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 ¢)
TAMNAMS information
Name	antipine
Prefix	apine-
Abbrev.	ap
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, named antipine in TAMNAMS, 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

Intervals of 1L 7s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-apinestep	Perfect 0-apinestep	P0aps	0	0.0 ¢
1-apinestep	Perfect 1-apinestep	P1aps	s	0.0 ¢ to 150.0 ¢
	Augmented 1-apinestep	A1aps	L	150.0 ¢ to 1200.0 ¢
2-apinestep	Minor 2-apinestep	m2aps	2s	0.0 ¢ to 300.0 ¢
	Major 2-apinestep	M2aps	L + s	300.0 ¢ to 1200.0 ¢
3-apinestep	Minor 3-apinestep	m3aps	3s	0.0 ¢ to 450.0 ¢
	Major 3-apinestep	M3aps	L + 2s	450.0 ¢ to 1200.0 ¢
4-apinestep	Minor 4-apinestep	m4aps	4s	0.0 ¢ to 600.0 ¢
	Major 4-apinestep	M4aps	L + 3s	600.0 ¢ to 1200.0 ¢
5-apinestep	Minor 5-apinestep	m5aps	5s	0.0 ¢ to 750.0 ¢
	Major 5-apinestep	M5aps	L + 4s	750.0 ¢ to 1200.0 ¢
6-apinestep	Minor 6-apinestep	m6aps	6s	0.0 ¢ to 900.0 ¢
	Major 6-apinestep	M6aps	L + 5s	900.0 ¢ to 1200.0 ¢
7-apinestep	Diminished 7-apinestep	d7aps	7s	0.0 ¢ to 1050.0 ¢
	Perfect 7-apinestep	P7aps	L + 6s	1050.0 ¢ to 1200.0 ¢
8-apinestep	Perfect 8-apinestep	P8aps	L + 7s	1200.0 ¢

Generator chain

Generator chain of 1L 7s

Bright gens	Scale degree	Abbrev.
8	Augmented 0-apinedegree	A0apd
7	Augmented 1-apinedegree	A1apd
6	Major 2-apinedegree	M2apd
5	Major 3-apinedegree	M3apd
4	Major 4-apinedegree	M4apd
3	Major 5-apinedegree	M5apd
2	Major 6-apinedegree	M6apd
1	Perfect 7-apinedegree	P7apd
0	Perfect 0-apinedegree Perfect 8-apinedegree	P0apd P8apd
−1	Perfect 1-apinedegree	P1apd
−2	Minor 2-apinedegree	m2apd
−3	Minor 3-apinedegree	m3apd
−4	Minor 4-apinedegree	m4apd
−5	Minor 5-apinedegree	m5apd
−6	Minor 6-apinedegree	m6apd
−7	Diminished 7-apinedegree	d7apd
−8	Diminished 8-apinedegree	d8apd

Modes

Scale degrees of the modes of 1L 7s

UDP	Cyclic order	Step pattern	Scale degree (apinedegree)
			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 ¢ (7\8) to 1200 ¢ (1\1)
• Chroma-negative generator: 0 ¢ (0\1) to 150 ¢ (1\8)

Scale tree and tuning spectrum of 1L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\8						1050.000	150.000	1:1	1.000	Equalized 1L 7s
					36\41	1053.659	146.341	6:5	1.200	Bohpier
				29\33		1054.545	145.455	5:4	1.250
					51\58	1055.172	144.828	9:7	1.286
			22\25			1056.000	144.000	4:3	1.333	Supersoft 1L 7s
					59\67	1056.716	143.284	11:8	1.375
				37\42		1057.143	142.857	7:5	1.400
					52\59	1057.627	142.373	10:7	1.429
		15\17				1058.824	141.176	3:2	1.500	Soft 1L 7s
					53\60	1060.000	140.000	11:7	1.571	Bleu
				38\43		1060.465	139.535	8:5	1.600	Jerome/bleu
					61\69	1060.870	139.130	13:8	1.625	Golden jerome (139.2429 ¢)
			23\26			1061.538	138.462	5:3	1.667	Semisoft 1L 7s
					54\61	1062.295	137.705	12:7	1.714
				31\35		1062.857	137.143	7:4	1.750
					39\44	1063.636	136.364	9:5	1.800	Twothirdtonic
	8\9					1066.667	133.333	2:1	2.000	Basic 1L 7s Scales with tunings softer than this are proper
					33\37	1070.270	129.730	9:4	2.250
				25\28		1071.429	128.571	7:3	2.333
					42\47	1072.340	127.660	12:5	2.400
			17\19			1073.684	126.316	5:2	2.500	Semihard 1L 7s Negri
					43\48	1075.000	125.000	13:5	2.600	Golden negri (124.7656 ¢)
				26\29		1075.862	124.138	8:3	2.667
					35\39	1076.923	123.077	11:4	2.750
		9\10				1080.000	120.000	3:1	3.000	Hard 1L 7s
					28\31	1083.871	116.129	10:3	3.333	Miracle
				19\21		1085.714	114.286	7:2	3.500
					29\32	1087.500	112.500	11:3	3.667
			10\11			1090.909	109.091	4:1	4.000	Superhard 1L 7s
					21\23	1095.652	104.348	9:2	4.500
				11\12		1100.000	100.000	5:1	5.000	Passion, ripple
					12\13	1107.692	92.308	6:1	6.000
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 7s

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 the Bohlen–Pierce scale.