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 is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 7 small steps, repeating every octave. 4L 7s is a child scale of 4L 3s, expanding it by 4 tones. Generators that produce this scale range from 872.7 ¢ to 900 ¢, or from 300 ¢ to 327.3 ¢. One of the harmonic entropy minimums in this range is Kleismic/Hanson.

Name

TAMNAMS formerly used the name kleistonic for the name of this scale (prefix klei-). Other names include p-chro smitonic or smipechromic.

Intervals

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals of 4L 7s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 109.1 ¢
	Major 1-mosstep	M1ms	L	109.1 ¢ to 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 218.2 ¢
	Major 2-mosstep	M2ms	L + s	218.2 ¢ to 300.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	300.0 ¢ to 327.3 ¢
	Augmented 3-mosstep	A3ms	2L + s	327.3 ¢ to 600.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	300.0 ¢ to 436.4 ¢
	Major 4-mosstep	M4ms	2L + 2s	436.4 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	300.0 ¢ to 545.5 ¢
	Major 5-mosstep	M5ms	2L + 3s	545.5 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	600.0 ¢ to 654.5 ¢
	Major 6-mosstep	M6ms	3L + 3s	654.5 ¢ to 900.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	600.0 ¢ to 763.6 ¢
	Major 7-mosstep	M7ms	3L + 4s	763.6 ¢ to 900.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	2L + 6s	600.0 ¢ to 872.7 ¢
	Perfect 8-mosstep	P8ms	3L + 5s	872.7 ¢ to 900.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	900.0 ¢ to 981.8 ¢
	Major 9-mosstep	M9ms	4L + 5s	981.8 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	900.0 ¢ to 1090.9 ¢
	Major 10-mosstep	M10ms	4L + 6s	1090.9 ¢ to 1200.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	4L + 7s	1200.0 ¢

Genchain

Generators	-11	-10	-9	-8	-7	-6	-5	-4	-3	-2	-1	0	+1	+2	+3	+4	+5	+6	+7	+8	+9	+10	+11
Interval quality	d11md	d8md	m5md	m2md	m10md	m7md	m4md	m1md	m9md	m6md	P3md	P0md	P8md	M5md	M2md	M10md	M7md	M4md	M1md	M9md	M6md	A3md	A0md

Tuning ranges

Soft range

The soft range for tunings of 4L 7s 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 edos include 15edo and 26edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various soft 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 4L 7s 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 edos include 15edo, 19edo, and 34edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various hypohard 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 4L 7s 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 approximate 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 edos include 19edo, 23edo, and 42edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various parahard 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 4L 7s 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 edos include 23edo, 31edo, and 27edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various hyperhard 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

Scale degrees of the modes of 4L 7s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11
10|0	1	LsLssLssLss	Perf.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
9|1	9	LssLsLssLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
8|2	6	LssLssLsLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Perf.
7|3	3	LssLssLssLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
6|4	11	sLsLssLssLs	Perf.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
5|5	8	sLssLsLssLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
4|6	5	sLssLssLsLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Perf.
3|7	2	sLssLssLssL	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
2|8	10	ssLsLssLssL	Perf.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
1|9	7	ssLssLsLssL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.
0|10	4	ssLssLssLsL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Perf.

Scales

• Oregon11
• Orgone11
• Magicaltet11
• Cata11
• Starlingtet11
• Myna11

Gallery

Cheat sheet for 19EDO, a hard tuning for 4L 7s (or kleistonic).