Xenharmonic Wiki

3L 5s: Difference between revisions

← Older edit
VisualWikitext
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
ArrowHead294 (talk | contribs)
14,512 edits
 
(8 intermediate revisions by 3 users not shown)
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.
 
== Theory ==
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.
 
=== 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 ==
=== Modes ===
=== 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}}
 
== Modes ==
{{MOS mode degrees}}
{{MOS mode degrees}}


=== Proposed names ===
==== Proposed mode 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 {{w|grand chess}} pieces.
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
{{MOS modes|Table Headers=Anti-modes of 5L 3s;Grand chess names<sup>[proposed]</sup>|Table Entries=Anti-Sarnathian (sar-NA(H)TH-iən);
| Table Headers=
King;
Anti-modes of 5L&nbsp;3s $
Anti-Hlanithian (lə-NITH-iən);
Grand chess names<sup>[proposed]</sup>
Queen;
| Table Entries=
Anti-Kadathian (kə-DA(H)TH-iən);
Anti-Sarnathian (sar-NA(H)TH-iən) $
Marshall;
King $
Anti-Mnarian (mə-NA(I)R-iən);
Anti-Hlanithian (lə-NITH-iən) $
Cardinal;
Queen $
Anti-Ultharian (ul-THA(I)R-iən);
Anti-Kadathian (kə-DA(H)TH-iən) $
Rook;
Marshall $
Anti-Celephaïsian (kel-ə-FAY-zhən);
Anti-Mnarian (mə-NA(I)R-iən) $
Bishop;
Cardinal $
Anti-Illarnekian (ill-ar-NEK-iən);
Anti-Ultharian (ul-THA(I)R-iən) $
Knight;
Rook $
Anti-Dylathian (də-LA(H)TH-iən);
Anti-Celephaïsian (kel-ə-FAY-zhən) $
Pawn;}}
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 202: Line 189:
| (J)
| (J)
|}
|}
== 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 ==
== Temperaments ==
Line 209: Line 218:


== 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)
 
{{MOS tuning spectrum
{{Scale tree|Comments=
| 7/5 = [[Sensi]] (optimal around here)
7/5: [[Sensi]] (optimal around here);
| 11/7 = [[Clyde]]
11/7: [[Clyde]];
| 13/8 = Golden [[sentry]] (759.4078{{c}})
13/8: Golden [[sentry]] (759.4078¢);
| 13/5 = Unnamed golden tuning (768.8815{{c}})
13/5: Unnamed golden tuning (768.8815¢);
| 11/4 = [[Hamity]]
11/4: [[Hamity]];
| 7/2 = [[Squares]] (optimal around here)
7/2: [[Squares]] (optimal around here);
| 6/1 = [[Roman]]↓, [[hocus]]↓
6/1: [[Roman]]↓, [[hocus]]↓;
}}
}}
[[Category:8-tone scales]]
Retrieved from "https://en.xen.wiki/w/3L_5s"