Ploidacot/Beta-pentacot - Revision history

Xenllium at 23:21, 7 January 2026

2026-01-07T23:21:56Z

← Older revision		Revision as of 23:21, 7 January 2026
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	{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=5\|Pergen=[P8, ccP4/5]\|Forms=25, 27, 29~~, 31~~\|Title=Beta-pentacot\|Wedgie=5}}		{{Infobox ploidacot\|Ploids=1\|Shears=2\|Cots=5\|Pergen=[P8, ccP4/5]\|Forms=23, 25, 27, 29\|Title=Beta-pentacot\|Wedgie=5}}
	'''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth [[3/2]]), and the period is a [[2/1]] octave. Beta-pentacot temperaments typically generate the [[2L 19s]], [[2L 21s]], [[2L 23s]], and [[2L 25s]] MOS scales, and either [[2L 27s]] (and thus [[29L 2s]]) or [[27L 2s]] as children.		'''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth [[3/2]]), and the period is a [[2/1]] octave. Beta-pentacot temperaments typically generate the [[2L 19s]], [[2L 21s]], [[2L 23s]], and [[2L 25s]] MOS scales, and either [[2L 27s]] (and thus [[29L 2s]]) or [[27L 2s]] as children.

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

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	An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31).		An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31).

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

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

2026-01-06T09:44:07Z

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

← Older revision		Revision as of 09:44, 6 January 2026
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	An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31).		An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31).

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

Xenllium: Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=5|Pergen=[P8, ccP4/5]|Forms=25, 27, 29, 31|Title=Beta-pentacot|Wedgie=5}} '''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make 6/1 (sixth harmonic, two octaves above a perfect fifth 3/2), and the period is a 2/1 octave. Beta-pentacot temperaments typically generate the 2L 19s, 2L 21s, 2L 23s, and 2L 25..."

2026-01-04T14:33:05Z

Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=2|Cots=5|Pergen=[P8, ccP4/5]|Forms=25, 27, 29, 31|Title=Beta-pentacot|Wedgie=5}} '''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make 6/1 (sixth harmonic, two octaves above a perfect fifth 3/2), and the period is a 2/1 octave. Beta-pentacot temperaments typically generate the 2L 19s, 2L 21s, 2L 23s, and 2L 25..."

New page

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=2|Cots=5|Pergen=[P8, ccP4/5]|Forms=25, 27, 29, 31|Title=Beta-pentacot|Wedgie=5}}
'''Beta-pentacot''' is a temperament archetype where the generator is a tritone of about 619–621¢, five of which make [[6/1]] (sixth harmonic, two octaves above a perfect fifth [[3/2]]), and the period is a [[2/1]] octave. Beta-pentacot temperaments typically generate the [[2L 19s]], [[2L 21s]], [[2L 23s]], and [[2L 25s]] MOS scales, and either [[2L 27s]] (and thus [[29L 2s]]) or [[27L 2s]] as children.

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

{| class="wikitable"
|+ style="font-size: 105%;" | Beta-pentacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −15
| 294.135
| Eb
| minor third
|-
| −14
| 914.526
|
|
|-
| −13
| 334.917
|
|
|-
| −12
| 955.308
|
|
|-
| −11
| 375.699
|
|
|-
| −10
| 996.090
| Bb
| minor seventh
|-
| −9
| 416.481
|
|
|-
| −8
| 1036.872
|
|
|-
| −7
| 457.263
|
|
|-
| −6
| 1077.654
|
|
|-
| −5
| 498.045
| F
| perfect fourth
|-
| −4
| 1118.436
|
|
|-
| −3
| 538.827
|
|
|-
| −2
| 1159.218
|
|
|-
| −1
| 579.609
|
|
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 620.391
|
|
|-
| 2
| 40.782
|
|
|-
| 3
| 661.173
|
|
|-
| 4
| 81.564
|
|
|-
| 5
| 701.955
| G
| perfect fifth
|-
| 6
| 122.346
|
|
|-
| 7
| 742.737
|
|
|-
| 8
| 163.128
|
|
|-
| 9
| 783.519
|
|
|-
| 10
| 203.910
| D
| major second
|-
| 11
| 824.301
|
|
|-
| 12
| 244.692
|
|
|-
| 13
| 865.083
|
|
|-
| 14
| 285.474
|
|
|-
| 15
| 905.865
| A
| major sixth
|}

== Temperament interpretations ==
An obvious interpretation for beta-pentacot is 2.3.7/5.11/5 restriction of [[trimyna]], where the generator is [[10/7]], three of them stack to make [[22/15]], and five of them stack to make [[3/2]]. Immediately it extends to full 11-limit [[tritonic]] (29 & 31).

[[Category:Ploidacot]]