1L 7s

	↑ 1L 6s	2L 6s ↗
	1L 7s	2L 7s →
	↓ 1L 8s	2L 8s ↘

┌╥┬┬┬┬┬┬┬┐ │║││││││││ ││││││││││ └┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	Lsssssss sssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	7\8 to 1\1 (1050.0¢ to 1200.0¢)
Dark	0\1 to 1\8 (0.0¢ to 150.0¢)
Related MOS scales
Parent	1L 6s
Sister	7L 1s
Daughters	8L 1s, 1L 8s
Neutralized	2L 6s
2-Flought	9L 7s, 1L 15s
Equal tunings
Equalized (L:s = 1:1)	7\8 (1050.0¢)
Supersoft (L:s = 4:3)	22\25 (1056.0¢)
Soft (L:s = 3:2)	15\17 (1058.8¢)
Semisoft (L:s = 5:3)	23\26 (1061.5¢)
Basic (L:s = 2:1)	8\9 (1066.7¢)
Semihard (L:s = 5:2)	17\19 (1073.7¢)
Hard (L:s = 3:1)	9\10 (1080.0¢)
Superhard (L:s = 4:1)	10\11 (1090.9¢)
Collapsed (L:s = 1:0)	1\1 (1200.0¢)

1L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 7 small steps, repeating every octave. Generators that produce this scale range from 1050¢ to 1200¢, or from 0¢ to 150¢. This MOS pattern is somewhat of a wasteland as far as low-harmonic-entropy scales are concerned. However, there is one interesting no-5's scale, bleu. In this scale, 5 steps make a 3/2, and the chord 11:12:13:14 is represented as three equal steps.

Name

TAMNAMS suggests the temperament-agnostic name antipine as the name of 1L 7s. The name is based on being the opposite pattern of 7L 1s (pine).

Scale properties

Intervals

The intervals of 1L 7s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 8-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

Intervals of 1L 7s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0¢ to 150.0¢
	Augmented 1-mosstep	A1ms	L	150.0¢ to 1200.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 300.0¢
	Major 2-mosstep	M2ms	L + s	300.0¢ to 1200.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 450.0¢
	Major 3-mosstep	M3ms	L + 2s	450.0¢ to 1200.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 600.0¢
	Major 4-mosstep	M4ms	L + 3s	600.0¢ to 1200.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 750.0¢
	Major 5-mosstep	M5ms	L + 4s	750.0¢ to 1200.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 900.0¢
	Major 6-mosstep	M6ms	L + 5s	900.0¢ to 1200.0¢
7-mosstep	Diminished 7-mosstep	d7ms	7s	0.0¢ to 1050.0¢
	Perfect 7-mosstep	P7ms	L + 6s	1050.0¢ to 1200.0¢
8-mosstep	Perfect 8-mosstep	P8ms	L + 7s	1200.0¢

Generator chain

A chain of bright generators, each a perfect 7-mosstep, produces the following scale degrees. A chain of 8 bright generators contains the scale degrees of one of the modes of 1L 7s. Expanding the chain to 9 scale degrees produces the modes of either 8L 1s (for soft-of-basic tunings) or 1L 8s (for hard-of-basic tunings).

Generator chain of 1L 7s

Bright gens	Scale Degree	-	8	Augmented 0-mosdegree	A0md
7	Augmented 1-mosdegree	A1md
6	Major 2-mosdegree	M2md
5	Major 3-mosdegree	M3md
4	Major 4-mosdegree	M4md
3	Major 5-mosdegree	M5md
2	Major 6-mosdegree	M6md
1	Perfect 7-mosdegree	P7md
0	Perfect 0-mosdegree Perfect 8-mosdegree	P0md P8md
-1	Perfect 1-mosdegree	P1md
-2	Minor 2-mosdegree	m2md
-3	Minor 3-mosdegree	m3md
-4	Minor 4-mosdegree	m4md
-5	Minor 5-mosdegree	m5md
-6	Minor 6-mosdegree	m6md
-7	Diminished 7-mosdegree	d7md
-8	Diminished 8-mosdegree	d8md

Modes

Scale degrees of the modes of 1L 7s 

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8
7|0	1	Lsssssss	Perf.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
6|1	8	sLssssss	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
5|2	7	ssLsssss	Perf.	Perf.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
4|3	6	sssLssss	Perf.	Perf.	Min.	Min.	Maj.	Maj.	Maj.	Perf.	Perf.
3|4	5	ssssLsss	Perf.	Perf.	Min.	Min.	Min.	Maj.	Maj.	Perf.	Perf.
2|5	4	sssssLss	Perf.	Perf.	Min.	Min.	Min.	Min.	Maj.	Perf.	Perf.
1|6	3	ssssssLs	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0|7	2	sssssssL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Dim.	Perf.

Scale tree

Generator ranges:

• Chroma-positive generator: 1050 cents (7\8) to 1200 cents (1\1)
• Chroma-negative generator: 0 cents (0\1) to 150 cents (1\8)

Small step (chroma-negative generator)						Cents	L	s	L/s	Comments
1\8						150.000	1	1	1.000
					5\41	146.341	6	5	1.200	Bohpier
				4\33		145.455	5	4	1.250
					7\58	144.828	9	7	1.286
			3\25			144.000	4	3	1.333
					8\67	143.284	11	8	1.375
				5\42		142.857	7	5	1.400
					7\59	142.373	10	7	1.429
		2\17				141.176	3	2	1.500
					7\60	140.000	11	7	1.571	Bleu
				5\43		139.535	8	5	1.600	Jerome/bleu
					8\69	139.130	13	8	1.625	Golden jerome (139.2429¢)
			3\26			138.462	5	3	1.667
					7\61	137.705	12	7	1.714
				4\35		137.143	7	4	1.750
					5\44	136.364	9	5	1.800	Twothirdtonic
	1\9					133.333	2	1	2.000	Basic 1L 7s (small steps larger than this are proper)
					4\37	129.730	9	4	2.250
				3\28		128.571	7	3	2.333
					5\47	127.660	12	5	2.400
			2\19			126.316	5	2	2.500	Negri
					5\48	125.000	13	5	2.600	Golden negri (124.7656¢)
				3\29		124.138	8	3	2.667
					4\39	123.077	11	4	2.750
		1\10				120.000	3	1	3.000
					3\31	116.129	10	3	3.333	Miracle
				2\21		114.286	7	2	3.500
					3\32	112.500	11	3	3.667
			1\11			109.091	4	1	4.000
					2\23	104.348	9	2	4.500
				1\12		100.000	5	1	5.000	Passion, ripple
					1\13	92.308	6	1	6.000
0\1						0.000	1	0	→ inf

Trivia

This scale is a leap year pattern of the tabular Iranian calendar, where the leap year is inserted 7 times once in 4 years, with 1 gap of 5 years. Curiously enough, one short step of this scale is close to the one step of Bohlen-Pierce.