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{{Infobox MOS
{{Infobox MOS
| Name = antioneirotonic
| Name = checkertonic
| Periods = 1
| Periods = 1
| nLargeSteps = 3
| nLargeSteps = 3
| nSmallSteps = 5
| nSmallSteps = 5
| Equalized = 3
| Equalized = 5
| Paucitonic = 1
| Collapsed = 2
| Pattern = ssLssLsL
| Pattern = LsLssLss
}}
}}
{{MOS intro|Other Names=anti-oneirotonic}}


'''3L 5s''' or '''antioneirotonic''' (/oʊnaɪrəˈtɒnɪk/ ''oh-ny-rə-TON-ik'' or /ənaɪrə-/ ''ə-ny-rə-'') refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degrees 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 named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched.
== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale.


There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent_family|Sensi]], in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. [[Meantone_family#Squares|Squares]], in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
==== Proposed mode names ====
The modes of checkertonic can be named after its sister mos [[5L 3s]] (oneirotonic). {{u|R-4981}} has also proposed names based on {{w|grand chess}} pieces.
{{MOS modes
| Table Headers=
Anti-modes of 5L 3s $
Grand chess names<sup>[proposed]</sup>
| Table Entries=
Anti-Sarnathian (sar-NA(H)TH-iən) $
King $
Anti-Hlanithian (lə-NITH-iən) $
Queen $
Anti-Kadathian (kə-DA(H)TH-iən) $
Marshall $
Anti-Mnarian (mə-NA(I)R-iən) $
Cardinal $
Anti-Ultharian (ul-THA(I)R-iən) $
Rook $
Anti-Celephaïsian (kel-ə-FAY-zhən) $
Bishop $
Anti-Illarnekian (ill-ar-NEK-iən) $
Knight $
Anti-Dylathian (də-LA(H)TH-iən) $
Pawn $
}}
The order of modes on the white keys JKLMNOPQ are:
 
* J Anti-Ultharian, Rook
* K Anti-Hlanithian, Queen
* L Anti-Illarnekian, Knight
* M Anti-Mnarian, Cardinal
* N Anti-Sarnathian, King
* O Anti-Celephaïsian, Bishop
* P Anti-Kadathian, Marshall
* Q Anti-Dylathian, Pawn


{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 105%;" | Scale degrees (on J, {{nowrap|sLssLsLs {{=}} JKLMNOPQ}})
|-
|-
! colspan="6" | Generator
! [[UDP]]
! | Cents
! Anti-modes of 5L 3s
! | Comments
! Chess-based names
! Step pattern
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! (9)
|-
|-
| | 1\3
| 7{{pipe}}0
| |  
| Anti-Sarnathian
| |  
| King
| |  
| LsLssLss
| |  
| J
| |
| K&amp;
| | 400
| L
| style="text-align:center;" |
| M&amp;
| N&amp;
| O
| P&amp;
| Q
| (J)
|-
|-
|
| 6{{pipe}}1
|
| Anti-Hlanithian
|
| Queen
|
| LssLsLss
|
| J
|8\23
| K&amp;
|417.39
| L
|
| M
| N&amp;
| O
| P&amp;
| Q
| (J)
|-
|-
|
| 5{{pipe}}2
|
| Anti-Kadathian
|
| Marshall
|
| LssLssLs
|7\20
| J
|
| K&amp;
|420
| L
|
| M
| N&amp;
| O
| P
| Q
| (J)
|-
|-
| |  
| 4{{pipe}}3
| |  
| Anti-Mnarian
| |  
| Cardinal
| | 6\17
| sLsLssLs
| |  
| J
| |
| K
| | 423.53
| L
| style="text-align:center;" | L/s = 4
| M
| N&amp;
| O
| P
| Q
| (J)
|-
|-
| |  
| 3{{pipe}}4
| |  
| Anti-Ultharian
| |  
| Rook
| |  
| sLssLsLs
| |  
| J
| | 17\48
| K
| | 425
| L
| style="text-align:center;" | Squares is around here
| M
| N
| O
| P
| Q
| (J)
|-
|-
| |  
| 2{{pipe}}5
| |  
| Anti-Celephaïsian
| |  
| Bishop
| |  
| sLssLssL
| | 11\31
| J
| |
| K
| | 425.81
| L
| style="text-align:center;" |
| M
| N
| O
| P
| Q@
| (J)
|-
|-
| |  
| 1{{pipe}}6
| |  
| Anti-Illarnekian
| |  
| Knight
| |  
| ssLsLssL
| |  
| J
| |
| K
| | 427.73
| L@
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
| M
| N
| O
| P
| Q@
| (J)
|-
|-
| |  
| 0{{pipe}}7
| |
| Anti-Dylathian
| | 5\14
| Pawn
| |
| ssLssLsL
| |
| J
| |
| K
| | 428.57
| L@
| style="text-align:center;" | L/s = 3
| M
|-
| N
| |
| O@
| |
| P
| |
| Q@
| |
| (J)
| |
|}
| |
 
| | 430.41
== Notation ==
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
The [[TAMNAMS]] system is used in this article to refer to {{PAGENAME}} step size ratios and step ratio ranges.
|-
 
| |
The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), &amp;/@ = up/down by chroma.
| |
 
| |
== Theory ==
| |
In contrast to oneirotonic ([[5L&nbsp;3s]]), which often require the usage of completely new chords to have consonant-sounding music, some checkertonic scales contain approximations to a perfect fifth ([[3/2]], usually as a dim. chk6th or maj. chk5th), and thus can be used for traditional root-3rd-P5 harmony.
| | 14\39
 
| |
=== Low harmonic entropy scales ===
| | 430.77
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, which is proper.
| |
* [[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, which is improper.
| |
 
| |
== Tuning ranges ==
| |
=== Simple tunings ===
| |
{{MOS tunings}}
| | 23\64
 
| | 431.25
=== Parasoft tunings ===
| |
Parasoft tunings (step ratios 4:3 to 3:2) are associated with [[sensi]] tempermament.
|-
{{MOS tunings|Step Ratios=Parasoft|JI Ratios=Subgroup: 2.3.5.7.13; Int Limit: 50; Tenney Height: 8; Complements Only: 1|Tolerance=10}}
| |
 
| |
== Temperaments ==
| |
The major temperaments in this area are:
| | 9\25
* [[Sensi]] (Parasoft checkertonic)
| |
* [[Squares]] (Parahard checkertonic)
| |  
 
| | 432
== Music ==
| |
; [[Uncreative Name]]
|-
* [https://www.youtube.com/watch?v=XZ3zB3EDKOM ''The Nachtlandian Somersault''] (19edo)
| |
| | 4\11
| |
| |
| |
| |
| | 436.36
| style="text-align:center;" | Boundary of propriety:


generators larger than this are proper
== Scale tree ==
|-
Generator ranges:
| |
* Chroma-positive generator: 750{{c}} (5\8) to 800{{c}} (2\3)
| |
* Chroma-negative generator: 400{{c}} (1\3) to 450{{c}} (3\8)
| |
{{MOS tuning spectrum
| |
| 7/5 = [[Sensi]] (optimal around here)
| |
| 11/7 = [[Clyde]]
| |
| 13/8 = Golden [[sentry]] (759.4078{{c}})
| | 439.23
| 13/5 = Unnamed golden tuning (768.8815{{c}})
| |
| 11/4 = [[Hamity]]
|-
| 7/2 = [[Squares]] (optimal around here)
| |
| 6/1 = [[Roman]]↓, [[hocus]]↓
| |
}}
| |
| | 11\30
| |
| |
| | 440
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 29\79
| | 440.51
| style="text-align:center;" | Golden antioneirotonic
|-
| |
| |
| |
| |
| | 18\49
| |
| | 440.82
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 441.185
| |
|-
| |
| |
| | 7\19
| |
| |
| |
| | 442.11
| style="text-align:center;" | Optimum rank range (L/s=3/2) sensi
|-
| |
| |
| |
| |
| | 17\46
| |
| | 443.48
| style="text-align:center;" | Sensi is around here
|-
| |
| |
| |
| | 10\27
| |
| |
| | 444.44
| style="text-align:center;" |
|-
|
|
|
|
|13\35
|
|445.71
|
|-
|
|
|
|
|
|16\43
|446.51
|
|-
| | 3\8
| |
| |
| |
| |
| |
| | 450
| style="text-align:center;" |
|}
[[Category:Abstract MOS patterns]]
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