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The true MOS is LsLsLs but interesting near-MOSs include LLsLss and LLssLs. The MOS is always proper but the other forms are only proper if the generator is larger than 1\9 of an octave (so not augmented).
 
Out of all ''[[Rothenberg propriety|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.
 
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
! Chroma-positive
! Chroma-negative
|-
| 1\6 || || || || || || 200.000 || 200.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 6\33 || 218.182 || 181.818 || 6 || 5 || 1.200 ||
|-
| || || || || 5\27 || || 222.222 || 177.778 || 5 || 4 || 1.250 ||
|-
| || || || || || 9\48 || 225.000 || 175.000 || 9 || 7 || 1.286 || Oodako
|-
| || || || 4\21 || || || 228.571 || 171.429 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\57 || 231.579 || 168.421 || 11 || 8 || 1.375 ||
|-
| || || || || 7\36 || || 233.333 || 166.667 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\51 || 235.294 || 164.706 || 10 || 7 || 1.428 ||
|-
| || || 3\15 || || || || 240.000 || 160.000 || 3 || 2 || 1.500 || L/s = 3/2
|-
| || || || || || 11\54 || 244.444 || 155.556 || 11 || 7 || 1.571 ||
|-
| || || || || 8\39 || || 246.154 || 153.846 || 8 || 5 || 1.600 || Triforce
|-
|-
! colspan="5" | Generator
| || || || || || 13\63 || 247.619 || 152.381 || 13 || 8 || 1.625 || Unnamed golden tuning<br>Trug (optimal around here)
! | Cents
! | Comments
|-
|-
| | 0\3
| || || || 5\24 || || || 250.000 || 150.000 || 5 || 3 || 1.667 ||  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 12\57 || 252.632 || 147.368 || 12 || 7 || 1.714 ||  
| |  
| |  
| | 1\15
| |  
| | 80
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || 7\33 || || 254.545 || 145.455 || 7 || 4 || 1.750 ||  
| |  
| |  
| |  
| | 2\27
| | 88.88
| style="text-align:center;" | Optimal augmented is around here
|-
|-
| |  
| || || || || || 9\42 || 257.143 || 142.857 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| | 400/(1+pi)
| |  
|-
|-
| |  
| || 2\9 || || || || || 266.667 || 133.333 || 2 || 1 || 2.000 || Basic 3L 3s
| |  
| | 1\12
| |  
| |  
| | 100
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || || 9\39 || 276.923 || 123.077 || 9 || 4 || 2.250 ||  
| |  
| |  
| |  
| |  
| | 400/(1+e)
| |  
|-
|-
| |  
| || || || || 7\30 || || 280.000 || 120.000 || 7 || 3 || 2.333 || Deflated (optimal around here)
| |  
| |  
| |  
| | 3\33
| | 109.09
| |  
|-
|-
| |  
| || || || || || 12\51 || 282.353 || 117.647 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| |  
| | 400/(2+phi)
| |  
|-
|-
| |  
| || || || 5\21 || || || 285.714 || 114.286 || 5 || 2 || 2.500 ||  
| |  
| |  
| | 2\21
| |  
| | 114.29
| |  
|-
|-
| |  
| || || || || || 13\54 || 288.889 || 111.111 || 13 || 5 || 2.600 || Unnamed golden tuning
| | 1\9
|-
| |  
| || || || || 8\33 || || 290.909 || 109.091 || 8 || 3 || 2.667 ||
| |  
|-
| |  
| || || || || || 11\45 || 293.333 || 106.667 || 11 || 4 || 2.750 || August
| | 133.33
|-
| style="text-align:center;" | Boundary of propriety for near-MOS
| || || 3\12 || || || || 300.000 || 100.000 || 3 || 1 || 3.000 || L/s = 3/1
 
|-
Optimum rank range (L/s=2/1) for MOS
| || || || || || 10\39 || 307.692 || 92.308 || 10 || 3 || 3.333 || Augene
|-
|-
| |  
| || || || || 7\27 || || 311.111 || 88.889 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| |  
| | 400/(1+sqrt(3))
| |  
|-
|-
| |  
| || || || || || 11\42 || 314.286 || 85.714 || 11 || 3 || 3.667 ||  
| |  
| |  
| | 3\24
| |  
| | 150
| style="text-align:center;" |  
|-
|-
| |  
| || || || 4\15 || || || 320.000 || 80.000 || 4 || 1 || 4.000 || Inflated
| |  
| |  
| |  
| |  
| | 400/(1+phi)
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 9\33 || 327.273 || 72.727 || 9 || 2 || 4.500 ||  
| |  
| |  
| |  
| | 5\39
| | 153.85
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 5\18 || || 333.333 || 66.667 || 5 || 1 || 5.000 ||  
| |  
| |  
| |  
| |  
| | 400/(1+pi/2)
| |  
|-
|-
| |  
| || || || || || 6\21 || 342.857 || 57.143 || 6 || 1 || 6.000 || Hemiug↓, hemiaug↓
| |  
| | 2\15
| |  
| |  
| | 160
| style="text-align:center;" |  
|-
|-
| | 1\6
| 1\3 || || || || || || 400.000 || 0.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| | 200
| style="text-align:center;" |  
|}
|}
The true MOS is LsLsLs but interesting near-MOSs include LLsLss and LLssLs. The MOS is always proper but the other forms are only proper if the generator is larger than 1\9 of an octave (so not augmented).
Out of all '''[[Rothenberg_propriety|proper]]''' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:Triwood| ]] <!-- main article -->
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