15L 2s (3/1-equivalent)

↖ 14L 1s⟨3/1⟩	↑ 15L 1s⟨3/1⟩	16L 1s⟨3/1⟩ ↗
← 14L 2s⟨3/1⟩	15L 2s (3/1-equivalent)	16L 2s⟨3/1⟩ →
↙ 14L 3s⟨3/1⟩	↓ 15L 3s⟨3/1⟩	16L 3s⟨3/1⟩ ↘

┌╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥┬┐ │║║║║║║║║│║║║║║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLsLLLLLLLs sLLLLLLLsLLLLLLLL
Equave	3/1 (1902.0¢)
Period	3/1 (1902.0¢)
Generator size(edt)
Bright	9\17 to 8\15 (1006.9¢ to 1014.4¢)
Dark	7\15 to 8\17 (887.6¢ to 895.0¢)
Related MOS scales
Parent	2L 13s⟨3/1⟩
Sister	2L 15s⟨3/1⟩
Daughters	17L 15s⟨3/1⟩, 15L 17s⟨3/1⟩
Neutralized	13L 4s⟨3/1⟩
2-Flought	32L 2s⟨3/1⟩, 15L 19s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	9\17 (1006.9¢)
Supersoft (L:s = 4:3)	35\66 (1008.6¢)
Soft (L:s = 3:2)	26\49 (1009.2¢)
Semisoft (L:s = 5:3)	43\81 (1009.7¢)
Basic (L:s = 2:1)	17\32 (1010.4¢)
Semihard (L:s = 5:2)	42\79 (1011.2¢)
Hard (L:s = 3:1)	25\47 (1011.7¢)
Superhard (L:s = 4:1)	33\62 (1012.3¢)
Collapsed (L:s = 1:0)	8\15 (1014.4¢)

15L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 15 large steps and 2 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1006.9¢ to 1014.4¢, or from 887.6¢ to 895¢.

Modes

Modes of 15L 2s⟨3/1⟩

UDP	Cyclic order	Step pattern
16|0	1	LLLLLLLLsLLLLLLLs
15|1	10	LLLLLLLsLLLLLLLLs
14|2	2	LLLLLLLsLLLLLLLsL
13|3	11	LLLLLLsLLLLLLLLsL
12|4	3	LLLLLLsLLLLLLLsLL
11|5	12	LLLLLsLLLLLLLLsLL
10|6	4	LLLLLsLLLLLLLsLLL
9|7	13	LLLLsLLLLLLLLsLLL
8|8	5	LLLLsLLLLLLLsLLLL
7|9	14	LLLsLLLLLLLLsLLLL
6|10	6	LLLsLLLLLLLsLLLLL
5|11	15	LLsLLLLLLLLsLLLLL
4|12	7	LLsLLLLLLLsLLLLLL
3|13	16	LsLLLLLLLLsLLLLLL
2|14	8	LsLLLLLLLsLLLLLLL
1|15	17	sLLLLLLLLsLLLLLLL
0|16	9	sLLLLLLLsLLLLLLLL

Intervals

Intervals of 15L 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 111.9¢
	Major 1-mosstep	M1ms	L	111.9¢ to 126.8¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	126.8¢ to 223.8¢
	Major 2-mosstep	M2ms	2L	223.8¢ to 253.6¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	253.6¢ to 335.6¢
	Major 3-mosstep	M3ms	3L	335.6¢ to 380.4¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	380.4¢ to 447.5¢
	Major 4-mosstep	M4ms	4L	447.5¢ to 507.2¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	507.2¢ to 559.4¢
	Major 5-mosstep	M5ms	5L	559.4¢ to 634.0¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	634.0¢ to 671.3¢
	Major 6-mosstep	M6ms	6L	671.3¢ to 760.8¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	760.8¢ to 783.2¢
	Major 7-mosstep	M7ms	7L	783.2¢ to 887.6¢
8-mosstep	Perfect 8-mosstep	P8ms	7L + s	887.6¢ to 895.0¢
	Augmented 8-mosstep	A8ms	8L	895.0¢ to 1014.4¢
9-mosstep	Diminished 9-mosstep	d9ms	7L + 2s	887.6¢ to 1006.9¢
	Perfect 9-mosstep	P9ms	8L + s	1006.9¢ to 1014.4¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	1014.4¢ to 1118.8¢
	Major 10-mosstep	M10ms	9L + s	1118.8¢ to 1141.2¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	1141.2¢ to 1230.7¢
	Major 11-mosstep	M11ms	10L + s	1230.7¢ to 1268.0¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	1268.0¢ to 1342.6¢
	Major 12-mosstep	M12ms	11L + s	1342.6¢ to 1394.8¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	1394.8¢ to 1454.4¢
	Major 13-mosstep	M13ms	12L + s	1454.4¢ to 1521.6¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	1521.6¢ to 1566.3¢
	Major 14-mosstep	M14ms	13L + s	1566.3¢ to 1648.4¢
15-mosstep	Minor 15-mosstep	m15ms	13L + 2s	1648.4¢ to 1678.2¢
	Major 15-mosstep	M15ms	14L + s	1678.2¢ to 1775.2¢
16-mosstep	Minor 16-mosstep	m16ms	14L + 2s	1775.2¢ to 1790.1¢
	Major 16-mosstep	M16ms	15L + s	1790.1¢ to 1902.0¢
17-mosstep	Perfect 17-mosstep	P17ms	15L + 2s	1902.0¢

Tuning spectrum

This MOS, which uses a moderately sharp ~5:3 as a generator, is the closest thing to an enharmonic scale that the "proper" Arcturus temperament can provide. Of course, it is not really an Arcturus scale in the strictest sense of what Arcturus tempering entails, but its 9th is still a reasonably good 5:3.

Generator							cents	L	s	2g	Notes
7\15							887.579 606.667	126.797 86.667	0.00	1775.158 1213.667	L=1 s=0
						50\107	888.764 607.477	124.427 85.047	17.775 12.1495	1777.528 1214.953	L=7 s=1
					43\92		888.957 607.609	124.0405 84.783	20.673 14.13	1777.9145 1215.217	L=6 s=1
						79\169	889.08 607.692	123.796 84.615	22.508 15.385	1778.159 1215.385
				36\77			889.226 607.792	123.504 84.416	24.701 16.883	1778.451 1215.584	L=5 s=1
						101\216	889.34 607.87	123.275 84.259	26.416 18.056	1778.68 1215.741
					65\139		889.403 607.914	123.148 84.173	27.366 18.705	1778.807 1215.827
						94\201	889.4715 607.96	123.012 84.08	28.387 194.403	1778.943 1215.92
			29\62				889.624 608.0645	122.707 83.871	30.677 20.968	1779.248 1216.129	L=4 s=1
						109\233	889.756 608.1545	122.4435 83.691	32.652 22.318	1779.5115 1216.309
					80\171		889.8035 608.187	122.348 83.626	33.368 22.807	1779.607 1216.374
						131\280	889.843 608.214	122.2685 83.571	33.9635 23.214	1779.6865 1216.429
				51\109			889.906 608.257	122.144 83.486	34.899 23.853	1779.811 1216.514	L=7 s=2
						124\265	889.971 608.302	122.012 83.396	35.886 24.528	1779.943 1216.604
					73\156		890.017 608.333	121.92 83.333	36.576 25	1780.035 1216.667
						95\203	890.0775 608.374	121.8 83.251	37.477 25.616	1780.155 1216.749
		22\47					890.277 608.511	121.401 82.988	40.467 27.66	1780.554 1217.012	L=3 s=1
						103\220	890.461 608.636	121.0335 82.727	43.226 29.5455	1780.9215 1217.273
					81\173		890.511 608.6705	120.934 82.659	43.976 30.058	1781.021 1217.341
						140\299	890.5475 608.696	120.86 82.609	44.528 30.435	1781.095 1217.391
				59\126			890.598 608.73	120.759 82.54	45.285 30.952	1781.196 1217.46
						155\331	890.644 608.761	120.668 82.477	45.969 27.492	1781.287 1217.523
					96\205		890.672 608.7805	120.612 82.439	46.389 31.707	1781.343 1217.561
						133\284	890.704 608.803	120.546 82.394	46.879 32.042	1781.409 1217.606
			37\79				890.789 608.861	120.377 82.2785	48.151 32.911	1781.578 1217.7215	L=5 s=2
						126\269	890.879 608.922	120.198 82.156	49.493 33.829	1781.757 1217.844
					89\190		890.916 608.947	120.1235 82.105	50.0515 34.2105	1781.8315 1217.895
						141\301	890.949 608.97	120.057 82.03	50.55 34.5515	1781.898 1217.94
				52\111			891.006 609.009	119.943 81.982	51.404 35.135	1782.012 1218.018	L=7 s=3
						119\254	891.073 609.055	119.808 81.89	52.416 35.827	1782.147 1218.11
					67\143		891.126 609.091	119.7035 81.818	53.2015 36.364	1782.2515 1218.182
						82\175	891.202 609.143	119.5515 81.714	54.342 37.143	1782.4035 1218.286
	15\32						891.541 609.375	118.872 81.25	59.436 40.625	1783.083 1218.375	L=2 s=1
						83\177	891.877 609.6045	118.2 80.791	64.473 44.068	1783.754 1219.209
					68\145		891.951 609.655	118.052 80.69	65.585 44.828	1783.903 1219.31
						121\258	892.002 609.69	117.951 80.62	66.347 45.349	1784.004 1219.38
				53\113			892.067 609.7345	117.82 80.531	67.326 46.018	1784.135 1219.469	L=7 s=4
						144\307	892.122 609.772	117.71 80.456	68.148 46.58	1784.244 1219.544
					91\194		892.154 609.794	117.647 80.412	68.627 46.907	1784.308 1219.588
						129\275	892.19 609.818	117.575 80.364	69.162 47.273	1784.38 1219.636
			38\81				892.275 609.8765	117.405 80.247	70.443 48.148	1784.55 1219.743	L=5 s=3
						137\292	892.356 609.9315	117.244 80.137	71.649 48.973	1784.711 1219.863
					99\211		892.3865 609.953	117.182 80.095	72.112 49.289	1784.773 1219.905
						160\341	892.413 609.971	117.129 80.059	72.509 49.56	1784.826 1219.941	Golden Super-Arcturus[17] is near here
				61\130			892.456 610	117.043 80	73.152 50	1784.912 1220
						145\309	892.503 610.032	116.949 79.935	73.862 50.485	1785.006 1220.065
					84\179		892.5375 610.056	116.88 79.888	74.378 50.838	1785.075 1220.112
						107\228	892.584 610.088	116.787 79.824	75.077 51.316	1785.168 1220.176
		23\49					892.754 610.204	116.446 79.592	77.63 53.06	1785.509 1220.408	L=3 s=2
						100\213	892.937 610.329	116.082 79.342	78.1625 54.93	1785.873 1220.658
					77\164		892.991 610.366	115.973 79.278	81.181 55.488	1785.982 1220.722
						131\279	893.033 610.394	115.89 79.2015	81.8045 55.914	1786.065 1220.7985
				54\115			893.092 610.434	115.771 79.131	82.694 56.522	1786.184 1220.869	L=7 s=5
						139\296	893.148 610.473	115.659 79.054	83.532 57.095	1786.296 1220.946
					85\181		893.183 610.497	115.558 79.0055	84.064 57.459	1786.367 1220.9945
						116\247	893.226 610.526	115.503 78.947	84.7025 57.895	1786.452 1221.053
			31\66				893.3425 610.606	115.27 78.788	86.4525 59.091	1786.685 1221.212	L=4 s=3
						101\215	893.4765 610.697	115.002 78.605	88.463 60.465	1786.953 1221.395
					70\149		893.536 610.738	114.883 78.5235	89.354 61.074	1787.072 1221.4765
						109\232	893.591 610.776	114.773 78.448	90.179 61.638	1787.182 1221.552
				39\83			893.69 610.843	114.576 78.313	91.6605 62.651	1787.379 1221.687	L=5 s=4
						86\183	893.815 610.929	114.325 78.142	93.539 63.934	1787.63 1221.858
					47\100		893.919 611	114.117 78	95.098 65	1787.838 1222	L=6 s=5
						55\117	894.081 611.111	113.792 77.778	97.536 66.667	1788.163 1222.222	L=7 s=6
8\17							895.038 611.765	111.88 76.471		1790.075 1223.529	L=1 s=1