3L 5s: Difference between revisions

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== Tuning ranges ==
== Tuning ranges ==
=== Parasoft ===
=== Parasoft ===
Parasoft sensoid 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):
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
* Q M P = ssLs sLs L = 5:7:9
* J N Q = sLss LsL s = the odd one out
* J N Q = sLss LsL s = the odd one out
Line 28: Line 28:
* P L O = LssL ssL s = 7:10:13
* P L O = LssL ssL s = 7:10:13
<!-- Tunings in this region have a regular temperament interpretation called [[Sensi]].-->
<!-- Tunings in this region have a regular temperament interpretation called [[Sensi]].-->
Sortable table of major and minor intervals in parasoft sensoid tunings:
{| 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 ==

Revision as of 03:19, 3 April 2021

User:IlL/Template:RTT restriction

↖ 2L 4s ↑ 3L 4s 4L 4s ↗
← 2L 5s 3L 5s 4L 5s →
↙ 2L 6s ↓ 3L 6s 4L 6s ↘ 
┌╥┬╥┬┬╥┬┬┐
│║│║││║│││
││││││││││
└┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLss
ssLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\8 to 2\3 (750.0 ¢ to 800.0 ¢)
Dark 1\3 to 3\8 (400.0 ¢ to 450.0 ¢)
TAMNAMS information
Name checkertonic
Prefix check-
Abbrev. chk
Related MOS scales
Parent 3L 2s
Sister 5L 3s
Daughters 8L 3s, 3L 8s
Neutralized 6L 2s
2-Flought 11L 5s, 3L 13s
Equal tunings
Equalized (L:s = 1:1) 5\8 (750.0 ¢)
Supersoft (L:s = 4:3) 17\27 (755.6 ¢)
Soft (L:s = 3:2) 12\19 (757.9 ¢)
Semisoft (L:s = 5:3) 19\30 (760.0 ¢)
Basic (L:s = 2:1) 7\11 (763.6 ¢)
Semihard (L:s = 5:2) 16\25 (768.0 ¢)
Hard (L:s = 3:1) 9\14 (771.4 ¢)
Superhard (L:s = 4:1) 11\17 (776.5 ¢)
Collapsed (L:s = 1:0) 2\3 (800.0 ¢)

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. 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. 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 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

Sortable table of major and minor intervals in parasoft sensoid tunings:

Degree Size in 19edo (soft) Size in 27edo (supersoft) Size in 46edo Note name on J 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

Sensoid modes can be named by prefixing anti- to their counterpart modes in the MOS sister oneirotonic.

  1. Anti-Sarnathian (sar-NA(H)TH-iən): LsLssLss
  2. Anti-Hlanithian (lə-NITH-iən): LssLsLss
  3. Anti-Kadathian (kə-DA(H)TH-iən): LssLssLs
  4. Anti-Mnarian (mə-NA(I)R-iən): sLsLssLs
  5. Anti-Ultharian (ul-THA(I)R-iən): sLssLsLs
  6. Anti-Celephaïsian (kel-ə-FAY-zhən): sLssLssL
  7. Anti-Illarnekian (ill-ar-NEK-iən): ssLsLssL
  8. 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
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

Generator Cents Comments
1\3 400
8\23 417.39
7\20 420
6\17 423.53 L/s = 4
17\48 425 Squares is around here
11\31 425.81
427.73 L/s = pi
5\14 428.57 L/s = 3
430.41 L/s = e
14\39 430.77
23\64 431.25
9\25 432
4\11 436.36 Boundary of propriety:

generators larger than this are proper

439.23
11\30 440
29\79 440.51 Golden sensoid
18\49 440.82
441.185
7\19 442.11 Optimum rank range (L/s=3/2) sensi
17\46 443.48 Sensi is around here
10\27 444.44
13\35 445.71
16\43 446.51
3\8 450
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