3L 5s: Difference between revisions

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-'''3L 5s''' or '''sensoid''' 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.
+'''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.
 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.
+== Notation ==
+The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), #/@ = up/down by chroma, N = C4 = 261.6255653 Hz.
+== Tuning ranges ==
+=== Parasoft ===
+Parasoft is the narrow region between 7\19 (442.1¢) and 10\27 (444.4¢). The root-mos5th-mos8th chords usually spell 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]].-->
+== Modes ==
+Sensoid modes can be named by prefixing ''anti-'' to their counterpart modes in the MOS sister [[oneirotonic]].
+# Anti-Sarnathian (sar-NA(H)TH-iən): LsLssLss
+# Anti-Hlanithian (lə-NITH-iən): LssLsLss
+# Anti-Kadathian (kə-DA(H)TH-iən): LssLssLs
+# Anti-Mnarian (mə-NA(I)R-iən): sLsLssLs
+# Anti-Ultharian (ul-THA(I)R-iən): sLssLsLs
+# Anti-Celephaïsian (kel-ə-FAY-zhən): sLssLssL
+# Anti-Illarnekian (ill-ar-NEK-iən): ssLsLssL
+# Anti-Dylathian (də-LA(H)TH-iən): ssLssLsL
+The modes on the white keys JKLMNOPQJ are:
+* J Anti-Ultharian
+* K Anti-Hlanithian
+* L Anti-Illarnekian
+* M Anti-Mnarian
+* N Anti-Sarnathian
+* O Anti-Celephaïsian
+* P Anti-Kadathian
+* Q Anti-Dylathian
+{| class="wikitable"
+|-
+|+ Table of modes (based on J, from darkest to brightest)
+|-
+! Mode
+! 1
+! 2
+! 3
+! 4
+! 5
+! 6
+! 7
+! 8
+! (9)
+|-
+| Anti-Sarnathian
+| J
+| K&
+| L
+| M&
+| N&
+| O
+| P&
+| Q
+| (J)
+|-
+| Anti-Hlanithian
+| J
+| K&
+| L
+| M
+| N&
+| O
+| P&
+| Q
+| (J)
+|-
+| Anti-Kadathian
+| J
+| K&
+| L
+| M
+| N&
+| O
+| P
+| Q
+| (J)
+|-
+| Anti-Mnarian
+| J
+| K
+| L
+| M
+| N&
+| O
+| P
+| Q
+| (J)
+|-
+| Anti-Ultharian
+| J
+| K
+| L
+| M
+| N
+| O
+| P
+| Q
+| (J)
+|-
+| Anti-Celephaïsian
+| J
+| K
+| L
+| M
+| N
+| O
+| P
+| Q@
+| (J)
+|-
+| Anti-Illarnekian
+| J
+| K
+| L@
+| M
+| N
+| O
+| P
+| Q@
+| (J)
+|-
+| Anti-Dylathian
+| J
+| K
+| L@
+| M
+| N
+| O@
+| P
+| Q@
+| (J)
+|}
+== Scale tree ==
 {| class="wikitable"
 |-