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Also reverting this, just to be safe.
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autopatrolled, emailconfirmed
15,004 edits
I think last version was overall ok, and I'm adding this piece of rtt info back from the FREEZE version
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2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo|7edo]]) and 1\2 (1 degree of [[2edo|2edo]] — the half-octave tritone that appears in every even-numbered edo).
{{Infobox MOS
| Name = antidiatonic, pelogoid
| Periods = 1
| nLargeSteps = 2
| nSmallSteps = 5
| Equalized = 3
| Paucitonic = 1
| Pattern = sLsssLs
| Neutral = 4L 3s
}}


The word "mavila" is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of "mavila." In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic_pairs#Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.
'''2L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 3\7 (3 degrees of [[7edo|7edo]] = 514.29¢) to 1\2 (one degree of [[2edo]] = 600¢). In the case of 7edo, L and s are the same size; in the case of 2edo, s becomes so small it disappears (and all that remains are the two equal L's).
 
While antidiatonic is closely associated with [[mavila temperament]] and [[7L 2s]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not [[7L 2s]] mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic_pairs#Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.)


In terms of harmonic entropy, the most significant minimum is at [[Meantone_family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
In terms of harmonic entropy, the most significant minimum is at [[Meantone_family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
In terms of harmonic entropy, the most significant minimum is at [[Meantone_family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
== Names ==
It is often called '''antidiatonic''', because it has the step pattern of diatonic ([[5L 2s]]), but with the large and small steps switched. [[TAMNAMS]] uses this name as well.
== Notation ==
We'll use the convention DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz, &/@ = raise and lower by one chroma.  The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up ''flattens'' a note by a chroma, rather than sharpening it as in diatonic ([[5L 2s]]).


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 3\7 || || || || || || 514.286 || 1 || 1 || 1.000 ||
|-
| || || || || || 16\37 || 518.919 || 6 || 5 || 1.200 ||
|-
| || || || || 13\30 || || 520.000 || 5 || 4 || 1.250 ||
|-
| || || || || || 23\53 || 520.755 || 9 || 7 || 1.286 ||
|-
|-
! colspan="7" | generator in degrees of an [[EDO|edo]]
| || || || 10\23 || || || 521.739 || 4 || 3 || 1.333 ||
! | generator in cents
! | tetrachord
! | L in cents
! | s in cents
! | L to s ratio
! | comments
|-
|-
| style="text-align:center;" | 3\7
| || || || || || 27\62 || 522.581 || 11 || 8 || 1.375 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |
| |  
| style="text-align:center;" | 514.3
| style="text-align:center;" | 1 1 1
| style="text-align:center;" | 171.4
| style="text-align:center;" | 171.4
| style="text-align:center;" | 1.00
| style="text-align:center;" |  
|-
|-
|
| || || || || 17\39 || || 523.077 || 7 || 5 || 1.400 ||
|
|
|
|
|
|19\44
|518.2
|6 6 7
|190.9
|163.6
|1.17
|
|-
|-
|
| || || || || || 24\55 || 523.636 || 10 || 7 || 1.428 ||
|
|
|
|
|16\37
|
|518.9
|5 5 6
|194.6
|162.2
|1.20
|
|-
|-
| style="text-align:center;" |  
| || || 7\16 || || || || 525.000 || 3 || 2 || 1.500 || L/s = 3/2, mavila is in this region
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" | 13\30
| |  
| |  
| style="text-align:center;" | 520.0
| style="text-align:center;" | 4 4 5
| style="text-align:center;" | 200.0
| style="text-align:center;" | 160.0
| style="text-align:center;" | 1.25
| style="text-align:center;" | Mavila extends from here...
|-
|-
| style="text-align:center;" |  
| || || || || || 25\57 || 526.316 || 11 || 7 || 1.571 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 10\23
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 521.7
| style="text-align:center;" | 3 3 4
| style="text-align:center;" | 208.7
| style="text-align:center;" | 156.5
| style="text-align:center;" | 1.33
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || 18\41 || || 526.829 || 8 || 5 || 1.600 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 17\39
| |  
| |  
| style="text-align:center;" | 523.1
| style="text-align:center;" | 5 5 7
| style="text-align:center;" | 215.4
| style="text-align:center;" | 153.8
| style="text-align:center;" | 1.40
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 29\66 || 527.273 || 13 || 8 || 1.625 || Golden mavila
| style="text-align:center;" |  
| style="text-align:center;" | 7\16
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 525.0
| style="text-align:center;" | 2 2 3
| style="text-align:center;" | 225.0
| style="text-align:center;" | 150.0
| style="text-align:center;" | 1.50
| style="text-align:center;" | Mavila in Armodue
 
Optimum rank range (L/s=3/2)
|-
|-
| |  
| || || || 11\25 || || || 528.000 || 5 || 3 || 1.667 ||
| |  
| |  
| |  
| |  
| |  
| |
| style="text-align:center;" | 526.3
| style="text-align:center;" | <span style="display: block; text-align: center;">2 2 pi</span>
| style="text-align:center;" | 231.5
| style="text-align:center;" | 147.4
| style="text-align:center;" | <span style="display: block; text-align: center;">pi/2</span>
| |  
|-
|-
| style="text-align:center;" |  
| || || || || || 26\59 || 528.814 || 12 || 7 || 1.714 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 18\41
| |
| |
| style="text-align:center;" | 526.8
| style="text-align:center;" | 5 5 8
| style="text-align:center;" | 234.1
| style="text-align:center;" | 146.3
| style="text-align:center;" | 1.60
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 15\34 || || 529.412 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 1200*5/(13-phi)
| style="text-align:center;" | 1 1 phi
| style="text-align:center;" | 235.7
| style="text-align:center;" | 145.7
| style="text-align:center;" | phi
| style="text-align:center;" | Golden mavila
|-
|-
| |  
| || || || || || 19\43 || 530.233 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| | 29\66
| |
| style="text-align:center;" | 527.3
| style="text-align:center;" | 8 8 13
| style="text-align:center;" | 236.4
| style="text-align:center;" | 145.5
| style="text-align:center;" | 1.625
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || 4\9 || || || || || 533.333 || 2 || 1 || 2.000 || Basic antidiatonic<br>(Generators smaller than this are proper)
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11\25
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 528.0
| style="text-align:center;" | 3 3 5
| style="text-align:center;" | 240.0
| style="text-align:center;" | 144.0
| style="text-align:center;" | 1.67
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 17\38 || 536.842 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| |  
| |
| style="text-align:center;" | 529.1
| style="text-align:center;" | <span style="background-color: #ffffff;"><span style="line-height: 1.5;">1 1 </span>√3 </span>
| style="text-align:center;" | 245.6
| style="text-align:center;" | 141.8
| style="text-align:center;" | <span style="background-color: #ffffff; display: block; text-align: center;">√3</span>
| |  
|-
|-
| style="text-align:center;" |  
| || || || || 13\29 || || 537.931 || 7 || 3 || 2.333 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 15\34
| |  
| |  
| style="text-align:center;" | 529.4
| style="text-align:center;" | 4 4 7
| style="text-align:center;" | 247.1
| style="text-align:center;" | 141.2
| style="text-align:center;" | 1.75
| style="text-align:center;" | ...to somewhere around here
|-
|-
| style="text-align:center;" |  
| || || || || || 22\49 || 538.776 || 12 || 5 || 2.400 ||
| style="text-align:center;" | 4\9
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 533.3
| style="text-align:center;" | 1 1 2
| style="text-align:center;" | 266.7
| style="text-align:center;" | 133.3
| style="text-align:center;" | 2.00
| style="text-align:center;" | Boundary of propriety (generators
 
smaller than this are proper)
|-
|-
| style="text-align:center;" |  
| || || || 9\20 || || || 540.000 || 5 || 2 || 2.500 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 13\29
| |  
| |  
| style="text-align:center;" | 537.9
| style="text-align:center;" | 3 3 7
| style="text-align:center;" | 289.7
| style="text-align:center;" | 124.1
| style="text-align:center;" | 2.33
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 23\51 || 541.176 || 13 || 5 || 2.600 || Unnamed golden tuning
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 9\20
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 540.0
| style="text-align:center;" | 2 2 5
| style="text-align:center;" | 300.0
| style="text-align:center;" | 120.0
| style="text-align:center;" | 2.50
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 14\31 || || 541.935 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |  
| |  
| |
| style="text-align:center;" | 541.4
| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span>
| style="text-align:center;" | 306.9
| style="text-align:center;" | 117.2
| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span>
| |  
|-
|-
| style="text-align:center;" |  
| || || || || || 19\42 || 542.857 || 11 || 4 || 2.750 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 14\31
| |  
| |
| style="text-align:center;" | 541.9
| style="text-align:center;" | 3 3 8
| style="text-align:center;" | 309.7
| style="text-align:center;" | 116.1
| style="text-align:center;" | 2.66
| style="text-align:center;" |  
|-
|-
| |  
| || || 5\11 || || || || 545.455 || 3 || 1 || 3.000 || L/s = 3/1
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 542<span style="line-height: 1.5;">.5</span>
| style="text-align:center;" | 1 1 e
| style="text-align:center;" | 321.55
| style="text-align:center;" | 115.0
| style="text-align:center;" | e
| style="text-align:center;" | L/s = e
|-
|-
| style="text-align:center;" |  
| || || || || || 16\35 || 548.571 || 10 || 3 || 3.333 ||
| style="text-align:center;" |  
| style="text-align:center;" | 5\11
| style="text-align:center;" |  
| style="text-align:center;" |  
| |
| |  
| style="text-align:center;" | 545.5
| style="text-align:center;" | 1 1 3
| style="text-align:center;" | 327.3
| style="text-align:center;" | 109.1
| style="text-align:center;" | 3.00
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || 11\24 || || 550.000 || 7 || 2 || 3.500 ||
| |  
| |  
| |  
| |  
| |  
| |
| style="text-align:center;" | 546.8
| style="text-align:center;" | 1 1 pi
| style="text-align:center;" | 334.1
| style="text-align:center;" | 106.35
| style="text-align:center;" | pi
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| style="text-align:center;" |  
| || || || || || 17\37 || 551.351 || 11 || 3 || 3.667 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 11\24
| |
| |
| style="text-align:center;" | 550.0
| style="text-align:center;" | 2 2 7
| style="text-align:center;" | 350.0
| style="text-align:center;" | 100.0
| style="text-align:center;" | 3.50
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || 6\13 || || || 553.846 || 4 || 1 || 4.000 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 6\13
| style="text-align:center;" |
| |  
| |  
| style="text-align:center;" | 553.8
| style="text-align:center;" | 1 1 4
| style="text-align:center;" | 369.2
| style="text-align:center;" | 92.3
| style="text-align:center;" | 4.00
| style="text-align:center;" | Thuja is optimal around here
 
L/s = 4
|-
|-
| style="text-align:center;" |  
| || || || || || 13\28 || 557.143 || 9 || 2 || 4.500 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 7\15
| |
| |
| style="text-align:center;" | 560.0
| style="text-align:center;" | 1 1 5
| style="text-align:center;" | 400.0
| style="text-align:center;" | 80.0
| style="text-align:center;" | 5.00
| style="text-align:center;" | ie. (11/8)^5 = 5/1
|-
|-
| style="text-align:center;" |  
| || || || || 7\15 || || 560.000 || 5 || 1 || 5.000 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 8\17
| style="text-align:center;" |  
| style="text-align:center;" | 564.7
| style="text-align:center;" | 1 1 6
| style="text-align:center;" | 423.5
| style="text-align:center;" | 70.6
| style="text-align:center;" | 6.00
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 8\17 || 564.706 || 6 || 1 || 6.000 || Liese↓, triton↓
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 9\19
| style="text-align:center;" | 568.4
| style="text-align:center;" | 1 1 7
| style="text-align:center;" | 442.1
| style="text-align:center;" | 63.2
| style="text-align:center;" | 7.00
| style="text-align:center;" | Liese/Triton is around here
|-
|-
| style="text-align:center;" | 1\2
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 600.0
| style="text-align:center;" | 0 0 1
| style="text-align:center;" | 600.0
| style="text-align:center;" | 0
| style="text-align:center;" | —
| style="text-align:center;" |  
|}
|}
[[Category:Scales]]
[[Category:MOS scales]]
[[Category:Abstract MOS patterns]]
Retrieved from "https://en.xen.wiki/w/2L_5s"