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3L 5s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = checkertonic
: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-28 03:01:51 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>248869005</tt>.<br>
| nLargeSteps = 3
: The revision comment was: <tt></tt><br>
| nSmallSteps = 5
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 5
<h4>Original Wikitext content:</h4>
| Collapsed = 2
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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]], in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.
| Pattern = LsLssLss
||||||||||||~ Generator ||~ Cents ||~ Comments ||
}}
|| 1\3 ||  ||  ||  ||  ||  || 400 ||=   ||
{{MOS intro|Other Names=anti-oneirotonic}}
||  ||  ||  || 6\17 ||  ||  || 423.53 ||=   ||
||  ||  ||  ||  ||  || 17\48 || 425 ||= Squares is around here ||
||  ||  ||  ||  || 11\31 ||  || 425.81 ||=   ||
||  ||  || 5\14 ||  ||  ||  || 428.57 ||=  ||
||  || 4\11 ||  ||  ||  ||  || 436.36 ||= Boundary of propriety: generators
larger than this are proper ||
||  ||  ||  || 11\30 ||  ||  || 440 ||=   ||
||  ||  ||  ||  ||  || 29\79 || 440.51 ||= Unnamed golden temperament ||
||  ||  ||  ||  || 18\49 ||  || 440.82 ||=  ||
||  ||  || 7\19 ||  ||  ||  || 442.11 ||=   ||
||  ||  ||  ||  || 17\46 ||  || 443.48 ||= Sensi is around here ||
||  ||  ||  || 10\27 ||  ||  || 444.44 ||=  ||
|| 3\8 ||  ||  ||  ||  ||  || 450 ||=  ||</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;3L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are two significant harmonic entropy minima with this MOS pattern. &lt;a class="wiki_link" href="/Sensipent%20family"&gt;Sensi&lt;/a&gt;, in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. &lt;a class="wiki_link" href="/Meantone%20family"&gt;Squares&lt;/a&gt;, in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.&lt;br /&gt;


== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale.


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &lt;th colspan="6"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;400&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6\17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;423.53&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17\48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;425&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Squares is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;425.81&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;428.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4\11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;436.36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety: generators&lt;br /&gt;
larger than this are proper&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29\79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440.51&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Unnamed golden temperament&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18\49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;440.82&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;442.11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;443.48&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Sensi is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;444.44&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;450&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== 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&nbsp;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"
|+ style="font-size: 105%;" | Scale degrees (on J, {{nowrap|sLssLsLs {{=}} JKLMNOPQ}})
|-
! [[UDP]]
! Anti-modes of 5L 3s
! Chess-based names
! Step pattern
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! (9)
|-
| 7{{pipe}}0
| Anti-Sarnathian
| King
| LsLssLss
| J
| K&amp;
| L
| M&amp;
| N&amp;
| O
| P&amp;
| Q
| (J)
|-
| 6{{pipe}}1
| Anti-Hlanithian
| Queen
| LssLsLss
| J
| K&amp;
| L
| M
| N&amp;
| O
| P&amp;
| Q
| (J)
|-
| 5{{pipe}}2
| Anti-Kadathian
| Marshall
| LssLssLs
| J
| K&amp;
| L
| M
| N&amp;
| O
| P
| Q
| (J)
|-
| 4{{pipe}}3
| Anti-Mnarian
| Cardinal
| sLsLssLs
| J
| K
| L
| M
| N&amp;
| O
| P
| Q
| (J)
|-
| 3{{pipe}}4
| Anti-Ultharian
| Rook
| sLssLsLs
| J
| K
| L
| M
| N
| O
| P
| Q
| (J)
|-
| 2{{pipe}}5
| Anti-Celephaïsian
| Bishop
| sLssLssL
| J
| K
| L
| M
| N
| O
| P
| Q@
| (J)
|-
| 1{{pipe}}6
| Anti-Illarnekian
| Knight
| ssLsLssL
| J
| K
| L@
| M
| N
| O
| P
| Q@
| (J)
|-
| 0{{pipe}}7
| Anti-Dylathian
| Pawn
| ssLssLsL
| J
| K
| L@
| M
| N
| O@
| P
| Q@
| (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 ==
The major temperaments in this area are:
* [[Sensi]] (Parasoft checkertonic)
* [[Squares]] (Parahard checkertonic)
 
== Music ==
; [[Uncreative Name]]
* [https://www.youtube.com/watch?v=XZ3zB3EDKOM ''The Nachtlandian Somersault''] (19edo)
 
== 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}})
| 13/5 = Unnamed golden tuning (768.8815{{c}})
| 11/4 = [[Hamity]]
| 7/2 = [[Squares]] (optimal around here)
| 6/1 = [[Roman]]↓, [[hocus]]↓
}}
Retrieved from "https://en.xen.wiki/w/3L_5s"