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3L 5s: Difference between revisions

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{{Todo|cleanup|inline=1|text=Adopt zero-indexed intervals/degrees, add scale tree entries from previous page version}}{{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 ==
{{TAMNAMS use}}
{{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 $
{{MOS tunings}}
Anti-Kadathian (kə-DA(H)TH-iən) $
 
Marshall $
===Parasoft tunings===
Anti-Mnarian (mə-NA(I)R-iən) $
Parasoft tunings (step ratios 4:3 to 3:2) are associated with [[sensi]] tempermament.
Cardinal $
{{MOS tunings|Step Ratios=Parasoft|JI Ratios=Subgroup: 2.3.5.7.13; Int Limit: 50; Tenney Height: 8; Complements Only: 1|Tolerance=10}}
Anti-Ultharian (ul-THA(I)R-iən) $
 
Rook $
==Modes==
Anti-Celephaïsian (kel-ə-FAY-zhən) $
{{MOS mode degrees}}
Bishop $
===Proposed Names===
Anti-Illarnekian (ill-ar-NEK-iən) $
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.
Knight $
{{MOS modes|Table Headers=Anti-modes of 5L 3s;Grand chess names<sup>[proposed]</sup>|Table Entries=Anti-Sarnathian (sar-NA(H)TH-iən);
Anti-Dylathian (də-LA(H)TH-iən) $
King;
Pawn $
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 71: 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 ==
== Music ==
* [[Uncreative Name]], [https://www.youtube.com/watch?v=XZ3zB3EDKOM The Nachtlandian Somersault] (19edo)
; [[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)
{{Scale tree}}
{{MOS tuning spectrum
 
| 7/5 = [[Sensi]] (optimal around here)
[[Category:8-tone scales]]
| 11/7 = [[Clyde]]
[[Category:checkertonic]]
| 13/8 = Golden [[sentry]] (759.4078{{c}})
| 13/5 = Unnamed golden tuning (768.8815{{c}})
| 11/4 = [[Hamity]]
| 7/2 = [[Squares]] (optimal around here)
| 6/1 = [[Roman]]↓, [[hocus]]↓
}}
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