3L 5s

↖ 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.

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¢). In the parasoft sensi MOS, root-mos5th-mos8th chords usually 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

Other otonal chords approximated in the parasoft sensoid MOS include:

• root - maj. sen7th - maj. sen8th ≈ 7:12:13
• root - maj. sen2nd - maj. sen5th ≈ 9:10:13
• root - min. sen3rd - dim. sen6th ≈ 6:7:9
• root - perf. sen4th - dim. sen6th ≈ 10:13:15 (ultramajor triad)
• root - perf. sen4th - maj. sen7th ≈ 7:9:13
• root - perf. sen4th - maj. sen5th - maj. sen7th ≈ 7:9:10:13
• root - perf. sen4th - min. sen7th ≈ 10:13:18
• root - perf. sen4th - min. sen5th - min. sen7th ≈ 10:13:14:18
• root - min. sen7th - min. sen3rd (+ octave) ≈ 3:5:7
• root - min. sen7th - min. sen2nd (+ octave) ≈ 6:10:13
• root - dim. sen6th - min. sen7th ≈ 6:9:10
• root - dim. sen6th - min. sen2nd (+octave) ≈ 6:9:13

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
				11\31		425.81
		5\14				428.57	L/s = 3
				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) sensoid
				17\46		443.48
			10\27			444.44
				13\35		445.71
					16\43	446.51
3\8						450