4L 7s

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Scale structure
Step pattern	LsLssLssLss ssLssLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	8\11 to 3\4 (872.7 ¢ to 900.0 ¢)
Dark	1\4 to 3\11 (300.0 ¢ to 327.3 ¢)
TAMNAMS information
Related to	4L 3s (smitonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	4L 3s
Sister	7L 4s
Daughters	11L 4s, 4L 11s
Neutralized	8L 3s
2-Flought	15L 7s, 4L 18s
Equal tunings
Equalized (L:s = 1:1)	8\11 (872.7 ¢)
Supersoft (L:s = 4:3)	27\37 (875.7 ¢)
Soft (L:s = 3:2)	19\26 (876.9 ¢)
Semisoft (L:s = 5:3)	30\41 (878.0 ¢)
Basic (L:s = 2:1)	11\15 (880.0 ¢)
Semihard (L:s = 5:2)	25\34 (882.4 ¢)
Hard (L:s = 3:1)	14\19 (884.2 ¢)
Superhard (L:s = 4:1)	17\23 (887.0 ¢)
Collapsed (L:s = 1:0)	3\4 (900.0 ¢)

4L 7s or kleistonic klyse-TON-ik /klaɪsˈtɒnɪk/ refers to the structure of MOS scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 3\11edo (three degrees of 11edo, 327.27¢), representing approximate diatonic minor thirds (6/5). The name refers to the temperament that is one of the harmonic entropy minimums in this range (Kleismic/Hanson), itself named after the interval known as the kleisma.

4L 7s has a heptatonic subset, which is the hard end of the spectrum of the smitonic scale (4L 3s).

Notation

The notation used in this article is LssLsLssLss = А҃В҃Г҃Д҃Е҃Ѕ҃З҃И҃Ѳ҃І҃Ѫ҃А҃, based on old Cyrillic numerals 1-10 using the titlo as a numeric sign, and the addition of the big yus (Ѫ) for 11. Chromas are represented by regular sharps and flats. Thus the 15edo gamut is as follows: А҃ А҃#/В҃b В҃ Г҃ Д҃ Д҃#/Е҃b Е҃ Ѕ҃ Ѕ҃#/З҃b З҃ И҃ Ѳ҃ Ѳ҃#/І҃b І҃ Ѫ҃ А҃

Letter names

The letters can be named in English as such: Az, Vede, Glagol, Dobro, Yest, Dzelo, Zemlya, Izhe, Thita, I(Ee), Yus. They can also be named as numbers 1-11.

Intervals

Generators	Notation (1/1 = А҃)	Interval category name	Generators	Notation of 2/1 inverse	Interval category name
The 11-note MOS has the following intervals (from some root):
0	А҃	perfect unison	0	А҃	dodecave (same as octave)
1	Д҃	perfect kleifourth (minor third)	-1	Ѳ҃	perfect kleininth (major sixth)
2	З҃b	minor kleiseventh	-2	Ѕ҃	major kleisixth
3	І҃b	minor kleitenth	-3	Г҃	major kleithird
4	В҃b	minor kleisecond	-4	Ѫ҃	major kleieleventh
5	Е҃b	minor kleififth	-5	И҃	major kleieight
6	И҃b	minor kleieight	-6	Е҃	major kleififth
7	Ѫ҃b	minor kleieleventh	-7	В҃	major kleisecond
8	Г҃b	minor kleithird	-8	І҃	major kleitenth
9	Ѕ҃b	minor kleisixth	-9	З҃	major kleiseventh
10	Ѳ҃b	diminished kleininth	-10	Д҃#	augmented kleithird
The chromatic 15-note MOS (either 4L 11s, 11L 4s, or 15edo) also has the following intervals (from some root):
11	А҃b	diminished dodecave	-11	А҃#	augmented unison (kleichroma, kleicomma)
12	Д҃b	diminished kleifourth	-12	Ѳ҃#	augmented kleininth
13	З҃bb	diminished kleiseventh	-13	Ѕ҃#	augmented kleisixth
14	І҃bb	diminished kleitenth	-14	Г҃#	augmented kleithird

Genchain

The generator chain for this scale is as follows:

Д҃b

А҃b

Ѳ҃b

Ѕ҃b

Г҃b

Ѫ҃b

И҃b

Е҃b

В҃b

І҃b

З҃b

Д҃

А҃

Ѳ҃

Ѕ҃

Г҃

Ѫ҃

И҃

Е҃

В҃

І҃

З҃

Д҃#

А҃#

Ѳ҃#

Ѕ҃#

Г҃#

Ѫ҃#

И҃#

Е҃#

В҃#

І҃#

З҃#

d4

d12

d9

m6

m3

m11

m8

m5

m2

m10

m7

P4

P1

P9

M6

M3

M11

M8

M5

M2

M10

M7

A4

A1

A9

A6

A3

A11

A8

A5

A2

A10

A7

Tuning ranges

Soft range

The soft range for tunings of kleistonic encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than 4\15 = 320¢. This is the range associated with extensions of Orgone[7]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds.

Soft kleistonic edos include 15edo and 26edo. The sizes of the generator, large step and small step of kleistonic are as follows in various soft kleistonic tunings:

	15edo (basic)	26edo (soft)	Some JI approximations
generator (g)	4\15, 320.00	7\26, 323.08	77/64, 6/5
L (octave - 3g)	2\15, 160.00	3\26, 138.46	12/11, 13/12
s (4g - octave)	1\15, 80.00	2\19, 92.31	21/20, 22/21, 20/19

Hypohard

Hypohard tunings of kleistonic have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315.79¢ and flatter than 4\15 = 320¢. This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth (3/2), an octave above. This is the range associated with the eponymous Kleismic (aka Hanson) temperament and its extensions.

Hypohard kleistonic edos include 15edo, 19edo, and 34edo. The sizes of the generator, large step and small step of kleistonic are as follows in various hypohard kleistonic tunings:

	15edo (basic)	19edo (hard)	34edo (semihard)	Some JI approximations
generator (g)	4\15, 320.00	5\19, 315.79	9\34, 317.65	6/5
L (octave - 3g)	2\15, 160.00	3\19, 189.47	5\34, 176.47	10/9, 11/10 (in 15edo)
s (4g - octave)	1\15, 80.00	1\19, 63.16	2\34, 70.59	25/24, 26/25 (in better kleismic tunings)

Parahard

Parahard tunings of kleistonic have step ratios between 3/1 and 4/1, implying a generator sharper than 6\23 = 313.04¢ and flatter than 5\19 = 315.79¢. The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. However, the large step is recognizable as a regular diatonic whole step, approximating both 10/9 and 9/8, while the small step is a slightly sharp of a quarter tone.

Parahard kleistonic edos include 19edo, 32edo, and 42edo. The sizes of the generator, large step and small step of kleistonic are as follows in various parahard kleistonic tunings:

	19edo (hard)	23edo (superhard)	42edo (parahard)	Some JI approximations
generator (g)	5\19, 315.79	6\23, 313.04	11\42, 314.29	6/5
L (octave - 3g)	3\19, 189.47	4\23, 208.70	7\42, 200.00	10/9, 9/8
s (4g - octave)	1\19, 63.16	1\23, 52.17	2\42, 57.14	28/27, 33/32

Hyperhard

Hyperhard tunings of kleistonic have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity, where the small step is generally flat of a quarter tone.

Hyperhard kleistonic edos include 23edo, 31edo, and 27edo. The sizes of the generator, large step and small step of kleistonic are as follows in various hyperhard kleistonic tunings:

	23edo (superhard)	31edo (extrahard)	27edo (pentahard)	Some JI approximations
generator (g)	6\23, 313.04	8\31, 309.68	7\27, 311.11	6/5
L (octave - 3g)	4\23, 208.70	6\31, 232.26	5\27, 222.22	8/7, 9/8
s (4g - octave)	1\23, 52.17	1\31, 38.71	1\27, 44.44	36/35, 45/44

Modes

The names are based on smitonic modes, modified with the "super-" prefix, with thematic additions, as there are an extra 4 modes available.

Mode	UDP	Name
LsLssLssLss	10|0	Supernerevarine
LssLsLssLss	9|1	Supervivecan
LssLssLsLss	8|2	Superbaardauan
LssLssLssLs	7|3	Superlorkhanic
sLsLssLssLs	6|4	Supervvardenic
sLssLsLssLs	5|5	Supersothic
sLssLssLsLs	4|6	Supernumidian
sLssLssLssL	3|7	Superkagrenacan
ssLsLssLssL	2|8	Supernecromic
ssLssLsLssL	1|9	Superalmalexian
ssLssLssLsL	0|10	Superdagothic

Scale tree

The spectrum looks like this:

1\4								300¢
							10\39	307.692
						9\35		308.571
					8\31			309.677	Myna
							23\89	310.112	Myna
						15\58		310.345	Myna
				7\27				311.111	Starlingtet
			6\23					313.043	Skateboard
					17\65			313.846
				11\42				314.286
					16\61			314.754
						21\80		315
							26\99	315.152	Parakleismic
								315.332
		5\19						315.789	Keemun
					19\72			316.667	Catakleismic
								316.785
				14\53				316.981	Hanson/Marveltwintri/Cata
								317.17
					23\87			317.241	Countercata
			9\34					317.647
	4\15							320	Boundary of propriety (generators larger than this are proper)
								321.539
			11\41					321.951	Superkleismic
								322.268
				18\67				322.388
								322.585
		7\26						323.068	Magicaltet/Orgone
			10\37					324.324	Orgone
				13\48				325	Oregon
					16\59			325.424	Oregon
						19\70		325.714	Oregon
							22/81	325.926	Oregon
3\11								327.273	Oregon