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| Pattern = LsLssLss
| Pattern = LsLssLss
}}
}}
{{MOS intro|Other Names=anti-oneirotonic}}


{{MOS intro|Other Names=anti-oneirotonic}}
== Name ==
== Name==
[[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale.
[[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale.


==Intervals==
== Scale properties ==
:''This article assumes [[TAMNAMS]] for naming step ratios, intevrvals, and scale degrees.''
{{TAMNAMS use}}


Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.
=== Intervals ===
{{MOS intervals}}
{{MOS intervals}}


== Notation ==
=== Generator chain ===
The [[TAMNAMS]] system is used in this article to refer to {{PAGENAME}} step size ratios and step ratio ranges.
{{MOS genchain}}


The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), &/@ = up/down by chroma.
=== Modes ===
{{MOS mode degrees}}


== Theory ==
==== Proposed mode names ====
In contrast to oneirotonic ([[5L 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.
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:


=== Low harmonic entropy scales ===
* J Anti-Ultharian, Rook
There are two significant harmonic entropy minima with this MOS pattern:
* 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


* [[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.
{| class="wikitable"
* [[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.
|+ style="font-size: 105%;" | Scale degrees (on J, {{nowrap|sLssLsLs {{=}} JKLMNOPQ}})
 
==Tuning ranges==
===Simple tunings===
{| class="wikitable right-2 right-3 right-4 sortable "
|-
|-
! class="unsortable" |Degree
! [[UDP]]
! Size in [[11edo]] (basic)
! Anti-modes of 5L 3s
!Size in [[14edo]] (hard)
! Chess-based names
!Size in [[19edo]] (soft)
! Step pattern
! class="unsortable" |Note name on J
! 1
!#Gens up
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! (9)
|-
|-
|min. chk2nd
| 7{{pipe}}0
|1\11, 109.1
| Anti-Sarnathian
| 1\14, 85.7
| King
|2\19, 126.3
| LsLssLss
|K
| J
| +3
| K&amp;
| L
| M&amp;
| N&amp;
| O
| P&amp;
| Q
| (J)
|-
|-
|maj. chk2nd
| 6{{pipe}}1
|2\11, 218.2
| Anti-Hlanithian
|3\14, 257.1
| Queen
|3\19, 189.5
| LssLsLss
|K&
| J
| -5
| K&amp;
| L
| M
| N&amp;
| O
| P&amp;
| Q
| (J)
|-
|-
|min. chk3rd
| 5{{pipe}}2
|2\11, 218.2
| Anti-Kadathian
|2\14, 171.4
| Marshall
|4\19, 252.6
| LssLssLs
|L@
| J
| +6
| K&amp;
|-
| L
| maj. chk3rd
|3\11, 327.3
| 4\14, 342.9
| 5\19, 315.8
|L
| -2
|-
|perf. chk4th
|4\11, 436.4
|5\14, 428.6
| 7\19, 442.1
| M
| M
| +1
| N&amp;
|-
|aug. chk4th
|5\11, 545.5
|7\14, 600.0
|8\19, 505.3
|M&
| -7
|-
|min. chk5th
|5\11, 545.5
|6\14, 514.3
|9\19, 568.4
|N
|  +4
|-
|maj. chk5th
|6\11, 656.6
|8\14, 685.7
|10\19, 631.6
|N&
|  -4
|-
|dim. chk6th
|6\11, 656.6
| 7\14, 600.0
|11\19, 694.7
|O@
| +7
|-
|perf. chk6th
|7\11, 763.6
|8\14, 771.4
|12\19, 757.9
| O
| O
| -1
|-
|min. chk7th
|8\11, 872.7
|10\14, 857.1
|14\19, 884.2
| P
| P
| +2
|-
|maj. chk7th
| 9\11, 981.8
|12\14, 1028.6
|15\19, 947.4
| P&
| -6
|-
|min. chk8th
|9\11, 981.8
|11\14, 942.9
|16\19, 1010.5
|Q@
| +5
|-
|maj. chk8th
|10\11, 1090.9
|13\14, 1114.3
|17\19, 1073.7
| Q
| Q
| -3
| (J)
|}
 
===Parasoft===
Parasoft checkertonic is the narrow region between 7\19 (442.1¢) and 10\27 (444.4¢).
 
Sortable table of major and minor intervals in parasoft checkertonic tunings:
 
{| class="wikitable right-2 right-3 right-4 sortable "
|-
|-
! class="unsortable" |Degree
| 4{{pipe}}3
!Size in [[19edo]] (soft)
| Anti-Mnarian
!Size in [[27edo]] (supersoft)
| Cardinal
!Size in [[46edo]]
| sLsLssLs
! class="unsortable" | Note name on J
| J
! class="unsortable" |Approximate ratios
| K
!#Gens up
| L
|-
|unison
|0\19, 0.00
|0\27, 0.00
|0\46, 0.00
|J
|1/1
|0
|-
|min. chk2nd
|2\19, 126.3
|3\27, 133.3
|5\46, 130.4
|K
|14/13
|  +3
|-
| maj. chk2nd
|3\19, 189.5
|4\27, 177.8
| 7\46, 182.6
|K&
|10/9
| -5
|-
|min. chk3rd
|4\19, 252.6
|6\27, 266.7
| 10\46, 260.9
|L@
|7/6
| +6
|-
|maj. chk3rd
|5\19, 315.8
|7\27, 311.1
| 12\46, 313.0
|L
|6/5
| -2
|-
|perf. chk4th
|7\19, 442.1
|10\27, 444.4
|17\46, 443.5
| M
| M
|9/7, 13/10
| N&amp;
| +1
| O
| P
| Q
| (J)
|-
|-
|aug. chk4th
| 3{{pipe}}4
|8\19, 505.3
| Anti-Ultharian
|11\27, 488.9
| Rook
|19\46, 495.7
| sLssLsLs
|M&
|4/3
|  -7
|-
|min. chk5th
|9\19, 568.4
|13\27, 577.8
| 22\46, 573.9
|N
|7/5, 18/13
| +4
|-
|maj. chk5th
|10\19, 631.6
| 14\27, 622.2
|24\46, 626.1
|N&
|10/7, 13/9
| -4
|-
|dim. chk6th
|11\19, 694.7
|16\27, 711.1
|27\46, 704.3
| O@
|3/2
| +7
|-
|perf. chk6th
|12\19, 757.9
| 17\27, 755.6
|20\46, 756.5
|O
| 14/9, 20/13
| -1
|-
|min. chk7th
|14\19, 884.2
| 20\27, 888.9
|34\46, 887.0
|P
|5/3
| +2
|-
|maj. chk7th
|15\19, 947.4
|21\27, 933.3
|36\46, 939.1
|P&
|12/7
| -6
|-
|min. chk8th
|16\19, 1010.5
|23\27, 1022.2
|39\46, 1017.4
|Q@
|9/5
| +5
|-
|maj. chk8th
| 17\19, 1073.7
|24\27, 1066.7
|41\46, 1069.6
|Q
|13/7
| -3
|}
 
Tunings in this region have a regular temperament interpretation called [[sensi]].
 
==Modes==
Checkertonic modes can be named by prefixing ''anti-'' to their counterpart modes in the MOS sister [[oneirotonic]].
 
#Anti-Sarnathian (sar-NA(H)TH-iən): LsLssLss
#Anti-Hlanithian (lə-NITH-iən): LssLsLss
#Anti-Kadathian (kə-DA(H)TH-iən): LssLssLs
# Anti-Mnarian (mə-NA(I)R-iən): sLsLssLs
#Anti-Ultharian (ul-THA(I)R-iən): sLssLsLs
#Anti-Celephaïsian (kel-ə-FAY-zhən): sLssLssL
#Anti-Illarnekian (ill-ar-NEK-iən): ssLsLssL
#Anti-Dylathian (də-LA(H)TH-iən): ssLssLsL
 
The modes on the white keys JKLMNOPQJ are:
*J Anti-Ultharian
* K Anti-Hlanithian
* L Anti-Illarnekian
*M Anti-Mnarian
*N Anti-Sarnathian
*O Anti-Celephaïsian
*P Anti-Kadathian
*Q Anti-Dylathian
 
{| class="wikitable"
|-
|+Table of modes (based on J, from brightest to darkest)
|-
!Mode
! 1
!2
!3
! 4
!5
!6
!7
!8
!(9)
|-
|Anti-Sarnathian
| J
| J
|K&
| K
|L
|M&
|N&
|O
| P&
|Q
|(J)
|-
|Anti-Hlanithian
|J
|K&
| L
| L
| M
| M
| N&
| N
|O
| O
|P&
| P
| Q
| Q
|(J)
| (J)
|-
|-
|Anti-Kadathian
| 2{{pipe}}5
|J
| Anti-Celephaïsian
| K&
| Bishop
|L
| sLssLssL
|M
| J
|N&
| K
|O
| L
|P
| M
|Q
| N
|(J)
| O
| P
| Q@
| (J)
|-
|-
|Anti-Mnarian
| 1{{pipe}}6
|J
| Anti-Illarnekian
|K
| Knight
|L
| ssLsLssL
|M
| J
|N&
| K
|O
| L@
|P
| M
|Q
|(J)
|-
| Anti-Ultharian
|J
|K
|L
|M
| N
| N
|O
|P
|Q
|(J)
|-
|Anti-Celephaïsian
|J
|K
|L
|M
|N
| O
| O
|P
| P
|Q@
| Q@
|(J)
| (J)
|-
|-
|Anti-Illarnekian
| 0{{pipe}}7
|J
| Anti-Dylathian
|K
| Pawn
|L@
| ssLssLsL
|M
| J
|N
| K
|O
| L@
| M
| N
| O@
| P
| P
|Q@
| Q@
|(J)
| (J)
|-
|Anti-Dylathian
|J
|K
|L@
|M
|N
|O@
|P
|Q@
|(J)
|}
|}


==Temperaments==
== Notation ==
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.
 
=== Low harmonic entropy scales ===
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}}
 
=== 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:
The major temperaments in this area are:
*[[Sensi]] (Parasoft checkertonic)
* [[Sensi]] (Parasoft checkertonic)
*[[Squares]] (Parahard checkertonic)
* [[Squares]] (Parahard checkertonic)


==Scale tree==
== Music ==
; [[Uncreative Name]]
* [https://www.youtube.com/watch?v=XZ3zB3EDKOM ''The Nachtlandian Somersault''] (19edo)
 
== Scale tree ==
Generator ranges:
Generator ranges:
*Chroma-positive generator: 750 cents (5\8) to 800 cents (2\3)
* Chroma-positive generator: 750{{c}} (5\8) to 800{{c}} (2\3)
* Chroma-negative generator: 400 cents (1\3) to 450 cents (3\8)
* Chroma-negative generator: 400{{c}} (1\3) to 450{{c}} (3\8)
 
{{MOS tuning spectrum
{| class="wikitable center-all"
| 7/5 = [[Sensi]] (optimal around here)
! colspan="6" |Generator
| 11/7 = [[Clyde]]
!Cents
| 13/8 = Golden [[sentry]] (759.4078{{c}})
! L
| 13/5 = Unnamed golden tuning (768.8815{{c}})
!s
| 11/4 = [[Hamity]]
!L/s
| 7/2 = [[Squares]] (optimal around here)
!Comments
| 6/1 = [[Roman]]↓, [[hocus]]↓
|-
}}
|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||
|-
| ||  ||  || || ||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]]
|-
| ||  ||  ||  ||31\49|| ||759.184|| 8|| 5|| 1.600||
|-
| || || || || ||50\79 || 759.494||13|| 8||1.625||Golden checkertonic/[[sentry]] (759.4078¢)
|-
| || || ||19\30|| || ||760.000||5|| 3|| 1.667||
|-
| || || || || ||45\71||760.563||12|| 7|| 1.714||
|-
|  ||  ||  ||  ||26\41|| || 760.976||7||4||1.750||
|-
| || || || || ||33\52||761.538 || 9|| 5|| 1.800||
|-
| ||7\11|| ||  ||  || ||763.636 ||2||1 || 2.000|| Basic checkertonic <br>(Generators smaller than this are proper)
|-
|  || || ||  || ||30\47||765.957||9||4 ||2.250 ||
|-
| || || || ||23\36|| ||766.667||7||3|| 2.333||
|-
| || ||  ||  || ||39\61||767.213||12||5|| 2.400||
|-
| ||  || || 16\25|| || ||768.000||5||2 ||2.500||
|-
| || || ||  ||  ||41\64|| 768.750||13 || 5||2.600||Unnamed golden tuning (768.8815¢)
|-
| || || || ||25\39|| ||769.231||8||3|| 2.667||
|-
| || || || || ||34\53||769.811||11||4||2.750||[[Hamity]]
|-
| || ||9\14|| ||  || || 771.429 ||3||1||3.000||
|-
| || || || || ||29\45||773.333 || 10||3||3.333 ||
|-
| ||  || || ||20\31|| ||774.194||7||2||3.500||[[Squares]] is in this region
|-
| ||  || || || ||31\48 ||775.000||11|| 3|| 3.667||
|-
|  ||  ||  || 11\17|| || ||776.471 || 4||1||4.000||
|-
| ||  ||  || || ||24\37||778.378||9|| 2|| 4.500||
|-
| || || || ||13\20||  || 780.000||5||1||5.000||
|-
| || || || || ||15\23||782.609 || 6|| 1||6.000||[[Roman]]↓, [[Hocus]]↓
|-
| 2\3|| || ||  ||  || ||800.000||1||0||→ inf||
|}
 
[[Category:8-tone scales]]
[[Category:checkertonic]]
Retrieved from "https://en.xen.wiki/w/3L_5s"