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{{Interwiki
|en=2L 3s
|es=
|de=
|ja=2L 3s
}}
{{Infobox MOS
{{Infobox MOS
| Name = pentic
| Name = pentic
Line 9: Line 15:
}}
}}


This scale is the "Classic" pentatonic. Perhaps the most common scale in the world.
: ''For the 3/2-equivalent 2L 3s pattern, see [[2L 3s (3/2-equivalent)]].''


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]].
{{MOS intro}} This scale is the "classic" pentatonic scale, which is 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]].


== 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
* 1|3 sLssL
* 0|4 ssLsL


== Scale Tree ==
=== Intervals ===
Generator ranges:
{{MOS intervals}}
* Chroma-positive generator: 480 cents (2\5) to 600 cents (1\2)
* Chroma-negative generator: 600 cents (1\2) to 720 cents (3\5)


{| class="wikitable"
=== Generator chain ===
|-
{{MOS genchain}}
! 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
=== Modes ===
|-
{{MOS mode degrees}}
| |
| |
| |
| |
| | 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)
=== 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=
| | 502.305
Fifthless $
| | 195.39
Phrygian $
| | 111.53
Jué (角) $
| | 83.86
Minor $
| | pi 2 pi 2 2
Aeolian $
| | pi 2
Yǔ (羽) $
| |
Thirdless Minor* $
|-
Dorian $
| |
Shāng (商) $
| |
Thirdless Major* $
| |
Mixolydian $
| |
Zhǐ (徵) $
| |
Major $
| | 18\43
Ionian $
| | 502.33
Gōng (宫) $
| | 195.35
}}
| | 111.63
<nowiki />* Thirdless Minor/Major is also known as Suspended Minor/Major
| | 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
== Scales ==
|-
=== Scale list ===
| |
* [[Archy5]] – 49edo tuning
| |
* [[Edson5]] – 29edo tuning
| |
* [[Pythagorean5]] – Pythagorean tuning
| |
* [[Meantone5]] – 31edo tuning
| |
| |
| | 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)
=== Scale tree ===
|-
{{MOS tuning spectrum
| |
| Depth = 6
| |
| 6/5 = Slendro (insofar as it resembles a MOS) would<br />be in this region
| |
| 9/7 = No-5s [[superpyth]]/dominant is around here
| |
| 13/9 = Pythagorean pentatonic is around here
| |
| 3/2 = Familiar [[12edo|12-equal]] pentatonic
| | 13\30
| 8/5 = Optimal meantone pentatonic is around here
| | 520
| 5/2 = Five-note subset of [[pelog]] (insofar as it<br />resembles a MOS) would be in this region
| | 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"