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| nLargeSteps = 3
| nLargeSteps = 3
| nSmallSteps = 5
| nSmallSteps = 5
| Equalized = 3
| Equalized = 5
| Paucitonic = 1
| Paucitonic = 2
| Pattern = ssLssLsL
| Pattern = LsLssLss
}}
}}


'''3L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degree of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched.
'''3L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degree of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched.


There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent_family|Sensi]], in which the generator is a 9/7, two of them make a 5/3, and seven of them make a 3/2, is the proper one. [[Meantone_family#Squares|Squares]], in which the generator is also a 9/7, but two of them make an 18/11 and four of them make a 4/3, is improper.
There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent family|Sensi]], in which the generator is a 9/7, two of them make a 5/3, and seven of them make a 3/2, is the proper one. [[Meantone family #Squares|Squares]], in which the generator is also a 9/7, but two of them make an 18/11 and four of them make a 4/3, is improper.


== Standing assumptions ==
== Standing assumptions ==
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The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), #/@ = up/down by chroma.
The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), #/@ = up/down by chroma.
== Names ==
== Names ==
The [[TAMNAMS]] name for 3L 5s is '''sensoid''' (named after the regular temperament [[sensi]]).
The [[TAMNAMS]] name for 3L 5s is '''sensoid''' (named after the regular temperament [[sensi]]).
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== Scale tree ==
== Scale tree ==
{| class="wikitable"
Generator ranges:
* Chroma-positive generator: 750 cents (5\8) to 800 cents (2\3)
* Chroma-negative generator: 400 cents (1\3) to 450 cents (3\8)
 
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 5\8 || || || || || || 750.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 27\43 || 753.488 || 6 || 5 || 1.200 ||
|-
| || || || || 22\35 || || 754.286 || 5 || 4 || 1.250 ||
|-
| || || || || || 39\62 || 754.839 || 9 || 7 || 1.286 ||
|-
| || || || 17\27 || || || 755.556 || 4 || 3 || 1.333 || [[Sensi]]/[[sensis]]
|-
| || || || || || 46\73 || 756.164 || 11 || 8 || 1.375 ||
|-
| || || || || 29\46 || || 756.522 || 7 || 5 || 1.400 || [[Sensi]] is in this region
|-
| || || || || || 41\65 || 756.923 || 10 || 7 || 1.429 ||
|-
| || || 12\19 || || || || 757.895 || 3 || 2 || 1.500 ||
|-
| || || || || || 43\68 || 758.824 || 11 || 7 || 1.571 || [[Clyde]]
|-
|-
! colspan="6" | Generator
| || || || || 31\49 || || 759.184 || 8 || 5 || 1.600 ||
! | Cents
! | Comments
|-
|-
| | 1\3
| || || || || || 50\79 || 759.494 || 13 || 8 || 1.625 || Golden sensoid (759.4078¢)
| |  
| |  
| |  
| |  
| |  
| | 400
| style="text-align:center;" |  
|-
|-
|
| || || || 19\30 || || || 760.000 || 5 || 3 || 1.667 ||  
|
|
|
|
|8\23
|417.39
|
|-
|-
|
| || || || || || 45\71 || 760.563 || 12 || 7 || 1.714 ||  
|
|
|
|7\20
|
|420
|
|-
|-
| |  
| || || || || 26\41 || || 760.976 || 7 || 4 || 1.750 ||  
| |  
| |  
| | 6\17
| |  
| |  
| | 423.53
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 33\52 || 761.538 || 9 || 5 || 1.800 ||  
| |  
| |  
| |  
| |  
| | 17\48
| | 425
| style="text-align:center;" | <!--Squares is around here-->
|-
|-
| |  
| || 7\11 || || || || || 763.636 || 2 || 1 || 2.000 || Basic sensoid <br>(Generators smaller than this are proper)
| |  
| |  
| |  
| | 11\31
| |  
| | 425.81
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 30\47 || 765.957 || 9 || 4 || 2.250 ||  
| |  
| | 5\14
| |  
| |  
| |  
| | 428.57
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || 23\36 || || 766.667 || 7 || 3 || 2.333 ||  
| |  
| |  
| |  
| | 14\39
| |  
| | 430.77
| |  
|-
|-
| |  
| || || || || || 39\61 || 767.213 || 12 || 5 || 2.400 ||  
| |  
| |  
| |  
| |  
| | 23\64
| | 431.25
| |  
|-
|-
| |  
| || || || 16\25 || || || 768.000 || 5 || 2 || 2.500 ||  
| |  
| |  
| | 9\25
| |  
| |  
| | 432
| |  
|-
|-
| |  
| || || || || || 41\64 || 768.750 || 13 || 5 || 2.600 || Golden tuning (768.8815¢)
| | 4\11
| |  
| |  
| |  
| |  
| | 436.36
| style="text-align:center;" | Boundary of propriety:<br/>generators larger than this are proper
|-
|-
| |  
| || || || || 25\39 || || 769.231 || 8 || 3 || 2.667 ||  
| |  
| |  
| |  
| |  
| |  
| | 439.23
| |  
|-
|-
| |  
| || || || || || 34\53 || 769.811 || 11 || 4 || 2.750 || [[Hamity]]
| |  
| |  
| | 11\30
| |  
| |  
| | 440
| style="text-align:center;" |  
|-
|-
| |  
| || || 9\14 || || || || 771.429 || 3 || 1 || 3.000 ||  
| |  
| |  
| |  
| |  
| | 29\79
| | 440.51
| style="text-align:center;" | Golden sensoid
|-
|-
| |  
| || || || || || 29\45 || 773.333 || 10 || 3 || 3.333 ||  
| |  
| |  
| |  
| | 18\49
| |  
| | 440.82
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 20\31 || || 774.194 || 7 || 2 || 3.500 || [[Squares]] is in this region
| |  
| |  
| |  
| |  
| |  
| | 441.185
| |  
|-
|-
| |  
| || || || || || 31\48 || 775.000 || 11 || 3 || 3.667 ||  
| |  
| | 7\19
| |  
| |  
| |  
| | 442.11
| style="text-align:center;" | Optimum rank range (L/s=3/2) sensoid
|-
|-
| |  
| || || || 11\17 || || || 776.471 || 4 || 1 || 4.000 ||  
| |  
| |  
| |  
| | 17\46
| |  
| | 443.48
| style="text-align:center;" | <!--Sensi is around here-->
|-
|-
| |  
| || || || || || 24\37 || 778.378 || 9 || 2 || 4.500 ||  
| |  
| |  
| | 10\27
| |  
| |  
| | 444.44
| style="text-align:center;" |  
|-
|-
|
| || || || || 13\20 || || 780.000 || 5 || 1 || 5.000 ||  
|
|
|
|13\35
|
|445.71
|
|-
|-
|
| || || || || || 15\23 || 782.609 || 6 || 1 || 6.000 || [[Roman]]↓, [[Hocus]]↓
|
|
|
|
|16\43
|446.51
|
|-
|-
| | 3\8
| 2\3 || || || || || || 800.000 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| |  
| | 450
| style="text-align:center;" |  
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:8-tone scales]]
[[Category:Sensoid]]
[[Category:Sensoid]]
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