tone alpha-pentacot with pure fifths (also known as pure-fifth magic scale)		* ''[https://youtube.com/watch?v=5iBXKRWE-_U Magical life]'' (2023) by [[User:Xenllium\|Xenllium]] – in 19-tone alpha-pentacot with pure fifths (also known as pure-fifth magic scale)

	[[Category:Ploidacots]]		[[Category:Ploidacots\|Alpha-pentacot]]

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

2026-01-06T09:44:32Z

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

← Older revision		Revision as of 09:44, 6 January 2026
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	* ''[https://youtube.com/watch?v=5iBXKRWE-_U Magical life]'' (2023) by [[User:Xenllium\|Xenllium]] – in 19-tone alpha-pentacot with pure fifths (also known as pure-fifth magic scale)		* ''[https://youtube.com/watch?v=5iBXKRWE-_U Magical life]'' (2023) by [[User:Xenllium\|Xenllium]] – in 19-tone alpha-pentacot with pure fifths (also known as pure-fifth magic scale)

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

Xenllium: /* Notation */

2026-01-04T15:14:39Z

Notation

← Older revision		Revision as of 15:14, 4 January 2026
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	== Notation ==		== Notation ==
	There is no agreed-upon notation for alpha-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 alpha-pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).		There is no agreed-upon notation for alpha-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 minor third. Note and interval names are provided where alpha-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=1|Cots=5|Pergen=[P8, P12/5]|Forms=7, 10, 13, 16, 19|Title=Alpha-pentacot|Wedgie=5}} '''Alpha-pentacot''' is a temperament archetype where the generator is a submajor third of about 379–381¢, five of which make a perfect twelfth of 3/1 (third harmonic, also known as "tritave"), and the period is a 2/1 octave. Alpha-pentacot temperaments typically generate the 3L 4s, 3L 7s, 3L 10s, and..."

2026-01-04T11:25:08Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=1|Cots=5|Pergen=[P8, P12/5]|Forms=7, 10, 13, 16, 19|Title=Alpha-pentacot|Wedgie=5}} '''Alpha-pentacot''' is a temperament archetype where the generator is a submajor third of about 379–381¢, five of which make a perfect twelfth of 3/1 (third harmonic, also known as "tritave"), and the period is a 2/1 octave. Alpha-pentacot temperaments typically generate the 3L 4s, 3L 7s, 3L 10s, and..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=1|Cots=5|Pergen=[P8, P12/5]|Forms=7, 10, 13, 16, 19|Title=Alpha-pentacot|Wedgie=5}}
'''Alpha-pentacot''' is a temperament archetype where the generator is a submajor third of about 379–381¢, five of which make a perfect twelfth of [[3/1]] (third harmonic, also known as "tritave"), and the period is a [[2/1]] octave. Alpha-pentacot temperaments typically generate the [[3L 4s]], [[3L 7s]], [[3L 10s]], and [[3L 13s]] MOS scales, and either [[3L 16s]] (and thus [[19L 3s]]) or [[16L 3s]] as children.

== Notation ==
There is no agreed-upon notation for alpha-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 alpha-pentacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).

{| class="wikitable"
|+ style="font-size: 105%;" | Alpha-pentacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −20
| 792.180
| Ab
| minor sixth
|-
| −19
| 1172.571
|
|
|-
| −18
| 352.962
|
|
|-
| −17
| 733.353
|
|
|-
| −16
| 1113.744
|
|
|-
| −15
| 294.135
| Eb
| minor third
|-
| −14
| 674.526
|
|
|-
| −13
| 1054.917
|
|
|-
| −12
| 235.308
|
|
|-
| −11
| 615.699
|
|
|-
| −10
| 996.090
| Bb
| minor seventh
|-
| −9
| 176.481
|
|
|-
| −8
| 556.872
|
|
|-
| −7
| 937.263
|
|
|-
| −6
| 117.654
|
|
|-
| −5
| 498.045
| F
| perfect fourth
|-
| −4
| 878.436
|
|
|-
| −3
| 58.827
|
|
|-
| −2
| 439.218
|
|
|-
| −1
| 819.609
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 380.391
|
|
|-
| 2
| 760.782
|
|
|-
| 3
| 1141.173
|
|
|-
| 4
| 321.564
|
|
|-
| 5
| 701.955
| G
| perfect fifth
|-
| 6
| 1082.346
|
|
|-
| 7
| 262.737
|
|
|-
| 8
| 643.128
|
|
|-
| 9
| 1023.519
|
|
|-
| 10
| 203.910
| D
| major second
|-
| 11
| 584.301
|
|
|-
| 12
| 964.692
|
|
|-
| 13
| 145.083
|
|
|-
| 14
| 525.474
|
|
|-
| 15
| 905.865
| A
| major sixth
|-
| 16
| 86.256
|
|
|-
| 17
| 466.647
|
|
|-
| 18
| 847.038
|
|
|-
| 19
| 27.429
|
|
|-
| 20
| 407.820
| E
| major third
|}

== Temperament interpretations ==
An obvious interpretation for alpha-pentacot is [[magic]], where the generator is [[5/4]] and five of them stack to make 3/1. There are many extensions for 7-limit: septimal magic (19 & 22), muggles (16 & 19), brightstone (22 & 25), and darkstone (3d & 16).

== Music ==
* ''[https://youtube.com/watch?v=5iBXKRWE-_U Magical life]'' (2023) by [[User:Xenllium|Xenllium]] – in 19-tone alpha-pentacot with pure fifths (also known as pure-fifth magic scale)

[[Category:Ploidacot]]