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{{Todo|cleanup|inline=1|text=Adopt zero-indexed intervals/degrees}}{{Infobox MOS
{{Infobox MOS
| Name = checkertonic
| Name = checkertonic
| Periods = 1
| Periods = 1
Line 8: Line 8:
| 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}}


=== 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
=== Low harmonic entropy scales ===
| Table Headers=
There are two significant harmonic entropy minima with this MOS pattern:
Anti-modes of 5L 3s $
 
Grand chess names<sup>[proposed]</sup>
* [[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.
| Table Entries=
* [[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.
Anti-Sarnathian (sar-NA(H)TH-iən) $
 
King $
==Tuning ranges==
Anti-Hlanithian (lə-NITH-iən) $
===Simple tunings===
Queen $
{| class="wikitable right-2 right-3 right-4 sortable "
Anti-Kadathian (kə-DA(H)TH-iən) $
|-
Marshall $
! class="unsortable" |Degree
Anti-Mnarian (mə-NA(I)R-iən) $
! Size in [[11edo]] (basic)
Cardinal $
!Size in [[14edo]] (hard)
Anti-Ultharian (ul-THA(I)R-iən) $
!Size in [[19edo]] (soft)
Rook $
! class="unsortable" |Note name on J
Anti-Celephaïsian (kel-ə-FAY-zhən) $
!#Gens up
Bishop $
|-
Anti-Illarnekian (ill-ar-NEK-iən) $
|min. chk2nd
Knight $
|1\11, 109.1
Anti-Dylathian (də-LA(H)TH-iən) $
| 1\14, 85.7
Pawn $
|2\19, 126.3
}}
|K
| +3
|-
|maj. chk2nd
|2\11, 218.2
|3\14, 257.1
|3\19, 189.5
|K&
|  -5
|-
|min. chk3rd
|2\11, 218.2
|2\14, 171.4
|4\19, 252.6
|L@
| +6
|-
| 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
| +1
|-
|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
| -1
|-
|min. chk7th
|8\11, 872.7
|10\14, 857.1
|14\19, 884.2
| 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
| -3
|}
 
===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
!Size in [[19edo]] (soft)
!Size in [[27edo]] (supersoft)
!Size in [[46edo]]
! class="unsortable" | Note name on J
! class="unsortable" |Approximate ratios
!#Gens up
|-
|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
|9/7, 13/10
| +1
|-
|aug. chk4th
|8\19, 505.3
|11\27, 488.9
|19\46, 495.7
|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==
{{MOS mode degrees}}
===Proposed Names===
The modes of checkertonic can be named after its sister MOS [[5L 3s]] (oneirotonic). [[User:R-4981|R-4981]] has also proposed names based on [[wikipedia:Grand_Chess|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:
The order of modes on the white keys JKLMNOPQ are:


Line 312: Line 61:


{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 105%;" | Scale degrees (on J, {{nowrap|sLssLsLs {{=}} JKLMNOPQ}})
|-
|-
|+Scale degrees (on J, sLssLsLs = JKLMNOPQ)
! [[UDP]]
|-
! Anti-modes of 5L 3s
![[UDP]]
! Chess-based names
!Anti-modes of 5L 3s
! Step pattern
!Chess-based names
!Step pattern
! 1
! 1
!2
! 2
!3
! 3
! 4
! 4
!5
! 5
!6
! 6
!7
! 7
!8
! 8
!(9)
! (9)
|-
|-
|<nowiki>7|0</nowiki>
| 7{{pipe}}0
|Anti-Sarnathian
| Anti-Sarnathian
|King
| King
|LsLssLss
| LsLssLss
| J
| J
|K&
| K&amp;
|L
| L
|M&
| M&amp;
|N&
| N&amp;
|O
| O
|P&
| P&amp;
|Q
| Q
|(J)
| (J)
|-
|-
|<nowiki>6|1</nowiki>
| 6{{pipe}}1
|Anti-Hlanithian
| Anti-Hlanithian
|Queen
| Queen
|LssLsLss
| LssLsLss
|J
| J
|K&
| K&amp;
| L
| L
| M
| M
| N&
| N&amp;
|O
| O
|P&
| P&amp;
|Q
| Q
|(J)
| (J)
|-
|-
|<nowiki>5|2</nowiki>
| 5{{pipe}}2
|Anti-Kadathian
| Anti-Kadathian
|Marshall
| Marshall
|LssLssLs
| LssLssLs
|J
| J
| K&
| K&amp;
|L
| L
|M
| M
|N&
| N&amp;
|O
| O
|P
| P
|Q
| Q
|(J)
| (J)
|-
|-
|<nowiki>4|3</nowiki>
| 4{{pipe}}3
|Anti-Mnarian
| Anti-Mnarian
|Cardinal
| Cardinal
|sLsLssLs
| sLsLssLs
|J
| J
|K
| K
|L
| L
|M
| M
|N&
| N&amp;
|O
| O
|P
| P
|Q
| Q
|(J)
| (J)
|-
|-
|<nowiki>3|4</nowiki>
| 3{{pipe}}4
| Anti-Ultharian
| Anti-Ultharian
|Rook
| Rook
|sLssLsLs
| sLssLsLs
|J
| J
|K
| K
|L
| L
|M
| M
| N
| N
|O
| O
|P
| P
|Q
| Q
|(J)
| (J)
|-
|-
|<nowiki>2|5</nowiki>
| 2{{pipe}}5
|Anti-Celephaïsian
| Anti-Celephaïsian
|Bishop
| Bishop
|sLssLssL
| sLssLssL
|J
| J
|K
| K
|L
| L
|M
| M
|N
| N
| O
| O
|P
| P
|Q@
| Q@
|(J)
| (J)
|-
|-
|<nowiki>1|6</nowiki>
| 1{{pipe}}6
|Anti-Illarnekian
| Anti-Illarnekian
|Knight
| Knight
|ssLsLssL
| ssLsLssL
|J
| J
|K
| K
|L@
| L@
|M
| M
|N
| N
|O
| O
|P
| P
|Q@
| Q@
|(J)
| (J)
|-
|-
|<nowiki>0|7</nowiki>
| 0{{pipe}}7
|Anti-Dylathian
| Anti-Dylathian
|Pawn
| Pawn
|ssLssLsL
| ssLssLsL
|J
| J
|K
| K
|L@
| L@
|M
| M
|N
| N
|O@
| O@
|P
| P
|Q@
| Q@
|(J)
| (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)
 
== Music ==
; [[Uncreative Name]]
* [https://www.youtube.com/watch?v=XZ3zB3EDKOM ''The Nachtlandian Somersault''] (19edo)


==Scale tree==
== 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"