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{{User:IlL/Template:RTT restriction}}
{{Infobox MOS
{{Infobox MOS
| Name = sensoid
| Name = checkertonic
| Periods = 1
| Periods = 1
| nLargeSteps = 3
| nLargeSteps = 3
| nSmallSteps = 5
| nSmallSteps = 5
| Equalized = 3
| Equalized = 5
| Paucitonic = 1
| Collapsed = 2
| Pattern = ssLssLsL
| Pattern = LsLssLss
}}
}}
{{MOS intro|Other Names=anti-oneirotonic}}


'''3L 5s''' or '''sensoid''' (named after the regular temperament [[sensi]]) refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degrees of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched.
== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale.


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|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.
== Scale properties ==
== Notation ==
{{TAMNAMS use}}
The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), #/@ = up/down by chroma, N = C4 = 261.6255653 Hz.


== Tuning ranges ==
=== Intervals ===
=== Parasoft ===
{{MOS intervals}}
Parasoft sensoid is the narrow region between 7\19 (442.1¢) and 10\27 (444.4¢). The root-mos5th-mos8th chords usually spell approximate 5:7:9 and 7:10:13 chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):
* Q M P = ssLs sLs L = 5:7:9
* J N Q = sLss LsL s = the odd one out
* K O J = LssL sLs s = 7:10:13
* L P K = ssLs Lss L = 5:7:9
* M Q L = sLsL ssL s = 7:10:13
* N J M = LsLs sLs s = 7:10:13
* O K N = sLss Lss L = 5:7:9
* P L O = LssL ssL s = 7:10:13
<!-- Tunings in this region have a regular temperament interpretation called [[Sensi]].-->


Sortable table of major and minor intervals in parasoft sensoid tunings:
=== Generator chain ===
 
{{MOS genchain}}
{| 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. sen2nd
| 2\19, 126.3
| 3\27, 133.3
| 5\46, 130.4
| K
| 14/13
| +3
|-
| maj. sen2nd
| 3\19, 189.5
| 4\27, 177.8
| 7\46, 182.6
| K&
| 10/9
| -5
|-
| min. sen3rd
| 4\19, 252.6
| 6\27, 266.7
| 10\46, 260.9
| L@
| 7/6
| +6
|-
| maj. sen3rd
| 5\19, 315.8
| 7\27, 311.1
| 12\46, 313.0
| L
| 6/5
| -2
|-
| perf. sen4th
| 7\19, 442.1
| 10\27, 444.4
| 17\46, 443.5
| M
| 9/7, 13/10
| +1
|-
| aug. sen4th
| 8\19, 505.3
| 11\27, 488.9
| 19\46, 495.7
| M&
| 4/3
| -7
|-
| min. sen5th
| 9\19, 568.4
| 13\27, 577.8
| 22\46, 573.9
| N
| 7/5, 18/13
| +4
|-
| maj. sen5th
| 10\19, 631.6
| 14\27, 622.2
| 24\46, 626.1
| N&
| 10/7, 13/9
| -4
|-
| dim. sen6th
| 11\19, 694.7
| 16\27, 711.1
| 27\46, 704.3
| O@
| 3/2
| +7
|-
| perf. sen6th
| 12\19, 757.9
| 17\27, 755.6
| 20\46, 756.5
| O
| 14/9, 20/13
| -1
|-
| min. sen7th
| 14\19, 884.2
| 20\27, 888.9
| 34\46, 887.0
| P
| 5/3
| +2
|-
| maj. sen7th
| 15\19, 947.4
| 21\27, 933.3
| 36\46, 939.1
| P&
| 12/7
| -6
|-
| min. sen8th
| 16\19, 1010.5
| 23\27, 1022.2
| 39\46, 1017.4
| Q
| 9/5
| +5
|-
| maj. sen8th
| 17\19, 1073.7
| 24\27, 1066.7
| 41\46, 1069.6
| Q&
| 13/7
| -3
|}


== Modes ==
=== Modes ===
Sensoid modes can be named by prefixing ''anti-'' to their counterpart modes in the MOS sister [[oneirotonic]].
{{MOS mode degrees}}


# Anti-Sarnathian (sar-NA(H)TH-iən): LsLssLss
==== Proposed mode names ====
# Anti-Hlanithian (lə-NITH-iən): LssLsLss
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.
# Anti-Kadathian (kə-DA(H)TH-iən): LssLssLs
{{MOS modes
# Anti-Mnarian (mə-NA(I)R-iən): sLsLssLs
| Table Headers=
# Anti-Ultharian (ul-THA(I)R-iən): sLssLsLs
Anti-modes of 5L&nbsp;3s $
# Anti-Celephaïsian (kel-ə-FAY-zhən): sLssLssL
Grand chess names<sup>[proposed]</sup>
# Anti-Illarnekian (ill-ar-NEK-iən): ssLsLssL
| Table Entries=
# Anti-Dylathian (də-LA(H)TH-iən): ssLssLsL
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 modes on the white keys JKLMNOPQJ are:
* J Anti-Ultharian, Rook
* J Anti-Ultharian
* K Anti-Hlanithian, Queen
* K Anti-Hlanithian
* L Anti-Illarnekian, Knight
* L Anti-Illarnekian
* M Anti-Mnarian, Cardinal
* M Anti-Mnarian
* N Anti-Sarnathian, King
* N Anti-Sarnathian
* O Anti-Celephaïsian, Bishop
* O Anti-Celephaïsian
* P Anti-Kadathian, Marshall
* P Anti-Kadathian
* Q Anti-Dylathian, Pawn
* Q Anti-Dylathian


{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 105%;" | Scale degrees (on J, {{nowrap|sLssLsLs {{=}} JKLMNOPQ}})
|-
|-
|+ Table of modes (based on J, from darkest to brightest)
! [[UDP]]
|-
! Anti-modes of 5L 3s
! Mode
! Chess-based names
! Step pattern
! 1
! 1
! 2
! 2
Line 199: Line 77:
! (9)
! (9)
|-
|-
| 7{{pipe}}0
| Anti-Sarnathian
| Anti-Sarnathian
| King
| LsLssLss
| J
| J
| K&
| K&amp;
| L
| L
| M&
| M&amp;
| N&
| N&amp;
| O
| O
| P&
| P&amp;
| Q
| Q
| (J)
| (J)
|-
|-
| 6{{pipe}}1
| Anti-Hlanithian
| Anti-Hlanithian
| Queen
| LssLsLss
| J
| J
| K&
| K&amp;
| L
| L
| M
| M
| N&
| N&amp;
| O
| O
| P&
| P&amp;
| Q
| Q
| (J)
| (J)
|-
|-
| 5{{pipe}}2
| Anti-Kadathian
| Anti-Kadathian
| Marshall
| LssLssLs
| J
| J
| K&
| K&amp;
| L
| L
| M
| M
| N&
| N&amp;
| O
| O
| P
| P
Line 232: Line 119:
| (J)
| (J)
|-
|-
| 4{{pipe}}3
| Anti-Mnarian
| Anti-Mnarian
| Cardinal
| sLsLssLs
| J
| J
| K
| K
| L
| L
| M
| M
| N&
| N&amp;
| O
| O
| P
| P
Line 243: Line 133:
| (J)
| (J)
|-
|-
| 3{{pipe}}4
| Anti-Ultharian
| Anti-Ultharian
| Rook
| sLssLsLs
| J
| J
| K
| K
Line 254: Line 147:
| (J)
| (J)
|-
|-
| 2{{pipe}}5
| Anti-Celephaïsian
| Anti-Celephaïsian
| Bishop
| sLssLssL
| J
| J
| K
| K
Line 265: Line 161:
| (J)
| (J)
|-
|-
| 1{{pipe}}6
| Anti-Illarnekian
| Anti-Illarnekian
| Knight
| ssLsLssL
| J
| J
| K
| K
Line 276: Line 175:
| (J)
| (J)
|-
|-
| 0{{pipe}}7
| Anti-Dylathian
| Anti-Dylathian
| Pawn
| ssLssLsL
| J
| J
| K
| K
Line 288: Line 190:
|}
|}


== Scale tree ==
== Notation ==
{| class="wikitable"
The [[TAMNAMS]] system is used in this article to refer to {{PAGENAME}} step size ratios and step ratio ranges.
|-
 
! colspan="6" | Generator
The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), &amp;/@ = up/down by chroma.
! | Cents
 
! | Comments
== 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.
| | 1\3
 
| |
=== 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.
| | 400
 
| style="text-align:center;" |
== 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}}
|8\23
 
|417.39
== Temperaments ==
|
The major temperaments in this area are:
|-
* [[Sensi]] (Parasoft checkertonic)
|
* [[Squares]] (Parahard checkertonic)
|
|
|
|7\20
|
|420
|
|-
| |
| |
| |
| | 6\17
| |
| |
| | 423.53
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| |
| | 17\48
| | 425
| style="text-align:center;" | Squares is around here
|-
| |
| |
| |
| |
| | 11\31
| |
| | 425.81
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 427.73
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| | 5\14
| |
| |
| |
| | 428.57
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| | 430.41
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| |
| |
| | 14\39
| |
| | 430.77
| |
|-
| |
| |
| |
| |
| |
| | 23\64
| | 431.25
| |
|-
| |
| |
| |
| | 9\25
| |
| |
| | 432
| |
|-
| |
| | 4\11
| |
| |
| |
| |
| | 436.36
| style="text-align:center;" | Boundary of propriety:


generators larger than this are proper
== Music ==
|-
; [[Uncreative Name]]
| |
* [https://www.youtube.com/watch?v=XZ3zB3EDKOM ''The Nachtlandian Somersault''] (19edo)
| |
| |
| |
| |
| |
| | 439.23
| |
|-
| |
| |
| |
| | 11\30
| |
| |
| | 440
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 29\79
| | 440.51
| style="text-align:center;" | Golden sensoid
|-
| |
| |
| |
| |
| | 18\49
| |
| | 440.82
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 441.185
| |
|-
| |
| |
| | 7\19
| |
| |
| |
| | 442.11
| style="text-align:center;" | Optimum rank range (L/s=3/2) sensi
|-
| |
| |
| |
| |
| | 17\46
| |
| | 443.48
| style="text-align:center;" | Sensi is around here
|-
| |
| |
| |
| | 10\27
| |
| |
| | 444.44
| style="text-align:center;" |
|-
|
|
|
|
|13\35
|
|445.71
|
|-
|
|
|
|
|
|16\43
|446.51
|
|-
| | 3\8
| |
| |
| |
| |
| |
| | 450
| style="text-align:center;" |
|}


[[Category:Scales]]
== Scale tree ==
[[Category:MOS scales]]
Generator ranges:
[[Category:Abstract MOS patterns]]
* 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]]↓
}}
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