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Associated with the [[Augmented_family|augmented family]], which comprises the only significant minimum of harmonic entropy for these scales.
{{Infobox MOS
| Name = triwood
| Periods = 3
| nLargeSteps = 3
| nSmallSteps = 3
| Equalized = 1
| Collapsed = 0
| Pattern = LsLsLs
}}


{| class="wikitable"
{{MOS intro}}
 
In addition to the true MOS (LsLsLs or sLsLsL), there are also near-MOS patterns of LLsLss and LLssLs, which are only proper if the generator is larger than [[9edo|1\9]].
 
Out of all ''[[Rothenberg propriety|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.
 
== Intervals ==
{{MOS intervals}}
 
== Modes==
{{MOS mode degrees}}
 
==Scale tree==
{{todo|inline=1|complete table|Convert manually-generated scale tree table to MOS tuning spectrum without losing information from the existing table}}
{| 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||
|-
|-
! colspan="5" | Generator
| || ||  ||  || ||11\54||244.444||155.556 || 11 ||7||1.571||
! | Cents
! | Comments
|-
|-
| | 0\3
| || || || ||8\39|| ||246.154|| 153.846||8||5||1.600||Triforce
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || ||13\63||247.619||152.381 || 13 ||8||1.625|| Unnamed golden tuning
| |  
| |  
| | 1\15
| |  
| | 80
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || ||5\24|| || ||250.000|| 150.000||5||3||1.667||
| |  
| |  
| |  
| | 2\27
| | 88.88
| style="text-align:center;" | Optimal augmented is around here
|-
|-
| |  
| || || || || ||12\57||252.632||147.368 || 12 ||7||1.714||  
| |  
| |  
| |  
| |  
| | 400/(1+pi)
| |  
|-
|-
| |  
| || || || ||7\33|| ||254.545|| 145.455||7||4||1.750||
| |  
| | 1\12
| |  
| |  
| | 100
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || ||9\42||257.143|| 142.857||9||5||1.800||
| |  
| |  
| |  
| |  
| | 400/(1+e)
| |  
|-
|-
| |  
| ||2\9 ||  || || || ||266.667||133.333 || 2||1||2.000||Basic triwood
| |  
| |  
| |  
| | 3\33
| | 109.09
| |  
|-
|-
| |  
| || || || || || 9\39||276.923|| 123.077||9||4||2.250||
| |  
| |  
| |  
| |  
| | 400/(2+phi)
| |  
|-
|-
| |  
| || || || ||7\30|| ||280.000|| 120.000||7||3||2.333||Deflated (optimal around here)
| |  
| |  
| | 2\21
| |  
| | 114.29
| |  
|-
|-
| |  
| || || || || ||12\51||282.353||117.647 || 12 ||5||2.400||
| | 1\9
|-
| |  
| || ||  || 5\21||  ||  ||285.714|| 114.286||5||2||2.500||
| |  
|-
| |  
| || ||  ||  || ||13\54||288.889||111.111 || 13 ||5||2.600|| Unnamed golden tuning
| | 133.33
|-
| style="text-align:center;" | Boundary of propriety for near-MOS
| || || || ||8\33|| ||290.909|| 109.091||8||3||2.667||
 
|-
Optimum rank range (L/s=2/1) for MOS
| || ||  ||  || ||11\45||293.333||106.667 || 11 ||4||2.750|| August
|-
| || ||3\12|| || || ||300.000|| 100.000|| 3||1||3.000||Trug (optimal around here)
|-
| || || || || ||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;" | Golden triforce
|-
|-
| |  
| || || || || ||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:Triwood| ]]
[[Category:6-tone scales]]
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