5L 5s

↖ 4L 4s	↑ 5L 4s	6L 4s ↗
← 4L 5s	5L 5s	6L 5s →
↙ 4L 6s	↓ 5L 6s	6L 6s ↘

Scale structure
Step pattern	LsLsLsLsLs sLsLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	1\5 (240.0 ¢)
Generator size
Bright	1\10 to 1\5 (120.0 ¢ to 240.0 ¢)
Dark	0\5 to 1\10 (0.0 ¢ to 120.0 ¢)
TAMNAMS information
Name	pentawood
Prefix	pentawd-
Abbrev.	pw
Related MOS scales
Parent	none
Sister	5L 5s (self)
Daughters	10L 5s, 5L 10s
Neutralized	10edo
2-Flought	15L 5s, 5L 15s
Equal tunings
Equalized (L:s = 1:1)	1\10 (120.0 ¢)
Supersoft (L:s = 4:3)	4\35 (137.1 ¢)
Soft (L:s = 3:2)	3\25 (144.0 ¢)
Semisoft (L:s = 5:3)	5\40 (150.0 ¢)
Basic (L:s = 2:1)	2\15 (160.0 ¢)
Semihard (L:s = 5:2)	5\35 (171.4 ¢)
Hard (L:s = 3:1)	3\20 (180.0 ¢)
Superhard (L:s = 4:1)	4\25 (192.0 ¢)
Collapsed (L:s = 1:0)	1\5 (240.0 ¢)
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5L 5s, named pentawood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 5 small steps, with a period of 1 large step and 1 small step that repeats every 240.0 ¢, or 5 times every octave. Generators that produce this scale range from 120 ¢ to 240 ¢, or from 0 ¢ to 120 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

There is only one significant harmonic entropy minimum with this MOS pattern: blackwood, in which intervals of the prime numbers 3 and 7 are all represented using steps of 5edo, and the generator reaches intervals of 5, such as 6/5, 5/4, and 7/5.

In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms, which are also single-alteration MODMOSses – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.

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 5L 5s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-pentawdstep	Perfect 0-pentawdstep	P0pws	0	0.0 ¢
1-pentawdstep	Minor 1-pentawdstep	m1pws	s	0.0 ¢ to 120.0 ¢
	Major 1-pentawdstep	M1pws	L	120.0 ¢ to 240.0 ¢
2-pentawdstep	Perfect 2-pentawdstep	P2pws	L + s	240.0 ¢
3-pentawdstep	Minor 3-pentawdstep	m3pws	L + 2s	240.0 ¢ to 360.0 ¢
	Major 3-pentawdstep	M3pws	2L + s	360.0 ¢ to 480.0 ¢
4-pentawdstep	Perfect 4-pentawdstep	P4pws	2L + 2s	480.0 ¢
5-pentawdstep	Minor 5-pentawdstep	m5pws	2L + 3s	480.0 ¢ to 600.0 ¢
	Major 5-pentawdstep	M5pws	3L + 2s	600.0 ¢ to 720.0 ¢
6-pentawdstep	Perfect 6-pentawdstep	P6pws	3L + 3s	720.0 ¢
7-pentawdstep	Minor 7-pentawdstep	m7pws	3L + 4s	720.0 ¢ to 840.0 ¢
	Major 7-pentawdstep	M7pws	4L + 3s	840.0 ¢ to 960.0 ¢
8-pentawdstep	Perfect 8-pentawdstep	P8pws	4L + 4s	960.0 ¢
9-pentawdstep	Minor 9-pentawdstep	m9pws	4L + 5s	960.0 ¢ to 1080.0 ¢
	Major 9-pentawdstep	M9pws	5L + 4s	1080.0 ¢ to 1200.0 ¢
10-pentawdstep	Perfect 10-pentawdstep	P10pws	5L + 5s	1200.0 ¢

Modes

Scale degrees of the modes of 5L 5s

UDP	Cyclic order	Step pattern	Scale degree (pentawddegree)
			0	1	2	3	4	5	6	7	8	9	10
5|0(5)	1	LsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.
0|5(5)	2	sLsLsLsLsL	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 5L 5s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\10						120.000	120.000	1:1	1.000	Equalized 5L 5s
					6\55	130.909	109.091	6:5	1.200	Qintosec ↑
				5\45		133.333	106.667	5:4	1.250
					9\80	135.000	105.000	9:7	1.286
			4\35			137.143	102.857	4:3	1.333	Supersoft 5L 5s
					11\95	138.947	101.053	11:8	1.375
				7\60		140.000	100.000	7:5	1.400	Warlock
					10\85	141.176	98.824	10:7	1.429
		3\25				144.000	96.000	3:2	1.500	Soft 5L 5s
					11\90	146.667	93.333	11:7	1.571
				8\65		147.692	92.308	8:5	1.600
					13\105	148.571	91.429	13:8	1.625	Unnamed golden tuning (148.328 ¢)
			5\40			150.000	90.000	5:3	1.667	Semisoft 5L 5s
					12\95	151.579	88.421	12:7	1.714
				7\55		152.727	87.273	7:4	1.750	Quinkee
					9\70	154.286	85.714	9:5	1.800
	2\15					160.000	80.000	2:1	2.000	Basic 5L 5s Blackwood (optimal around here)
					9\65	166.154	73.846	9:4	2.250	Trisedodge
				7\50		168.000	72.000	7:3	2.333
					12\85	169.412	70.588	12:5	2.400
			5\35			171.429	68.571	5:2	2.500	Semihard 5L 5s
					13\90	173.333	66.667	13:5	2.600	Unnamed golden tuning (173.666 ¢)
				8\55		174.545	65.455	8:3	2.667
					11\75	176.000	64.000	11:4	2.750
		3\20				180.000	60.000	3:1	3.000	Hard 5L 5s
					10\65	184.615	55.385	10:3	3.333
				7\45		186.667	53.333	7:2	3.500
					11\70	188.571	51.429	11:3	3.667
			4\25			192.000	48.000	4:1	4.000	Superhard 5L 5s
					9\55	196.364	43.636	9:2	4.500
				5\30		200.000	40.000	5:1	5.000
					6\35	205.714	34.286	6:1	6.000	Cloudtone ↓
1\5						240.000	0.000	1:0	→ ∞	Collapsed 5L 5s