User:Moremajorthanmajor/10L 3s (19/9-equivalent)

↖9L 2s⟨19/9⟩	↑10L 2s⟨19/9⟩	11L 2s⟨19/9⟩↗
←9L 3s⟨19/9⟩	10L 3s<19/9>	11L 3s⟨19/9⟩→
↙9L 4s⟨19/9⟩	↓10L 4s⟨19/9⟩	11L 4s⟨19/9⟩↘

┌╥╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLLLsLLLsLLLs
sLLLsLLLsLLLL

Equave

19/9 (1293.6¢)

Period

19/9 (1293.6¢)

Generator size^(ed19/9)

Bright

9\13 to 7\10 (895.6¢ to 905.5¢)

Dark

3\10 to 4\13 (388.1¢ to 398.0¢)

Related MOS scales

13L 10s⟨19/9⟩
10L 13s⟨19/9⟩

Equal tunings^(ed19/9)

Equalized (L:s = 1:1)

9\13 (895.6¢)

Supersoft (L:s = 4:3)

34\49 (897.6¢)

Soft (L:s = 3:2)

25\36 (898.3¢)

Semisoft (L:s = 5:3)

41\59 (898.9¢)

Basic (L:s = 2:1)

16\23 (899.9¢)

Semihard (L:s = 5:2)

39\56 (900.9¢)

Hard (L:s = 3:1)

23\33 (901.6¢)

Superhard (L:s = 4:1)

30\43 (902.5¢)

Collapsed (L:s = 1:0)

7\10 (905.5¢)

10L 3s⟨19/9⟩ is a 19/9-equivalent (non-octave) moment of symmetry scale containing 10 large steps and 3 small steps, repeating every interval of 19/9 (1293.6¢). Generators that produce this scale range from 895.6¢ to 905.5¢, or from 388.1¢ to 398¢.

It is the highest just tuning for greater luachoid, a scale pattern that expands on greater sephiroid (3L 7s). A tempered flat chain of 27/16 really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered in descending order so that the the tempered 27/16 is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.

Circle of fifths	Ascending scale	Mode
I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X	L L L L s L L L s L L L s	Tishrei
x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI	L L L s L L L s L L L s L	Cheshvan
vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II	L L s L L L s L L L s L L	Kislev
ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI	L s L L L s L L L s L L L	Tevet
xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII	s L L L s L L L s L L L L	Shvat
vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III	L L L s L L L s L L L L s	Adar minor
iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII	L L s L L L s L L L L s L	Adar major
xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII	L s L L L s L L L L s L L	Nisan
viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV	s L L L s L L L L s L L L	Iyar
iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII	L L L s L L L L s L L L s	Sivan
xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX	L L s L L L L s L L L s L	Tammuz
ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V	L s L L L L s L L L s L L	Av
v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I	s L L L L s L L L s L L L	Elul

Scale tree and tuning spectrum of 10L 3s⟨19/9⟩
Generator ^(ed19/9)						Cents		Step ratio		Comments
Generator ^(ed19/9)						Bright	Dark	L:s	Hardness	Comments
9\13						895.571	398.032	1:1	1.000	Equalized 10L 3s⟨19/9⟩
					52\75	896.898	396.705	6:5	1.200
				43\62		897.176	396.427	5:4	1.250
					77\111	897.364	396.239	9:7	1.286
			34\49			897.602	396.001	4:3	1.333	Supersoft 10L 3s⟨19/9⟩
					93\134	897.799	395.804	11:8	1.375
				59\85		897.913	395.690	7:5	1.400
					84\121	898.038	395.565	10:7	1.429
		25\36				898.335	395.268	3:2	1.500	Soft 10L 3s⟨19/9⟩
					91\131	898.610	394.993	11:7	1.571
				66\95		898.714	394.889	8:5	1.600
					107\154	898.802	394.801	13:8	1.625
			41\59			898.944	394.659	5:3	1.667	Semisoft 10L 3s⟨19/9⟩
					98\141	899.100	394.503	12:7	1.714
				57\82		899.212	394.391	7:4	1.750
					73\105	899.362	394.241	9:5	1.800
	16\23					899.898	393.705	2:1	2.000	Basic 10L 3s⟨19/9⟩ Scales with tunings softer than this are proper
					71\102	900.449	393.154	9:4	2.250
				55\79		900.610	392.993	7:3	2.333
					94\135	900.731	392.872	12:5	2.400
			39\56			900.902	392.701	5:2	2.500	Semihard 10L 3s⟨19/9⟩
					101\145	901.061	392.542	13:5	2.600
				62\89		901.162	392.441	8:3	2.667
					85\122	901.281	392.322	11:4	2.750
		23\33				901.602	392.001	3:1	3.000	Hard 10L 3s⟨19/9⟩
					76\109	901.962	391.641	10:3	3.333
				53\76		902.118	391.485	7:2	3.500
					83\119	902.261	391.342	11:3	3.667
			30\43			902.514	391.089	4:1	4.000	Superhard 10L 3s⟨19/9⟩
					67\96	902.827	390.776	9:2	4.500
				37\53		903.081	390.522	5:1	5.000
					44\63	903.469	390.134	6:1	6.000
7\10						905.522	388.081	1:0	→ ∞	Collapsed 10L 3s⟨19/9⟩

User:Moremajorthanmajor/10L 3s (19/9-equivalent)

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