2L 8s

↖ 1L 7s	↑ 2L 7s	3L 7s ↗
← 1L 8s	2L 8s	3L 8s →
↙ 1L 9s	↓ 2L 9s	3L 9s ↘

Scale structure
Step pattern	LssssLssss ssssLssssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	4\10 to 1\2 (480.0 ¢ to 600.0 ¢)
Dark	0\2 to 1\10 (0.0 ¢ to 120.0 ¢)
TAMNAMS information
Name	jaric
Prefix	jara-
Abbrev.	ja
Related MOS scales
Parent	2L 6s
Sister	8L 2s
Daughters	10L 2s, 2L 10s
Neutralized	4L 6s
2-Flought	12L 8s, 2L 18s
Equal tunings
Equalized (L:s = 1:1)	4\10 (480.0 ¢)
Supersoft (L:s = 4:3)	13\32 (487.5 ¢)
Soft (L:s = 3:2)	9\22 (490.9 ¢)
Semisoft (L:s = 5:3)	14\34 (494.1 ¢)
Basic (L:s = 2:1)	5\12 (500.0 ¢)
Semihard (L:s = 5:2)	11\26 (507.7 ¢)
Hard (L:s = 3:1)	6\14 (514.3 ¢)
Superhard (L:s = 4:1)	7\16 (525.0 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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2L 8s, named jaric in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 8 small steps, with a period of 1 large step and 4 small steps that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 480 ¢ to 600 ¢, or from 0 ¢ to 120 ¢. 2L 8s is the MOS pattern of the decatonic scale of Paul Erlich and others.

The only significant harmonic entropy minimum that is proper is the decatonic scale itself (pajara[10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes 4/3, and another generator down makes 5/4. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found at either of these links:

http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf

http://www.lumma.org/tuning/erlich/

Improper harmonic entropy minima include injera (which is similar to pajara except that 5/4 is now four generators up and no periods) and shrutar (which is basically pajara with the generator divided in two).

In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords).

Notation

The notation used in this article is ssLssssLss = JKLMNOPQRSJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)

Thus the 12edo gamut is as follows:

J K L L& M N O P Q Q& R S J

Modes

• 8|0(2) LssssLssss, J-K&-L&-M-N-O-P&-Q&-R-S-J
• 6|2(2) sLssssLsss, J-K-L&-M-N-O-P-Q&-R-S-J
• 4|4(2) ssLssssLss, J-K-L-M-N-O-P-Q-R-S-J
• 2|6(2) sssLssssLs, J-K-L-M@-N-O-P-Q-R@-S-J
• 0|8(2) ssssLssssL, J-K-L-M@-N@-O-P-Q-R@-S@-J

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 2L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\10						480.000	120.000	1:1	1.000	Equalized 2L 8s
					21\52	484.615	115.385	6:5	1.200
				17\42		485.714	114.286	5:4	1.250
					30\74	486.486	113.514	9:7	1.286
			13\32			487.500	112.500	4:3	1.333	Supersoft 2L 8s
					35\86	488.372	111.628	11:8	1.375
				22\54		488.889	111.111	7:5	1.400
					31\76	489.474	110.526	10:7	1.429
		9\22				490.909	109.091	3:2	1.500	Soft 2L 8s
					32\78	492.308	107.692	11:7	1.571
				23\56		492.857	107.143	8:5	1.600
					37\90	493.333	106.667	13:8	1.625
			14\34			494.118	105.882	5:3	1.667	Semisoft 2L 8s
					33\80	495.000	105.000	12:7	1.714
				19\46		495.652	104.348	7:4	1.750
					24\58	496.552	103.448	9:5	1.800
	5\12					500.000	100.000	2:1	2.000	Basic 2L 8s Scales with tunings softer than this are proper
					21\50	504.000	96.000	9:4	2.250
				16\38		505.263	94.737	7:3	2.333
					27\64	506.250	93.750	12:5	2.400
			11\26			507.692	92.308	5:2	2.500	Semihard 2L 8s
					28\66	509.091	90.909	13:5	2.600
				17\40		510.000	90.000	8:3	2.667
					23\54	511.111	88.889	11:4	2.750
		6\14				514.286	85.714	3:1	3.000	Hard 2L 8s
					19\44	518.182	81.818	10:3	3.333
				13\30		520.000	80.000	7:2	3.500
					20\46	521.739	78.261	11:3	3.667
			7\16			525.000	75.000	4:1	4.000	Superhard 2L 8s
					15\34	529.412	70.588	9:2	4.500
				8\18		533.333	66.667	5:1	5.000
					9\20	540.000	60.000	6:1	6.000
1\2						600.000	0.000	1:0	→ ∞	Collapsed 2L 8s