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Line 6: Line 6:
| Equalized = 3
| Equalized = 3
| Paucitonic = 1
| Paucitonic = 1
| Pattern = sLsssLs
| Pattern = LssLsss
| Neutral = 4L 3s
| Neutral = 4L 3s
}}
}}


'''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).
'''2L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 3\7 (3 degrees of [[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.)
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|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.


== Names ==
== 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.
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 ==
== 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]]).
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]]).
== Intervals ==
== Intervals ==
Note: In TAMNAMS, a k-step interval class in antidiatonic may be called a "k-step", "k-mosstep", or "k-pelstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
Note: In TAMNAMS, a k-step interval class in antidiatonic may be called a "k-step", "k-mosstep", or "k-pelstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
== Modes ==
* 6|0 LssLsss (anti-locrian)
* 5|1 LsssLss (anti-phrygian)
* 4|2 sLssLss (anti-aeolian)
* 3|3 sLsssLs (anti-dorian)
* 2|4 ssLssLs (anti-mixolydian)
* 1|5 ssLsssL (anti-ionian)
* 0|6 sssLssL (anti-lydian)


== Scale tree ==
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
* Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
Line 34: Line 49:
| 3\7 || || || || || || 514.286 || 1 || 1 || 1.000 ||  
| 3\7 || || || || || || 514.286 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 16\37 || 518.919 || 6 || 5 || 1.200 ||  
| || || || || || 16\37 || 518.919 || 6 || 5 || 1.200 || [[Gravity]]↑
|-
|-
| || || || || 13\30 || || 520.000 || 5 || 4 || 1.250 ||  
| || || || || 13\30 || || 520.000 || 5 || 4 || 1.250 ||  
Line 48: Line 63:
| || || || || || 24\55 || 523.636 || 10 || 7 || 1.428 ||
| || || || || || 24\55 || 523.636 || 10 || 7 || 1.428 ||
|-
|-
| || || 7\16 || || || || 525.000 || 3 || 2 || 1.500 || L/s = 3/2, mavila is in this region
| || || 7\16 || || || || 525.000 || 3 || 2 || 1.500 || [[Mavila]] is in this region
|-
|-
| || || || || || 25\57 || 526.316 || 11 || 7 || 1.571 ||
| || || || || || 25\57 || 526.316 || 11 || 7 || 1.571 ||
Line 54: Line 69:
| || || || || 18\41 || || 526.829 || 8 || 5 || 1.600 ||  
| || || || || 18\41 || || 526.829 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 29\66 || 527.273 || 13 || 8 || 1.625 || Golden mavila
| || || || || || 29\66 || 527.273 || 13 || 8 || 1.625 || Golden mavila (527.1497¢)
|-
|-
| || || || 11\25 || || || 528.000 || 5 || 3 || 1.667 ||
| || || || 11\25 || || || 528.000 || 5 || 3 || 1.667 ||
Line 60: Line 75:
| || || || || || 26\59 || 528.814 || 12 || 7 || 1.714 ||  
| || || || || || 26\59 || 528.814 || 12 || 7 || 1.714 ||  
|-
|-
| || || || || 15\34 || || 529.412 || 7 || 4 || 1.750 ||
| || || || || 15\34 || || 529.412 || 7 || 4 || 1.750 ||  
|-
|-
| || || || || || 19\43 || 530.233 || 9 || 5 || 1.800 ||
| || || || || || 19\43 || 530.233 || 9 || 5 || 1.800 || [[Mabila]] / [[Amavil]]
|-
|-
| || 4\9 || || || || || 533.333 || 2 || 1 || 2.000 || Basic antidiatonic<br>(Generators smaller than this are proper)
| || 4\9 || || || || || 533.333 || 2 || 1 || 2.000 || Basic antidiatonic <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 17\38 || 536.842 || 9 || 4 || 2.250 ||
| || || || || || 17\38 || 536.842 || 9 || 4 || 2.250 ||
Line 74: Line 89:
| || || || 9\20 || || || 540.000 || 5 || 2 || 2.500 || Score
| || || || 9\20 || || || 540.000 || 5 || 2 || 2.500 || Score
|-
|-
| || || || || || 23\51 || 541.176 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 23\51 || 541.176 || 13 || 5 || 2.600 || Unnamed golden tuning (541.3837¢)
|-
|-
| || || || || 14\31 || || 541.935 || 8 || 3 || 2.667 || Casablanca is around here
| || || || || 14\31 || || 541.935 || 8 || 3 || 2.667 || [[Casablanca]] is around here
|-
|-
| || || || || || 19\42 || 542.857 || 11 || 4 || 2.750 ||
| || || || || || 19\42 || 542.857 || 11 || 4 || 2.750 ||
|-
|-
| || || 5\11 || || || || 545.455 || 3 || 1 || 3.000 || L/s = 3/1
| || || 5\11 || || || || 545.455 || 3 || 1 || 3.000 ||  
|-
|-
| || || || || || 16\35 || 548.571 || 10 || 3 || 3.333 ||
| || || || || || 16\35 || 548.571 || 10 || 3 || 3.333 ||
Line 86: Line 101:
| || || || || 11\24 || || 550.000 || 7 || 2 || 3.500 ||
| || || || || 11\24 || || 550.000 || 7 || 2 || 3.500 ||
|-
|-
| || || || || || 17\37 || 551.351 || 11 || 3 || 3.667 || Freivald, emka
| || || || || || 17\37 || 551.351 || 11 || 3 || 3.667 || [[Freivald]] / [[emka]]
|-
|-
| || || || 6\13 || || || 553.846 || 4 || 1 || 4.000 ||
| || || || 6\13 || || || 553.846 || 4 || 1 || 4.000 ||
Line 92: Line 107:
| || || || || || 13\28 || 557.143 || 9 || 2 || 4.500 ||
| || || || || || 13\28 || 557.143 || 9 || 2 || 4.500 ||
|-
|-
| || || || || 7\15 || || 560.000 || 5 || 1 || 5.000 || Thuja is around here
| || || || || 7\15 || || 560.000 || 5 || 1 || 5.000 || [[Thuja]] is around here
|-
|-
| || || || || || 8\17 || 564.706 || 6 || 1 || 6.000 || Liese↓, triton↓
| || || || || || 8\17 || 564.706 || 6 || 1 || 6.000 || [[Liese]]↓, [[triton]]↓
|-
|-
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
Retrieved from "https://en.xen.wiki/w/2L_5s"