2L 17s (3/1-equivalent)

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

┌╥┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┐ │║││││││││║││││││││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssssssLsssssssss sssssssssLssssssssL
Equave	3/1 (1902.0¢)
Period	3/1 (1902.0¢)
Generator size(edt)
Bright	9\19 to 1\2 (900.9¢ to 951.0¢)
Dark	1\2 to 10\19 (951.0¢ to 1001.0¢)
Related MOS scales
Parent	2L 15s⟨3/1⟩
Sister	17L 2s⟨3/1⟩
Daughters	19L 2s⟨3/1⟩, 2L 19s⟨3/1⟩
Neutralized	4L 15s⟨3/1⟩
2-Flought	21L 17s⟨3/1⟩, 2L 36s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	9\19 (900.9¢)
Supersoft (L:s = 4:3)	28\59 (902.6¢)
Soft (L:s = 3:2)	19\40 (903.4¢)
Semisoft (L:s = 5:3)	29\61 (904.2¢)
Basic (L:s = 2:1)	10\21 (905.7¢)
Semihard (L:s = 5:2)	21\44 (907.8¢)
Hard (L:s = 3:1)	11\23 (909.6¢)
Superhard (L:s = 4:1)	12\25 (912.9¢)
Collapsed (L:s = 1:0)	1\2 (951.0¢)

2L 17s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 17 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 900.9¢ to 951¢, or from 951¢ to 1001¢.

The generator for this scale far sharper than 5/3 (884¢). However, the accumulated sharpness of the generator leads to "ordinary" 8/5 and 5/3 intervals in three steps after factoring out tritaves.

Modes

Modes of 2L 17s⟨3/1⟩

UDP	Cyclic order	Step pattern
18|0	1	LssssssssLsssssssss
17|1	10	LsssssssssLssssssss
16|2	19	sLssssssssLssssssss
15|3	9	sLsssssssssLsssssss
14|4	18	ssLssssssssLsssssss
13|5	8	ssLsssssssssLssssss
12|6	17	sssLssssssssLssssss
11|7	7	sssLsssssssssLsssss
10|8	16	ssssLssssssssLsssss
9|9	6	ssssLsssssssssLssss
8|10	15	sssssLssssssssLssss
7|11	5	sssssLsssssssssLsss
6|12	14	ssssssLssssssssLsss
5|13	4	ssssssLsssssssssLss
4|14	13	sssssssLssssssssLss
3|15	3	sssssssLsssssssssLs
2|16	12	ssssssssLssssssssLs
1|17	2	ssssssssLsssssssssL
0|18	11	sssssssssLssssssssL

Intervals

Intervals of 2L 17s⟨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 951.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 200.2¢
	Major 2-mosstep	M2ms	L + s	200.2¢ to 951.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 300.3¢
	Major 3-mosstep	M3ms	L + 2s	300.3¢ to 951.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 400.4¢
	Major 4-mosstep	M4ms	L + 3s	400.4¢ to 951.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 500.5¢
	Major 5-mosstep	M5ms	L + 4s	500.5¢ to 951.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 600.6¢
	Major 6-mosstep	M6ms	L + 5s	600.6¢ to 951.0¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0¢ to 700.7¢
	Major 7-mosstep	M7ms	L + 6s	700.7¢ to 951.0¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0¢ to 800.8¢
	Major 8-mosstep	M8ms	L + 7s	800.8¢ to 951.0¢
9-mosstep	Diminished 9-mosstep	d9ms	9s	0.0¢ to 900.9¢
	Perfect 9-mosstep	P9ms	L + 8s	900.9¢ to 951.0¢
10-mosstep	Perfect 10-mosstep	P10ms	L + 9s	951.0¢ to 1001.0¢
	Augmented 10-mosstep	A10ms	2L + 8s	1001.0¢ to 1902.0¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	951.0¢ to 1101.1¢
	Major 11-mosstep	M11ms	2L + 9s	1101.1¢ to 1902.0¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	951.0¢ to 1201.2¢
	Major 12-mosstep	M12ms	2L + 10s	1201.2¢ to 1902.0¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	951.0¢ to 1301.3¢
	Major 13-mosstep	M13ms	2L + 11s	1301.3¢ to 1902.0¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	951.0¢ to 1401.4¢
	Major 14-mosstep	M14ms	2L + 12s	1401.4¢ to 1902.0¢
15-mosstep	Minor 15-mosstep	m15ms	L + 14s	951.0¢ to 1501.5¢
	Major 15-mosstep	M15ms	2L + 13s	1501.5¢ to 1902.0¢
16-mosstep	Minor 16-mosstep	m16ms	L + 15s	951.0¢ to 1601.6¢
	Major 16-mosstep	M16ms	2L + 14s	1601.6¢ to 1902.0¢
17-mosstep	Minor 17-mosstep	m17ms	L + 16s	951.0¢ to 1701.7¢
	Major 17-mosstep	M17ms	2L + 15s	1701.7¢ to 1902.0¢
18-mosstep	Minor 18-mosstep	m18ms	L + 17s	951.0¢ to 1801.9¢
	Major 18-mosstep	M18ms	2L + 16s	1801.9¢ to 1902.0¢
19-mosstep	Perfect 19-mosstep	P19ms	2L + 17s	1902.0¢

Scale tree

Generator							cents	L	s	3g	Notes
9\19							900.926 615.7895	100.103 68.421		800.823 547.368	L=1 s=1
						55\116	901.789 616.379	114.773 78.448	98.377 67.241	803.412 549.138	L=7 s=6
					46\97		901.958 616.495	117.647 80.412	98.039 67.01	803.919 549.485	L=6 s=5
						83\175	902.07 616.571	119.5515 81.714	97.815 66.857	804.255 549.714
				37\78			902.209 616.667	121.92 83.333	97.536 66.667	804.673 550	L=5 s=4
						102\215	902.323 616.744	123.848 84.651	97.309 66.518	805.013 550.226
					65\137		902.387 616.788	124.946 85.4015	97.18 66.423	805.207 550.365
						93\196	902.458 616.837	126.15 86.2245	97.0385 66.3265	805.42 550.51
			28\59				902.623 616.949	128.946 88.136	96.71 66.102	805.913 550.8475	L=4 s=3
						103\217	902.771 617.051	131.4715 89.862	96.4125 65.899	806.359 551.152
					75\158		902.827 617.089	132.415 90.506	96.3015 65.823	806.521 551.266
						122\257	902.874 617.121	133.211 91.051	96.208 65.759	806.666 551.362
				47\99			902.948 617.172	134.482 91.919	96.058 65.6565	806.89 551.515	L=7 s=5
						113\238	903.029 617.227	135.854 92.857	95.897 65.546	807.132 551.681
					66\139		903.0865 617.266	136.831 93.525	95.782 65.468	807.3045 551.798
						85\179	903.163 617.318	138.131 94.413	95.629 65.363	807.534 551.985
		19\40					903.429 617.5	142.647 97.5	95.098 65	808.331 552.5	L=3 s=2
						86\181	903.6913 617.68	147.1125 100.5525	94.572 64.641	809.119 553.039
					67\141		903.766 617.7305	148.3795 101.418	94.423 64.539	809.343 553.1915
						115\242	903.822 617.769	149.327 102.066	94.312 64.463	809.51 553.406
				48\101			903.899 617.822	150.65 102.97	94.156 64.357	809.743 553.465
						125\263	903.971 617.871	151.867 103.802	94.013 64.259	809.958 553.612	Golden Trans-Arcturus[19] is near here
					77\162		904.016 617.901	152.626 104.321	93.924 64.1975	810.092 553.703
						106\223	904.068 617.937	153.521 104.933	93.818 64.126	810.25 553.811
			29\61				904.2081 618.033	155.898 106.557	93.539 63.934	810.669 554.098	L=5 s=3
						97\204	904.361 618.137	158.496 108.333	93.233 63.7255	811.128 554.412
					68\143		904.426 618.182	159.605 109.091	93.103 63.636	811.324 554.5455
						107\225	904.485 618.222	160.6095 109.778	92.9845 63.556	811.5 554.667
				39\82			904.5884 618.293	162.362 110.976	92.778 63.415	811.81 554.878	L=7 s=4
						88\185	904.714 618.378	164.493 112.432	92.5275 63.243	812.186 555.135
					49\103		904.8135 618.447	166.19 113.592	92.328 63.107	812.4855 555.34
						59\124	904.9625 618.548	168.722 115.323	92.03 62.903	812.9325 555.645
	10\21						905.693 619.047	181.139 123.8095	90.569 61.905	815.124 557.143	L=2 s=1
						51\107	906.5393 619.626	195.528 133.645	88.876 60.748	817.663 558.8785
					41\86		906.746 619.767	199.042 136.0465	88.463 60.465	818.283 559.302
						72\151	906.8925 619.8675	201.532 137.7483	88.17 60.265	818.7225 559.603
				31\65			907.086 620	204.826 140	87.7825 60	819.304 560	L=7 s=3
						83\174	907.254 620.115	207.685 141.954	87.446 59.78	819.808 560.335
					52\109		907.355 620.1835	209.3895 143.119	87.246 59.633	820.109 560.5505
						73\153	907.469 620.261	211.328 144.444	87.0175 59.477	820.451 560.794
			21\44				907.751 620.4545	216.131 147.727	86.4525 59.091	821.299 561.364	L=5 s=2
						74\155	908.03 620.645	220.872 150.968	85.895 58.71	822.135 561.9355
					53\111		908.141 620.721	222.7515 152.252	85.674 58.559	822.467 562.162
						85\178	908.237 620.7865	224.388 153.371	85.481 58.427	822.756 562.36
				32\67			908.396 620.8955	227.099 155.224	85.162 58.209	823.234 562.687
						75\157	908.577 621.019	230.173 157.325	84.8005 57.962	823.777 563.057
					43\90		908.712 621.111	232.461 158.889	84.531 57.778	824.18 563.333
						54\113	908.899 621.239	235.64 161.062	84.157 57.522	824.741 563.717
		11\23					909.631 621.739	248.081 169.565	82.694 56.522	826.937 565.217	L=3 s=1
						45\94	910.51 622.34	263.036 179.787	80.934 55.319	829.576 567.021
					34\71		910.795 622.535	267.881 183.098	80.364 54.93	830.431 567.605
						57\119	911.0205 622.689	271.708 185.714	79.914 54.622	831.1065 568.067
				23\48			911.353 622.917	277.368 189.583	79.248 54.167	832.105 568.75	L=7 s=2
						58\121	911.681 623.1405	282.9355 193.388	78.593 53.719	833.088 569.4215	cube root of 3*phi is near here
					35\73		911.896 623.288	286.596 195.89	78.1625 53.425	833.734 569.763
						47\98	912.162 623.469	291.116 198.98	77.631 53.061	834.531 570.408
			12\25				912.938 624	304.313 208	76.078 52	836.86 572	L=4 s=1
						37\77	913.926 624.675	321.109 219.4805	74.102 50.649	839.824 574.026
					25\52		914.401 625	329.1845 225	73.152 50	841.249 575
						38\79	914.864 625.3165	337.055 230.378	72.226 49.377	842.638 575.949
				13\27			915.756 625.926	352.214 240.741	70.443 48.148	845.313 577.778	L=5 s=1
						27\56	917.014 626.786	373.598 255.357	67.927 46.429	849.087 580.357
					14\29		918.185 627.586	393.508 268.9655	65.585 44.828	852.601 582.862	L=6 s=1
						15\31	920.301 629.032	429.474 293.548	61.353 41.9355	858.947 587.097	L=7 s=1
1/2							950.9775 650		0.00	950.9775 650	L=1 s=0