17L 12s

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↖16L 11s	↑17L 11s	18L 11s↗
←16L 12s	17L 12s	18L 12s→
↙16L 13s	↓17L 13s	18L 13s↘

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Scale structure

Step pattern

LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLsLLsLsLLsLsLL

Equave

2/1 (1200.0¢)

Period

2/1 (1200.0¢)

Generator size

Bright

17\29 to 10\17 (703.4¢ to 705.9¢)

Dark

7\17 to 12\29 (494.1¢ to 496.6¢)

TAMNAMS information

Descends from

5L 2s (diatonic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

17\29 (703.4¢)

Supersoft (L:s = 4:3)

61\104 (703.8¢)

Soft (L:s = 3:2)

44\75 (704.0¢)

Semisoft (L:s = 5:3)

71\121 (704.1¢)

Basic (L:s = 2:1)

27\46 (704.3¢)

Semihard (L:s = 5:2)

64\109 (704.6¢)

Hard (L:s = 3:1)

37\63 (704.8¢)

Superhard (L:s = 4:1)

47\80 (705.0¢)

Collapsed (L:s = 1:0)

10\17 (705.9¢)

17L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 12 small steps, repeating every octave. 17L 12s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 703.4¢ to 705.9¢, or from 494.1¢ to 496.6¢.

This MOS, belonging to the Leapday and Grackle temperaments, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of 17edo and 29edo and divides at 80edo into Margo Schulter's gentle region extending down to 29edo and a yet-unnamed region extending up to 17edo.

Scale tree

Scale tree and tuning spectrum of 17L 12s
Generator (in steps of edo)								Cents		Step ratio		Comments
Generator (in steps of edo)								Bright	Dark	L:s	Hardness	Comments
17\29								703.448	496.552	1:1	1.000	Equalized 17L 12s
							129\220	703.636	496.364	8:7	1.143
						112\191		703.665	496.335	7:6	1.167
							207\353	703.683	496.317	13:11	1.182
					95\162			703.704	496.296	6:5	1.200
							268\457	703.720	496.280	17:14	1.214
						173\295		703.729	496.271	11:9	1.222
							251\428	703.738	496.262	16:13	1.231
				78\133				703.759	496.241	5:4	1.250
							295\503	703.777	496.223	19:15	1.267
						217\370		703.784	496.216	14:11	1.273
							356\607	703.789	496.211	23:18	1.278
					139\237			703.797	496.203	9:7	1.286
							339\578	703.806	496.194	22:17	1.294
						200\341		703.812	496.188	13:10	1.300
							261\445	703.820	496.180	17:13	1.308
			61\104					703.846	496.154	4:3	1.333	Supersoft 17L 12s
							288\491	703.870	496.130	19:14	1.357
						227\387		703.876	496.124	15:11	1.364
							393\670	703.881	496.119	26:19	1.368
					166\283			703.887	496.113	11:8	1.375
							437\745	703.893	496.107	29:21	1.381
						271\462		703.896	496.104	18:13	1.385
							376\641	703.900	496.100	25:18	1.389
				105\179				703.911	496.089	7:5	1.400
							359\612	703.922	496.078	24:17	1.412
						254\433		703.926	496.074	17:12	1.417
							403\687	703.930	496.070	27:19	1.421
					149\254			703.937	496.063	10:7	1.429
							342\583	703.945	496.055	23:16	1.438
						193\329		703.951	496.049	13:9	1.444
							237\404	703.960	496.040	16:11	1.455
		44\75						704.000	496.000	3:2	1.500	Soft 17L 12s
							247\421	704.038	495.962	17:11	1.545
						203\346		704.046	495.954	14:9	1.556
							362\617	704.052	495.948	25:16	1.562
					159\271			704.059	495.941	11:7	1.571
							433\738	704.065	495.935	30:19	1.579
						274\467		704.069	495.931	19:12	1.583
							389\663	704.072	495.928	27:17	1.588
				115\196				704.082	495.918	8:5	1.600
							416\709	704.090	495.910	29:18	1.611
						301\513		704.094	495.906	21:13	1.615
							487\830	704.096	495.904	34:21	1.619
					186\317			704.101	495.899	13:8	1.625
							443\755	704.106	495.894	31:19	1.632
						257\438		704.110	495.890	18:11	1.636
							328\559	704.114	495.886	23:14	1.643
			71\121					704.132	495.868	5:3	1.667	Semisoft 17L 12s
							311\530	704.151	495.849	22:13	1.692
						240\409		704.156	495.844	17:10	1.700
							409\697	704.161	495.839	29:17	1.706
					169\288			704.167	495.833	12:7	1.714
							436\743	704.172	495.828	31:18	1.722
						267\455		704.176	495.824	19:11	1.727
							365\622	704.180	495.820	26:15	1.733
				98\167				704.192	495.808	7:4	1.750
							321\547	704.205	495.795	23:13	1.769
						223\380		704.211	495.789	16:9	1.778
							348\593	704.216	495.784	25:14	1.786
					125\213			704.225	495.775	9:5	1.800
							277\472	704.237	495.763	20:11	1.818
						152\259		704.247	495.753	11:6	1.833
							179\305	704.262	495.738	13:7	1.857
	27\46							704.348	495.652	2:1	2.000	Basic 17L 12s Scales with tunings softer than this are proper
							172\293	704.437	495.563	13:6	2.167
						145\247		704.453	495.547	11:5	2.200
							263\448	704.464	495.536	20:9	2.222
					118\201			704.478	495.522	9:4	2.250
							327\557	704.488	495.512	25:11	2.273
						209\356		704.494	495.506	16:7	2.286
							300\511	704.501	495.499	23:10	2.300
				91\155				704.516	495.484	7:3	2.333
							337\574	704.530	495.470	26:11	2.364
						246\419		704.535	495.465	19:8	2.375
							401\683	704.539	495.461	31:13	2.385
					155\264			704.545	495.455	12:5	2.400
							374\637	704.553	495.447	29:12	2.417
						219\373		704.558	495.442	17:7	2.429
							283\482	704.564	495.436	22:9	2.444
			64\109					704.587	495.413	5:2	2.500	Semihard 17L 12s
							293\499	704.609	495.391	23:9	2.556
						229\390		704.615	495.385	18:7	2.571
							394\671	704.620	495.380	31:12	2.583
					165\281			704.626	495.374	13:5	2.600
							431\734	704.632	495.368	34:13	2.615
						266\453		704.636	495.364	21:8	2.625
							367\625	704.640	495.360	29:11	2.636
				101\172				704.651	495.349	8:3	2.667
							340\579	704.663	495.337	27:10	2.700
						239\407		704.668	495.332	19:7	2.714
							377\642	704.673	495.327	30:11	2.727
					138\235			704.681	495.319	11:4	2.750
							313\533	704.690	495.310	25:9	2.778
						175\298		704.698	495.302	14:5	2.800
							212\361	704.709	495.291	17:6	2.833
		37\63						704.762	495.238	3:1	3.000	Hard 17L 12s
							195\332	704.819	495.181	16:5	3.200
						158\269		704.833	495.167	13:4	3.250
							279\475	704.842	495.158	23:7	3.286
					121\206			704.854	495.146	10:3	3.333
							326\555	704.865	495.135	27:8	3.375
						205\349		704.871	495.129	17:5	3.400
							289\492	704.878	495.122	24:7	3.429
				84\143				704.895	495.105	7:2	3.500
							299\509	704.912	495.088	25:7	3.571
						215\366		704.918	495.082	18:5	3.600
							346\589	704.924	495.076	29:8	3.625
					131\223			704.933	495.067	11:3	3.667
							309\526	704.943	495.057	26:7	3.714
						178\303		704.950	495.050	15:4	3.750
							225\383	704.961	495.039	19:5	3.800
			47\80					705.000	495.000	4:1	4.000	Superhard 17L 12s
							198\337	705.045	494.955	17:4	4.250
						151\257		705.058	494.942	13:3	4.333
							255\434	705.069	494.931	22:5	4.400
					104\177			705.085	494.915	9:2	4.500
							265\451	705.100	494.900	23:5	4.600
						161\274		705.109	494.891	14:3	4.667
							218\371	705.121	494.879	19:4	4.750
				57\97				705.155	494.845	5:1	5.000
							181\308	705.195	494.805	16:3	5.333
						124\211		705.213	494.787	11:2	5.500
							191\325	705.231	494.769	17:3	5.667
					67\114			705.263	494.737	6:1	6.000
							144\245	705.306	494.694	13:2	6.500
						77\131		705.344	494.656	7:1	7.000
							87\148	705.405	494.595	8:1	8.000
10\17								705.882	494.118	1:0	→ ∞	Collapsed 17L 12s

17L 12s

Scale tree

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