7L 19s

7L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 19 small steps, repeating every octave. 7L 19s is a great-grandchild scale of 5L 2s, expanding it by 19 tones. Generators that produce this scale range from 507.7 ¢ to 514.3 ¢, or from 685.7 ¢ to 692.3 ¢.

↖ 6L 18s	↑ 7L 18s	8L 18s ↗
← 6L 19s	7L 19s	8L 19s →
↙ 6L 20s	↓ 7L 20s	8L 20s ↘

Scale structure
Step pattern	LssLsssLsssLssLsssLsssLsss sssLsssLsssLssLsssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\26 to 3\7 (507.7 ¢ to 514.3 ¢)
Dark	4\7 to 15\26 (685.7 ¢ to 692.3 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent	7L 12s
Sister	19L 7s
Daughters	26L 7s, 7L 26s
Neutralized	14L 12s
2-Flought	33L 19s, 7L 45s
Equal tunings
Equalized (L:s = 1:1)	11\26 (507.7 ¢)
Supersoft (L:s = 4:3)	36\85 (508.2 ¢)
Soft (L:s = 3:2)	25\59 (508.5 ¢)
Semisoft (L:s = 5:3)	39\92 (508.7 ¢)
Basic (L:s = 2:1)	14\33 (509.1 ¢)
Semihard (L:s = 5:2)	31\73 (509.6 ¢)
Hard (L:s = 3:1)	17\40 (510.0 ¢)
Superhard (L:s = 4:1)	20\47 (510.6 ¢)
Collapsed (L:s = 1:0)	3\7 (514.3 ¢)
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Even this far towards 7edo in the 5L 2s descendants, there are still multiple available temperaments. If the (bright) generator is taken as 4/3, we are rather beyond the range of standard meantone or even flattone. Instead, we have flattertone in the soft range (with a 33-tone scale of 26L 7s) and deeptone in the hard one (where the 33-tone scale is 7L 26s).

In flattertone, the minor 8-mosstep is a large neutral or submajor third that can still be considered to approximate 5/4, while in deeptone, this approximation fails and 5/4 is instead equated to the minor 9-mosstep. While the major 8-mosstep, minor 10-mosstep and even diminished 11-mosstep can also be close, no major temperament seems to equate 5/4 to these intervals, although the 26 & 33 temperament (equating 5/4 to the major 8-mosstep) seems promising, if rather complex.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Template:MOS data is deprecated. Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 7L 19s

Generator(edo)							Cents		Step ratio		Comments
							Bright	Dark	L:s	Hardness
11\26							507.692	692.308	1:1	1.000	Equalized 7L 19s
						69\163	507.975	692.025	7:6	1.167
					58\137		508.029	691.971	6:5	1.200
						105\248	508.065	691.935	11:9	1.222
				47\111			508.108	691.892	5:4	1.250
						130\307	508.143	691.857	14:11	1.273
					83\196		508.163	691.837	9:7	1.286
						119\281	508.185	691.815	13:10	1.300
			36\85				508.235	691.765	4:3	1.333	Supersoft 7L 19s
						133\314	508.280	691.720	15:11	1.364
					97\229		508.297	691.703	11:8	1.375
						158\373	508.311	691.689	18:13	1.385
				61\144			508.333	691.667	7:5	1.400
						147\347	508.357	691.643	17:12	1.417
					86\203		508.374	691.626	10:7	1.429
						111\262	508.397	691.603	13:9	1.444
		25\59					508.475	691.525	3:2	1.500	Soft 7L 19s
						114\269	508.550	691.450	14:9	1.556
					89\210		508.571	691.429	11:7	1.571
						153\361	508.587	691.413	19:12	1.583
				64\151			508.609	691.391	8:5	1.600
						167\394	508.629	691.371	21:13	1.615
					103\243		508.642	691.358	13:8	1.625
						142\335	508.657	691.343	18:11	1.636
			39\92				508.696	691.304	5:3	1.667	Semisoft 7L 19s
						131\309	508.738	691.262	17:10	1.700
					92\217		508.756	691.244	12:7	1.714
						145\342	508.772	691.228	19:11	1.727
				53\125			508.800	691.200	7:4	1.750
						120\283	508.834	691.166	16:9	1.778
					67\158		508.861	691.139	9:5	1.800
						81\191	508.901	691.099	11:6	1.833
	14\33						509.091	690.909	2:1	2.000	Basic 7L 19s Scales with tunings softer than this are proper
						73\172	509.302	690.698	11:5	2.200
					59\139		509.353	690.647	9:4	2.250
						104\245	509.388	690.612	16:7	2.286
				45\106			509.434	690.566	7:3	2.333
						121\285	509.474	690.526	19:8	2.375
					76\179		509.497	690.503	12:5	2.400
						107\252	509.524	690.476	17:7	2.429
			31\73				509.589	690.411	5:2	2.500	Semihard 7L 19s
						110\259	509.653	690.347	18:7	2.571
					79\186		509.677	690.323	13:5	2.600
						127\299	509.699	690.301	21:8	2.625
				48\113			509.735	690.265	8:3	2.667
						113\266	509.774	690.226	19:7	2.714
					65\153		509.804	690.196	11:4	2.750
						82\193	509.845	690.155	14:5	2.800
		17\40					510.000	690.000	3:1	3.000	Hard 7L 19s
						71\167	510.180	689.820	13:4	3.250
					54\127		510.236	689.764	10:3	3.333
						91\214	510.280	689.720	17:5	3.400
				37\87			510.345	689.655	7:2	3.500
						94\221	510.407	689.593	18:5	3.600
					57\134		510.448	689.552	11:3	3.667
						77\181	510.497	689.503	15:4	3.750
			20\47				510.638	689.362	4:1	4.000	Superhard 7L 19s
						63\148	510.811	689.189	13:3	4.333
					43\101		510.891	689.109	9:2	4.500
						66\155	510.968	689.032	14:3	4.667
				23\54			511.111	688.889	5:1	5.000
						49\115	511.304	688.696	11:2	5.500
					26\61		511.475	688.525	6:1	6.000
						29\68	511.765	688.235	7:1	7.000
3\7							514.286	685.714	1:0	→ ∞	Collapsed 7L 19s

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