4L 5s

↖ 3L 4s ↑ 4L 4s 5L 4s ↗

← 3L 5s 4L 5s 5L 5s →

↙ 3L 6s ↓ 4L 6s 5L 6s ↘
	Scale structure
Step pattern	LsLsLsLss; ssLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
	Generator size
Bright	2\9 to 1\4 (266.7 ¢ to 300.0 ¢)
Dark	3\4 to 7\9 (900.0 ¢ to 933.3 ¢)
	TAMNAMS information
Name	gramitonic
Prefix	gram-
Abbrev.	gm
	Related MOS scales
Parent	4L 1s
Sister	5L 4s
Daughters	9L 4s, 4L 9s
Neutralized	8L 1s
2-Flought	13L 5s, 4L 14s
	Equal tunings
Equalized (L:s = 1:1)	2\9 (266.7 ¢)
Supersoft (L:s = 4:3)	7\31 (271.0 ¢)
Soft (L:s = 3:2)	5\22 (272.7 ¢)
Semisoft (L:s = 5:3)	8\35 (274.3 ¢)
Basic (L:s = 2:1)	3\13 (276.9 ¢)
Semihard (L:s = 5:2)	7\30 (280.0 ¢)
Hard (L:s = 3:1)	4\17 (282.4 ¢)
Superhard (L:s = 4:1)	5\21 (285.7 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
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For the tritave-equivalent 4L 5s pattern, see 4L 5s (3/1-equivalent).

4L 5s, named gramitonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 5 small steps, repeating every octave. Generators that produce this scale range from 266.7 ¢ to 300 ¢, or from 900 ¢ to 933.3 ¢.

Names

The TAMNAMS name for this pattern is gramitonic (from grave minor third).

Scale properties

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

Intervals of 4L 5s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-gramstep	Perfect 0-gramstep	P0gms	0	0.0 ¢
1-gramstep	Minor 1-gramstep	m1gms	s	0.0 ¢ to 133.3 ¢
1-gramstep	Major 1-gramstep	M1gms	L	133.3 ¢ to 300.0 ¢
2-gramstep	Diminished 2-gramstep	d2gms	2s	0.0 ¢ to 266.7 ¢
2-gramstep	Perfect 2-gramstep	P2gms	L + s	266.7 ¢ to 300.0 ¢
3-gramstep	Minor 3-gramstep	m3gms	L + 2s	300.0 ¢ to 400.0 ¢
3-gramstep	Major 3-gramstep	M3gms	2L + s	400.0 ¢ to 600.0 ¢
4-gramstep	Minor 4-gramstep	m4gms	L + 3s	300.0 ¢ to 533.3 ¢
4-gramstep	Major 4-gramstep	M4gms	2L + 2s	533.3 ¢ to 600.0 ¢
5-gramstep	Minor 5-gramstep	m5gms	2L + 3s	600.0 ¢ to 666.7 ¢
5-gramstep	Major 5-gramstep	M5gms	3L + 2s	666.7 ¢ to 900.0 ¢
6-gramstep	Minor 6-gramstep	m6gms	2L + 4s	600.0 ¢ to 800.0 ¢
6-gramstep	Major 6-gramstep	M6gms	3L + 3s	800.0 ¢ to 900.0 ¢
7-gramstep	Perfect 7-gramstep	P7gms	3L + 4s	900.0 ¢ to 933.3 ¢
7-gramstep	Augmented 7-gramstep	A7gms	4L + 3s	933.3 ¢ to 1200.0 ¢
8-gramstep	Minor 8-gramstep	m8gms	3L + 5s	900.0 ¢ to 1066.7 ¢
8-gramstep	Major 8-gramstep	M8gms	4L + 4s	1066.7 ¢ to 1200.0 ¢
9-gramstep	Perfect 9-gramstep	P9gms	4L + 5s	1200.0 ¢

Modes

Scale degrees of the modes of 4L 5s
UDP	Cyclic order	Step pattern	Scale degree (gramdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9
8\|0	1	LsLsLsLss	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Perf.
7\|1	3	LsLsLssLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
6\|2	5	LsLssLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
5\|3	7	LssLsLsLs	Perf.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
4\|4	9	sLsLsLsLs	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
3\|5	2	sLsLsLssL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Perf.
2\|6	4	sLsLssLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Perf.
1\|7	6	sLssLsLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
0\|8	8	ssLsLsLsL	Perf.	Min.	Dim.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.

Proposed Names

Lilly Flores proposed using the Greek name relating to water as mode names. The names are in reference to the scale's former name orwelloid because the word Orwell comes from 'a spring situated near a promontory'.

Modes of 4L 5s
UDP	Cyclic order	Step pattern
8\|0	1	LsLsLsLss
7\|1	3	LsLsLssLs
6\|2	5	LsLssLsLs
5\|3	7	LssLsLsLs
4\|4	9	sLsLsLsLs
3\|5	2	sLsLsLssL
2\|6	4	sLsLssLsL
1\|7	6	sLssLsLsL
0\|8	8	ssLsLsLsL

Theory

The only low harmonic entropy minimum corresponds to orwell temperament, where 1 generator approximates 7/6, 2 generators approximate 11/8, and 3 generators approximate 8/5.

Tuning ranges

Parasoft

Parasoft tunings of 4L 5s have a step ratio between 4/3 and 3/2, implying a generator sharper than 7\31 = 270.97¢ and flatter than 5\22 = 272.73¢.

Parasoft 4L 5s EDOs include 22edo, 31edo, 53edo, and 84edo.

22edo can be used to make large and small steps more distinct (the step ratio is 3/2).
31edo can be used for its nearly pure 5/4.
53edo can be used for its nearly pure 3/2 and good 5/4.

The sizes of the generator, large step and small step of 4L 5s are as follows in various parasoft 4L 5s tunings.

	22edo	31edo	53edo	84edo	JI intervals represented
generator (g)	5\22, 272.73	7\31, 270.97	12\53, 271.70	19\84, 271.43	7/6
L (5g - octave)	3\22, 163.64	4\31, 154.84	7\53, 158.49	11\84, 157.14	12/11, 11/10
s (octave - 4g)	2\22, 109.09	3\31, 116.13	5\53, 113.21	8\84, 114.29	16/15, 15/14

This set of JI interpretations (g = 7/6, 2g = 11/8, 3g = 8/5, 7g = 3/2) is called 11-limit orwell temperament in regular temperament theory.

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 4L 5s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
2\9						266.667	933.333	1:1	1.000	Equalized 4L 5s
					11\49	269.388	930.612	6:5	1.200
				9\40		270.000	930.000	5:4	1.250
					16\71	270.423	929.577	9:7	1.286
			7\31			270.968	929.032	4:3	1.333	Supersoft 4L 5s
					19\84	271.429	928.571	11:8	1.375
				12\53		271.698	928.302	7:5	1.400
					17\75	272.000	928.000	10:7	1.429
		5\22				272.727	927.273	3:2	1.500	Soft 4L 5s
					18\79	273.418	926.582	11:7	1.571
				13\57		273.684	926.316	8:5	1.600
					21\92	273.913	926.087	13:8	1.625
			8\35			274.286	925.714	5:3	1.667	Semisoft 4L 5s
					19\83	274.699	925.301	12:7	1.714
				11\48		275.000	925.000	7:4	1.750
					14\61	275.410	924.590	9:5	1.800
	3\13					276.923	923.077	2:1	2.000	Basic 4L 5s Scales with tunings softer than this are proper
					13\56	278.571	921.429	9:4	2.250
				10\43		279.070	920.930	7:3	2.333
					17\73	279.452	920.548	12:5	2.400
			7\30			280.000	920.000	5:2	2.500	Semihard 4L 5s
					18\77	280.519	919.481	13:5	2.600
				11\47		280.851	919.149	8:3	2.667
					15\64	281.250	918.750	11:4	2.750
		4\17				282.353	917.647	3:1	3.000	Hard 4L 5s
					13\55	283.636	916.364	10:3	3.333
				9\38		284.211	915.789	7:2	3.500
					14\59	284.746	915.254	11:3	3.667
			5\21			285.714	914.286	4:1	4.000	Superhard 4L 5s
					11\46	286.957	913.043	9:2	4.500
				6\25		288.000	912.000	5:1	5.000
					7\29	289.655	910.345	6:1	6.000
1\4						300.000	900.000	1:0	→ ∞	Collapsed 4L 5s