2L 3s

This scale is the "Classic" pentatonic. Perhaps the most common scale in the world.

The meantone pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly proper.

Names

The TAMNAMS system suggests the name pentic, derived from an informal clipping of "pentatonic" that is sometimes used to refer to this scale.

Scale Tree

Generator						Cents	s	L-s	|L-2s|	Scale steps	Trichord	Comments
2\5						480	240	0	240	1 1 1 1 1	1 1
					11\27	488.89	222.22	44.44	177.78	6 5 5 6 5	6 5	Slendro (insofar as it resembles a MOS) would be in this region
				9\22		490.91	218.18	54.545	163.64	5 4 4 5 4	5 4
					16\39	492.31	215.38	61.54	153.85	9 7 7 9 7	9 7	No-5's superpyth/dominant is around here
			7\17			494.12	211.76	70.59	141.18	4 3 3 4 3	4 3
					19\46	495.65	208.7	78.26	130.435	11 8 8 11 8	11 8
				12\29		496.55	206.9	82.76	124.14	7 5 5 7 5	7 5
					17\41	497.56	204.88	87.8	117.07	10 7 7 10 7	10 7	Pythagorean pentatonic is around here
		5\12				500	200	100	100	3 2 2 3 2	3 2	Familiar 12-equal pentatonic (also optimum rank range: L/s=3/2)
						502.305	195.39	111.53	83.86	pi 2 pi 2 2	pi 2
					18\43	502.33	195.35	111.63	83.72	11 7 7 11 7	11 7
				13\31		503.23	193.55	116.13	77.42	8 5 5 8 5	8 5	Optimal meantone pentatonic is around here
						1200/(4-phi)	192.43	118.93	73.50	phi 1 1 phi 1	phi 1	Golden meantone
					21\50	504	192	120	72	13 8 8 13 8	13 8
			8\19			505.26	189.47	126.32	63.16	5 3 3 5 3	5 3
					19\45	506.67	186.67	133.33	53.33	12 7 7 12 7	12 7
						507.18	185.64	135.9	49.74	√3 1 √3 1 1	√3 1
				11\26		507.69	184.615	138.46	46.15	7 4 4 7 4	7 4
					14\33	509.09	181.82	145.455	36.36	9 5 5 9 5	9 5
	3\7					514.29	171.43	171.43	0	2 1 1 2 1	2 1	(Boundary of propriety: smaller generators than this are strictly proper)
					13\30	520	160	200	40	9 4 4 9 4	9 4
				10\23		521.74	156.52	208.7	52.17	7 3 3 7 3	7 3
					17\39	523.08	153.84	215.385	61.54	12 5 5 12 5	12 5
			7\16			525	150	225	75	5 2 2 5 2	5 2	5-note subset of pelog (insofar as it resembles a MOS) would be in this region
					18\41	526.83	146.34	234.15	87.8	13 5 5 13 5	13 5
						600(25+√5)/31	145.7	235.75	90.05	phi+1 1 1 phi+1 1	phi+1 1
				11\25		528	144	240	96	8 3 3 8 3	8 3
						528.88	142.24	244.405	102.17	e 1 e 1 1	e 1	L/s = e
					15\34	529.41	141.18	247.06	105.88	11 4 4 11 4	11 4
		4\9				533.33	133.33	266.67	133.33	3 1 1 3 1	3 1	L/s = 3
						535.36	129.26	276.835	147.57	pi 1 pi 1 1	pi 1	L/s = pi
					13\29	537.93	124.14	289.655	165.52	10 3 3 10 3	10 3
				9\20		540	120	240	180	7 2 2 7 2	7 2
					14\31	541.935	116.13	309.68	193.55	11 3 3 11 3	11 3
			5\11			545.45	109.09	327.27	218.18	4 1 1 4 1	4 1	L/s = 4
					11\24	550	100	350	250	9 2 2 9 2	9 2
				6\13		553.85	92.31	369.23	276.92	5 1 1 5 1	5 1
					7\15	560	80	480	400	6 1 1 6 1	6 1
1\2						600	0	600	600	1 0 0 1 0	1 0	a degenerated pentatonic scale with only 2 different steps

From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.

From a 5-limit perspective, the most interesting temperaments with this kind of pentatonic scale are meantone and mavila.

There is also the interesting 2.3.7 temperament that tempers out 64/63 ("no-fives dominant").