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{{Interwiki
|en=2L 3s
|es=
|de=
|ja=2L 3s
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{{Infobox MOS
{{Infobox MOS
| Name = pentic
| Name = pentic
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}}
}}


: ''For the 3/2-equivalent 2L 3s pattern, see [[2L 3s (3/2-equivalent)]].''
: ''For the 3/2-equivalent 2L 3s pattern, see [[2L 3s (3/2-equivalent)]].''


{{MOS intro}}
{{MOS intro}} This scale is the "classic" pentatonic scale, which is perhaps the most common scale in the world.
This scale is the "Classic" pentatonic. Perhaps the most common scale in the world.


The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]].
The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest [[harmonic entropy]] of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]].


== Names ==
== Names ==
The [[TAMNAMS]] system suggests the name '''pentic''', derived from an [[Wiktionary: pent #Etymology 2|informal clipping of "pentatonic"]] that is sometimes used to refer to this scale.
The [[TAMNAMS]] system suggests the name '''pentic''', derived from an [[Wiktionary: pent #Etymology 2|informal clipping of "pentatonic"]] that is sometimes used to refer to this scale.


== Modes ==
== Scale properties ==
* 4|0 LsLss
{{TAMNAMS use}}
* 3|1 LssLs
 
* 2|2 sLsLs
=== Intervals ===
* 1|3 sLssL
{{MOS intervals}}
* 0|4 ssLsL
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Mode names ===
There are three sets of mode names: descriptive, modal (5 of the 7 heptatonic modes), and traditional Chinese.
{{MOS modes
| Table Headers=
Descriptive $
Modal $
Chinese $
| Table Entries=
Fifthless $
Phrygian $
Jué (角) $
Minor $
Aeolian $
Yǔ (羽) $
Thirdless Minor* $
Dorian $
Shāng (商) $
Thirdless Major* $
Mixolydian $
Zhǐ (徵) $
Major $
Ionian $
Gōng (宫) $
}}
<nowiki />* Thirdless Minor/Major is also known as Suspended Minor/Major


== Scales ==
== Scales ==
* [[Archy5]] – 472edo tuning
=== Scale list ===
* [[Archy5]] – 49edo tuning
* [[Edson5]] – 29edo tuning
* [[Edson5]] – 29edo tuning
* [[Pythagorean5]] – Pythagorean tuning
* [[Pythagorean5]] – Pythagorean tuning
* [[Meantone5]] – 31edo tuning
* [[Meantone5]] – 31edo tuning


== Scale tree ==
=== Scale tree ===
Generator ranges:
{{MOS tuning spectrum
* Chroma-positive generator: 480 cents (2\5) to 600 cents (1\2)
| Depth = 6
* Chroma-negative generator: 600 cents (1\2) to 720 cents (3\5)
| 6/5 = Slendro (insofar as it resembles a MOS) would<br />be in this region
 
| 9/7 = No-5s [[superpyth]]/dominant is around here
{{Todo| cleanup |inline=1|comment=Rework this scale tree.}}
| 13/9 = Pythagorean pentatonic is around here
 
| 3/2 = Familiar [[12edo|12-equal]] pentatonic
{| class="wikitable"
| 8/5 = Optimal meantone pentatonic is around here
|-
| 5/2 = Five-note subset of [[pelog]] (insofar as it<br />resembles a MOS) would be in this region
! colspan="6" | Generator
}}
! | Cents
! | s
! | L-s
! | |L-2s|
! | Scale steps
! | Trichord
! | Comments
|-
| | 2\5
| |
| |
| |
| |
| |
| | 480
| | 240
| | 0
| | 240
| | 1 1 1 1 1
| | 1 1
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 11\27
| | 488.89
| | 222.22
| | 44.44
| | 177.78
| | 6 5 5 6 5
| | 6 5
| style="text-align:center;" | Slendro (insofar as it resembles a MOS)
 
would be in this region
|-
| |
| |
| |
| |
| | 9\22
| |
| | 490.91
| | 218.18
| | 54.545
| | 163.64
| | 5 4 4 5 4
| | 5 4
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 16\39
| | 492.31
| | 215.38
| | 61.54
| | 153.85
| | 9 7 7 9 7
| | 9 7
| style="text-align:center;" | No-5's superpyth/dominant is around here
|-
| |
| |
| |
| | 7\17
| |
| |
| | 494.12
| | 211.76
| | 70.59
| | 141.18
| | 4 3 3 4 3
| | 4 3
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 19\46
| | 495.65
| | 208.7
| | 78.26
| | 130.435
| | 11 8 8 11 8
| | 11 8
| |
|-
| |
| |
| |
| |
| | 12\29
| |
| | 496.55
| | 206.9
| | 82.76
| | 124.14
| | 7 5 5 7 5
| | 7 5
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 17\41
| | 497.56
| | 204.88
| | 87.8
| | 117.07
| | 10 7 7 10 7
| | 10 7
| style="text-align:center;" | Pythagorean pentatonic is around here
|-
| |
| |
| | 5\12
| |
| |
| |
| | 500
| | 200
| | 100
| | 100
| | 3 2 2 3 2
| | 3 2
| style="text-align:center;" | Familiar 12-equal pentatonic
 
(also optimum rank range: L/s=3/2)
|-
| |
| |
| |
| |
| |
| |
| | 502.305
| | 195.39
| | 111.53
| | 83.86
| | pi 2 pi 2 2
| | pi 2
| |
|-
| |
| |
| |
| |
| |
| | 18\43
| | 502.33
| | 195.35
| | 111.63
| | 83.72
| | 11 7 7 11 7
| | 11 7
| |
|-
| |
| |
| |
| |
| | 13\31
| |
| | 503.23
| | 193.55
| | 116.13
| | 77.42
| | 8 5 5 8 5
| | 8 5
| style="text-align:center;" | Optimal meantone pentatonic
 
is around here
|-
| |
| |
| |
| |
| |
| |
| | 1200/(4-phi)
| | 192.43
| | 118.93
| | 73.50
| | phi 1 1 phi 1
| | phi 1
| style="text-align:center;" | Golden meantone
|-
| |
| |
| |
| |
| |
| | 21\50
| | 504
| | 192
| | 120
| | 72
| | 13 8 8 13 8
| | 13 8
| style="text-align:center;" |
|-
| |
| |
| |
| | 8\19
| |
| |
| | 505.26
| | 189.47
| | 126.32
| | 63.16
| | 5 3 3 5 3
| | 5 3
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 19\45
| | 506.67
| | 186.67
| | 133.33
| | 53.33
| | 12 7 7 12 7
| | 12 7
| |
|-
| |
| |
| |
| |
| |
| |
| | 507.18
| | 185.64
| | 135.9
| | 49.74
| | √3 1 √3 1 1
| | √3 1
| |
|-
| |
| |
| |
| |
| | 11\26
| |
| | 507.69
| | 184.615
| | 138.46
| | 46.15
| | 7 4 4 7 4
| | 7 4
| |
|-
| |
| |
| |
| |
| |
| | 14\33
| | 509.09
| | 181.82
| | 145.455
| | 36.36
| | 9 5 5 9 5
| | 9 5
| |
|-
| |
| | 3\7
| |
| |
| |
| |
| | 514.29
| | 171.43
| | 171.43
| | 0
| | 2 1 1 2 1
| | 2 1
| style="text-align:center;" | (Boundary of propriety: smaller
 
generators than this are strictly proper)
|-
| |
| |
| |
| |
| |
| | 13\30
| | 520
| | 160
| | 200
| | 40
| | 9 4 4 9 4
| | 9 4
| |
|-
| |
| |
| |
| |
| | 10\23
| |
| | 521.74
| | 156.52
| | 208.7
| | 52.17
| | 7 3 3 7 3
| | 7 3
| |
|-
| |
| |
| |
| |
| |
| | 17\39
| | 523.08
| | 153.84
| | 215.385
| | 61.54
| | 12 5 5 12 5
| | 12 5
| |
|-
| |
| |
| |
| | 7\16
| |
| |
| | 525
| | 150
| | 225
| | 75
| | 5 2 2 5 2
| | 5 2
| style="text-align:center;" | 5-note subset of pelog (insofar as it
 
resembles a MOS) would be in this region
|-
| |
| |
| |
| |
| |
| | 18\41
| | 526.83
| | 146.34
| | 234.15
| | 87.8
| | 13 5 5 13 5
| | 13 5
| |
|-
| |
| |
| |
| |
| |
| |
| | 600(25+√5)/31
| | 145.7
| | 235.75
| | 90.05
| | phi+1 1 1 phi+1 1
| | phi+1 1
| |
|-
| |
| |
| |
| |
| | 11\25
| |
| | 528
| | 144
| | 240
| | 96
| | 8 3 3 8 3
| | 8 3
| |
|-
| |
| |
| |
| |
| |
| |
| | 528.88
| | 142.24
| | 244.405
| | 102.17
| | e 1 e 1 1
| | e 1
| style="text-align:center;" | L/s = e
|-
| |
| |
| |
| |
| |
| | 15\34
| | 529.41
| | 141.18
| | 247.06
| | 105.88
| | 11 4 4 11 4
| | 11 4
| |
|-
| |
| |
| | 4\9
| |
| |
| |
| | 533.33
| | 133.33
| | 266.67
| | 133.33
| | 3 1 1 3 1
| | 3 1
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| | 535.36
| | 129.26
| | 276.835
| | 147.57
| | pi 1 pi 1 1
| | pi 1
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| |
| |
| |
| | 13\29
| | 537.93
| | 124.14
| | 289.655
| | 165.52
| | 10 3 3 10 3
| | 10 3
| |
|-
| |
| |
| |
| |
| | 9\20
| |
| | 540
| | 120
| | 240
| | 180
| | 7 2 2 7 2
| | 7 2
| |
|-
| |
| |
| |
| |
| |
| | 14\31
| | 541.935
| | 116.13
| | 309.68
| | 193.55
| | 11 3 3 11 3
| | 11 3
| |
|-
| |
| |
| |
| | 5\11
| |
| |
| | 545.45
| | 109.09
| | 327.27
| | 218.18
| | 4 1 1 4 1
| | 4 1
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| |
| | 11\24
| | 550
| | 100
| | 350
| | 250
| | 9 2 2 9 2
| | 9 2
| |
|-
| |
| |
| |
| |
| | 6\13
| |
| | 553.85
| | 92.31
| | 369.23
| | 276.92
| | 5 1 1 5 1
| | 5 1
| |
|-
| |
| |
| |
| |
| |
| | 7\15
| | 560
| | 80
| | 480
| | 400
| | 6 1 1 6 1
| | 6 1
| |
|-
| | 1\2
| |
| |
| |
| |
| |
| | 600
| | 0
| | 600
| | 600
| | 1 0 0 1 0
| | 1 0
| style="text-align:center;" | a degenerated pentatonic scale with only 2 different steps
|}


From a [[3-limit]] perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.
From a [[3-limit]] perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.


From a [[5-limit]] perspective, the most interesting temperaments with this kind of pentatonic scale are [[meantone]] and [[Pelogic family|mavila]].
From a [[5-limit]] perspective, the most interesting temperaments with this kind of pentatonic scale are [[meantone]] and [[mavila]].


There is also the interesting 2.3.7 temperament that tempers out [[64/63]] ([[archy]], "no-fives [[Meantone family #Dominant|dominant]]").
There is also the 2.3.7 temperament that tempers out [[64/63]] ([[archy]], "no-fives [[Meantone family#Dominant|dominant]]").


[[Category:Pentic]]
[[Category:Pentic]]
[[Category:5-tone scales]]
[[Category:5-tone scales]]
Retrieved from "https://en.xen.wiki/w/2L_3s"