17L 2s (3/1-equivalent)

↖ 16L 1s⟨3/1⟩	↑ 17L 1s⟨3/1⟩	18L 1s⟨3/1⟩ ↗
← 16L 2s⟨3/1⟩	17L 2s (3/1-equivalent)	18L 2s⟨3/1⟩ →
↙ 16L 3s⟨3/1⟩	↓ 17L 3s⟨3/1⟩	18L 3s⟨3/1⟩ ↘

┌╥╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║│║║║║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLLsLLLLLLLLs sLLLLLLLLsLLLLLLLLL
Equave	3/1 (1902.0¢)
Period	3/1 (1902.0¢)
Generator size(edt)
Bright	10\19 to 9\17 (1001.0¢ to 1006.9¢)
Dark	8\17 to 9\19 (895.0¢ to 900.9¢)
Related MOS scales
Parent	2L 15s⟨3/1⟩
Sister	2L 17s⟨3/1⟩
Daughters	19L 17s⟨3/1⟩, 17L 19s⟨3/1⟩
Neutralized	15L 4s⟨3/1⟩
2-Flought	36L 2s⟨3/1⟩, 17L 21s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	10\19 (1001.0¢)
Supersoft (L:s = 4:3)	39\74 (1002.4¢)
Soft (L:s = 3:2)	29\55 (1002.8¢)
Semisoft (L:s = 5:3)	48\91 (1003.2¢)
Basic (L:s = 2:1)	19\36 (1003.8¢)
Semihard (L:s = 5:2)	47\89 (1004.4¢)
Hard (L:s = 3:1)	28\53 (1004.8¢)
Superhard (L:s = 4:1)	37\70 (1005.3¢)
Collapsed (L:s = 1:0)	9\17 (1006.9¢)

17L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 17 large steps and 2 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1001¢ to 1006.9¢, or from 895¢ to 900.9¢.

Using a generator as which is as sharp as possible for an 'ordinary' ~5:3, this MOS is the most complex parent scale for an Arcturus-like temperament. It is also the most complex parent MOS for a temperament where two generators make an "ordinary" ~14:5 (the simplest is the proper Arcturus scale).

Modes

Modes of 17L 2s⟨3/1⟩

UDP	Cyclic order	Step pattern
18|0	1	LLLLLLLLLsLLLLLLLLs
17|1	11	LLLLLLLLsLLLLLLLLLs
16|2	2	LLLLLLLLsLLLLLLLLsL
15|3	12	LLLLLLLsLLLLLLLLLsL
14|4	3	LLLLLLLsLLLLLLLLsLL
13|5	13	LLLLLLsLLLLLLLLLsLL
12|6	4	LLLLLLsLLLLLLLLsLLL
11|7	14	LLLLLsLLLLLLLLLsLLL
10|8	5	LLLLLsLLLLLLLLsLLLL
9|9	15	LLLLsLLLLLLLLLsLLLL
8|10	6	LLLLsLLLLLLLLsLLLLL
7|11	16	LLLsLLLLLLLLLsLLLLL
6|12	7	LLLsLLLLLLLLsLLLLLL
5|13	17	LLsLLLLLLLLLsLLLLLL
4|14	8	LLsLLLLLLLLsLLLLLLL
3|15	18	LsLLLLLLLLLsLLLLLLL
2|16	9	LsLLLLLLLLsLLLLLLLL
1|17	19	sLLLLLLLLLsLLLLLLLL
0|18	10	sLLLLLLLLsLLLLLLLLL

Intervals

Intervals of 17L 2s⟨3/1⟩

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0¢ to 100.1¢
	Major 1-mosstep	M1ms	L	100.1¢ to 111.9¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	111.9¢ to 200.2¢
	Major 2-mosstep	M2ms	2L	200.2¢ to 223.8¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	223.8¢ to 300.3¢
	Major 3-mosstep	M3ms	3L	300.3¢ to 335.6¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	335.6¢ to 400.4¢
	Major 4-mosstep	M4ms	4L	400.4¢ to 447.5¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	447.5¢ to 500.5¢
	Major 5-mosstep	M5ms	5L	500.5¢ to 559.4¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	559.4¢ to 600.6¢
	Major 6-mosstep	M6ms	6L	600.6¢ to 671.3¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	671.3¢ to 700.7¢
	Major 7-mosstep	M7ms	7L	700.7¢ to 783.2¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	783.2¢ to 800.8¢
	Major 8-mosstep	M8ms	8L	800.8¢ to 895.0¢
9-mosstep	Perfect 9-mosstep	P9ms	8L + s	895.0¢ to 900.9¢
	Augmented 9-mosstep	A9ms	9L	900.9¢ to 1006.9¢
10-mosstep	Diminished 10-mosstep	d10ms	8L + 2s	895.0¢ to 1001.0¢
	Perfect 10-mosstep	P10ms	9L + s	1001.0¢ to 1006.9¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	1006.9¢ to 1101.1¢
	Major 11-mosstep	M11ms	10L + s	1101.1¢ to 1118.8¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	1118.8¢ to 1201.2¢
	Major 12-mosstep	M12ms	11L + s	1201.2¢ to 1230.7¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	1230.7¢ to 1301.3¢
	Major 13-mosstep	M13ms	12L + s	1301.3¢ to 1342.6¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	1342.6¢ to 1401.4¢
	Major 14-mosstep	M14ms	13L + s	1401.4¢ to 1454.4¢
15-mosstep	Minor 15-mosstep	m15ms	13L + 2s	1454.4¢ to 1501.5¢
	Major 15-mosstep	M15ms	14L + s	1501.5¢ to 1566.3¢
16-mosstep	Minor 16-mosstep	m16ms	14L + 2s	1566.3¢ to 1601.6¢
	Major 16-mosstep	M16ms	15L + s	1601.6¢ to 1678.2¢
17-mosstep	Minor 17-mosstep	m17ms	15L + 2s	1678.2¢ to 1701.7¢
	Major 17-mosstep	M17ms	16L + s	1701.7¢ to 1790.1¢
18-mosstep	Minor 18-mosstep	m18ms	16L + 2s	1790.1¢ to 1801.9¢
	Major 18-mosstep	M18ms	17L + s	1801.9¢ to 1902.0¢
19-mosstep	Perfect 19-mosstep	P19ms	17L + 2s	1902.0¢

Scale tree

Generator							cents	L	s	2g	Notes
8\17							895.038 611.765	111.88 76.471	0.00	1790.075 1223.529	L=1 s=0
						57\121	895.962 612.397	110.0305 75.207	15.719 10.744	1791.925 1224.793	L=7 s=1
					49\104		896.113 612.5	109.728 75	18.288 12.5	1792.227 1225	L=6 s=1
						90\191	896.209 612.565	109.537 74.869	19.916 13.913	1792.418 1225.131
				41\87			896.324 612.644	109.308 74.713	21.862 14.9425	1792.647 1225.287	L=5 s=1
						115\244	896.413 612.705	109.129 74.59	23.385 15.984	1792.826 1225.41
					74\157		896.463 612.739	109.029 74.522	24.229 16.5605	1792.926 1225.478
						107\227	896.516 612.775	108.9225 74.449	25.136 17.181	1793.032 1225.551
			33\70				896.636 612.857	108.683 74.286	27.171 18.571	1793.272 1225.714	L=4 s=1
						124\263	896.739 612.928	108.4765 74.1445	28.927 19.772	1793.478 1225.8555
					91\193		896.777 612.953	108.402 74.093	33.368 20.207	1793.553 1225.907
						149\316	896.808 612.975	108.339 74.051	30.094 20.57	1793.616 1225.949
				58\123			896.857 613.008	108.241 73.984	30.926 21.138	1793.714 1226.016	L=7 s=2
						141\299	896.9085 613.0435	108.138 73.913	31.805 21.739	1793.817 1226.087
					83\176		896.945 613.068	108.066 73.864	32.42 22.159	1793.889 1226.136
						108\229	896.992 613.1	107.971 73.799	33.222 22.707	1793.984 1226.201
		25\53					897.149 613.2075	107.658 73.585	35.886 24.528	1794.297 1226.415	L=3 s=1
						117\248	897.293 613.3065	107.368 73.381	38.346 26.21	1794.587 1226.613
					92\195		897.333 613.333	107.29 73.333	39.0145 26.667	1794.665 1226.667
						159\337	897.362 613.353	107.232 73.294	39.5065 27.003	1794.723 1226.706
				67\142			897.401 613.38	107.152 73.239	40.182 27.465	1794.803 1226.761
						176\373	897.437 613.405	107.081 73.19	40.793 27.397	1794.874 1226.81
					109\231		897.459 613.42	107.036 73.16	41.168 28.1385	1794.919 1226.84
						151\320	897.485 613.4375	106.985 73.125	41.605 28.4375	1794.97 1226.875
			42\89				897.552 613.483	106.851 73.034	42.741 29.2135	1795.104 1226.966	L=5 s=2
						143\303	897.622 613.531	106.71 72.947	43.94 30.033	1795.245 1227.063
					101\214		897.652 613.551	106.652 72.897	44.438 30.374	1795.303 1227.103
						160\339	897.678 613.569	106.599 72.86	44.884 30.6785	1795.356 1227.14
				59\125			897.723 613.6	106.5095 72.8	45.647 31.2	1795.446 1227.2	L=7 s=3
						135\286	897.776 613.636	106.403 72.727	46.551 31.818	1795.552 1227.273
					76\161		897.817 613.665	106.3205 72.671	47.2535 32.298	1795.635 1227.329
						93\197	897.877 613.706	106.2005 72.589	48.273 32.995	1795.754 1227.411
	17\36						898.145 613.889	105.664 72.222	52.832 36.111	1796.291 1227.778	L=2 s=1
						94\199	898.411 614.07	105.133 71.859	57.345 39.196	1796.822 1228.141
					77\163		898.4695 614.11	105.016 71.779	58.342 39.877	1796.939 1228.221
						137\290	898.51 614.138	104.935 71.732	59.026 40.345	1797.02 1228.276
				60\127			898.561 614.173	104.832 71.654	59.904 40.945	1797.123 1228.346	L=7 s=4
						163\345	898.605 614.203	104.745 71.594	60.642 41.449	1797.201 1228.406
					103\218		898.63 614.22	104.695 71.56	61.072 41.743	1797.26 1228.44
						146\309	898.658 614.2395	104.638 71.521	61.552 42.071	1797.317 1228.479
			43\91				898.726 614.286	104.503 71.571	62.702 42.857	1797.452 1228.571	L=5 s=3
						155\328	898.79 614.329	104.376 71.3415	63.785 43.598	1797.579 1228.6585
					112\237		898.814 614.346	104.327 71.308	64.201 43.882	1797.628 1228.692
						181\383	898.835 614.36	104.285 71.28	64.557 44.125	1797.67 1228.72	Golden Super-Arcturus[19] is near here
				69\146			898.869 614.384	104.217 71.231	65.135 44.5205	1797.738 1228.769
						164\347	898.901 614.409	104.142 71.182	65.774 44.957	1797.813 1228.818
					95\201		898.934 614.428	104.087 71.144	66.237 45.274	1797.868 1228.856
						121\256	898.971 614.453	104.013 71.094	66.866 45.703	1797.942 1228.906
		26\55					899.106 614.5455	103.743 70.909	69.162 47.273	1798.212 1229.091	L=3 s=2
						113\239	899.251 614.644	103.454 70.711	71.622 48.954	1798.501 1229.289
					87\184		899.294 614.674	103.367 70.652	72.357 49.4565	1798.589 1229.348
						148\313	899.327 614.6965	103.301 70.607	72.918 49.84	1798.654 1229.393
				61\129			899.374 614.729	103.207 70.543	73.719 50.388	1798.748 1229.457	L=7 s=5
						157\332	899.4185 614.759	103.118 70.482	74.474 50.904	1798.837 1229.518
					96\203		899.447 614.778	103.062 70.443	74.954 51.2315	1798.893 1229.557
						131\277	899.4805 614.801	102.994 70.397	75.529 51.6245	1798.961 1229.603
			35\74				899.573 614.865	102.808 70.37	77.106 52.703	1799.147 1229.63	L=4 s=3
						114/241	899.68 614.938	102.595 70.1345	78.919 53.942	1799.36 1229.8655
					79\167		899.727 614.97	102.501 70.06	79.723 54.491	1799.454 1229.94
						123\260	899.771 615	102.413 70	80.467 55	1799.542 1230
				44\93			899.85 615.054	102.256 69.8925	81.8045 55.914	1799.699 1230.1075	L=5 s=4
						97\205	899.949 615.122	102.056 69.756	83.5005 57.073	1799.899 1230.244
					53\112		900.032 615.179	101.89 69.643	84.909 58.036	1800.065 1230.357	L=6 s=5
						62\131	900.162 615.267	101.631 69.466	87.112 59.542	1800.324 1230.534	L=7 s=6
9\19							900.926 615.7895	100.103 68.421		1801.852 1231.579	L=1 s=1