User:MisterShafXen/25L 8s

25L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 25 large steps and 8 small steps, repeating every octave. 25L 8s is a great-grandchild scale of 8L 1s, expanding it by 24 tones. Generators that produce this scale range from 1054.5 ¢ to 1056 ¢, or from 144 ¢ to 145.5 ¢.

↖ 24L 7s	↑ 25L 7s	26L 7s ↗
← 24L 8s	25L 8s	26L 8s →
↙ 24L 9s	↓ 25L 9s	26L 9s ↘

Scale structure
Step pattern	LLLLsLLLsLLLsLLLsLLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLLsLLLsLLLsLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	29\33 to 22\25 (1054.5 ¢ to 1056.0 ¢)
Dark	3\25 to 4\33 (144.0 ¢ to 145.5 ¢)
TAMNAMS information
Related to	8L 1s (subneutralic)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	8L 17s
Sister	8L 25s
Daughters	33L 25s, 25L 33s
Neutralized	17L 16s
2-Flought	58L 8s, 25L 41s
Equal tunings
Equalized (L:s = 1:1)	29\33 (1054.5 ¢)
Supersoft (L:s = 4:3)	109\124 (1054.8 ¢)
Soft (L:s = 3:2)	80\91 (1054.9 ¢)
Semisoft (L:s = 5:3)	131\149 (1055.0 ¢)
Basic (L:s = 2:1)	51\58 (1055.2 ¢)
Semihard (L:s = 5:2)	124\141 (1055.3 ¢)
Hard (L:s = 3:1)	73\83 (1055.4 ¢)
Superhard (L:s = 4:1)	95\108 (1055.6 ¢)
Collapsed (L:s = 1:0)	22\25 (1056.0 ¢)
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Scale properties

Intervals of 25L 8s

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 36.4 ¢
	Major 1-mosstep	M1ms	L	36.4 ¢ to 48.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	48.0 ¢ to 72.7 ¢
	Major 2-mosstep	M2ms	2L	72.7 ¢ to 96.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	96.0 ¢ to 109.1 ¢
	Major 3-mosstep	M3ms	3L	109.1 ¢ to 144.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	144.0 ¢ to 145.5 ¢
	Augmented 4-mosstep	A4ms	4L	145.5 ¢ to 192.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	144.0 ¢ to 181.8 ¢
	Major 5-mosstep	M5ms	4L + s	181.8 ¢ to 192.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	192.0 ¢ to 218.2 ¢
	Major 6-mosstep	M6ms	5L + s	218.2 ¢ to 240.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	240.0 ¢ to 254.5 ¢
	Major 7-mosstep	M7ms	6L + s	254.5 ¢ to 288.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	288.0 ¢ to 290.9 ¢
	Major 8-mosstep	M8ms	7L + s	290.9 ¢ to 336.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	288.0 ¢ to 327.3 ¢
	Major 9-mosstep	M9ms	7L + 2s	327.3 ¢ to 336.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	336.0 ¢ to 363.6 ¢
	Major 10-mosstep	M10ms	8L + 2s	363.6 ¢ to 384.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	384.0 ¢ to 400.0 ¢
	Major 11-mosstep	M11ms	9L + 2s	400.0 ¢ to 432.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	432.0 ¢ to 436.4 ¢
	Major 12-mosstep	M12ms	10L + 2s	436.4 ¢ to 480.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	432.0 ¢ to 472.7 ¢
	Major 13-mosstep	M13ms	10L + 3s	472.7 ¢ to 480.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	480.0 ¢ to 509.1 ¢
	Major 14-mosstep	M14ms	11L + 3s	509.1 ¢ to 528.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	528.0 ¢ to 545.5 ¢
	Major 15-mosstep	M15ms	12L + 3s	545.5 ¢ to 576.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	576.0 ¢ to 581.8 ¢
	Major 16-mosstep	M16ms	13L + 3s	581.8 ¢ to 624.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	12L + 5s	576.0 ¢ to 618.2 ¢
	Major 17-mosstep	M17ms	13L + 4s	618.2 ¢ to 624.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	13L + 5s	624.0 ¢ to 654.5 ¢
	Major 18-mosstep	M18ms	14L + 4s	654.5 ¢ to 672.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	14L + 5s	672.0 ¢ to 690.9 ¢
	Major 19-mosstep	M19ms	15L + 4s	690.9 ¢ to 720.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	15L + 5s	720.0 ¢ to 727.3 ¢
	Major 20-mosstep	M20ms	16L + 4s	727.3 ¢ to 768.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	15L + 6s	720.0 ¢ to 763.6 ¢
	Major 21-mosstep	M21ms	16L + 5s	763.6 ¢ to 768.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	16L + 6s	768.0 ¢ to 800.0 ¢
	Major 22-mosstep	M22ms	17L + 5s	800.0 ¢ to 816.0 ¢
23-mosstep	Minor 23-mosstep	m23ms	17L + 6s	816.0 ¢ to 836.4 ¢
	Major 23-mosstep	M23ms	18L + 5s	836.4 ¢ to 864.0 ¢
24-mosstep	Minor 24-mosstep	m24ms	18L + 6s	864.0 ¢ to 872.7 ¢
	Major 24-mosstep	M24ms	19L + 5s	872.7 ¢ to 912.0 ¢
25-mosstep	Minor 25-mosstep	m25ms	18L + 7s	864.0 ¢ to 909.1 ¢
	Major 25-mosstep	M25ms	19L + 6s	909.1 ¢ to 912.0 ¢
26-mosstep	Minor 26-mosstep	m26ms	19L + 7s	912.0 ¢ to 945.5 ¢
	Major 26-mosstep	M26ms	20L + 6s	945.5 ¢ to 960.0 ¢
27-mosstep	Minor 27-mosstep	m27ms	20L + 7s	960.0 ¢ to 981.8 ¢
	Major 27-mosstep	M27ms	21L + 6s	981.8 ¢ to 1008.0 ¢
28-mosstep	Minor 28-mosstep	m28ms	21L + 7s	1008.0 ¢ to 1018.2 ¢
	Major 28-mosstep	M28ms	22L + 6s	1018.2 ¢ to 1056.0 ¢
29-mosstep	Diminished 29-mosstep	d29ms	21L + 8s	1008.0 ¢ to 1054.5 ¢
	Perfect 29-mosstep	P29ms	22L + 7s	1054.5 ¢ to 1056.0 ¢
30-mosstep	Minor 30-mosstep	m30ms	22L + 8s	1056.0 ¢ to 1090.9 ¢
	Major 30-mosstep	M30ms	23L + 7s	1090.9 ¢ to 1104.0 ¢
31-mosstep	Minor 31-mosstep	m31ms	23L + 8s	1104.0 ¢ to 1127.3 ¢
	Major 31-mosstep	M31ms	24L + 7s	1127.3 ¢ to 1152.0 ¢
32-mosstep	Minor 32-mosstep	m32ms	24L + 8s	1152.0 ¢ to 1163.6 ¢
	Major 32-mosstep	M32ms	25L + 7s	1163.6 ¢ to 1200.0 ¢
33-mosstep	Perfect 33-mosstep	P33ms	25L + 8s	1200.0 ¢

Generator chain of 25L 8s

Bright gens	Scale degree	Abbrev.
57	Augmented 3-mosdegree	A3md
56	Augmented 7-mosdegree	A7md
55	Augmented 11-mosdegree	A11md
54	Augmented 15-mosdegree	A15md
53	Augmented 19-mosdegree	A19md
52	Augmented 23-mosdegree	A23md
51	Augmented 27-mosdegree	A27md
50	Augmented 31-mosdegree	A31md
49	Augmented 2-mosdegree	A2md
48	Augmented 6-mosdegree	A6md
47	Augmented 10-mosdegree	A10md
46	Augmented 14-mosdegree	A14md
45	Augmented 18-mosdegree	A18md
44	Augmented 22-mosdegree	A22md
43	Augmented 26-mosdegree	A26md
42	Augmented 30-mosdegree	A30md
41	Augmented 1-mosdegree	A1md
40	Augmented 5-mosdegree	A5md
39	Augmented 9-mosdegree	A9md
38	Augmented 13-mosdegree	A13md
37	Augmented 17-mosdegree	A17md
36	Augmented 21-mosdegree	A21md
35	Augmented 25-mosdegree	A25md
34	Augmented 29-mosdegree	A29md
33	Augmented 0-mosdegree	A0md
32	Augmented 4-mosdegree	A4md
31	Major 8-mosdegree	M8md
30	Major 12-mosdegree	M12md
29	Major 16-mosdegree	M16md
28	Major 20-mosdegree	M20md
27	Major 24-mosdegree	M24md
26	Major 28-mosdegree	M28md
25	Major 32-mosdegree	M32md
24	Major 3-mosdegree	M3md
23	Major 7-mosdegree	M7md
22	Major 11-mosdegree	M11md
21	Major 15-mosdegree	M15md
20	Major 19-mosdegree	M19md
19	Major 23-mosdegree	M23md
18	Major 27-mosdegree	M27md
17	Major 31-mosdegree	M31md
16	Major 2-mosdegree	M2md
15	Major 6-mosdegree	M6md
14	Major 10-mosdegree	M10md
13	Major 14-mosdegree	M14md
12	Major 18-mosdegree	M18md
11	Major 22-mosdegree	M22md
10	Major 26-mosdegree	M26md
9	Major 30-mosdegree	M30md
8	Major 1-mosdegree	M1md
7	Major 5-mosdegree	M5md
6	Major 9-mosdegree	M9md
5	Major 13-mosdegree	M13md
4	Major 17-mosdegree	M17md
3	Major 21-mosdegree	M21md
2	Major 25-mosdegree	M25md
1	Perfect 29-mosdegree	P29md
0	Perfect 0-mosdegree Perfect 33-mosdegree	P0md P33md
−1	Perfect 4-mosdegree	P4md
−2	Minor 8-mosdegree	m8md
−3	Minor 12-mosdegree	m12md
−4	Minor 16-mosdegree	m16md
−5	Minor 20-mosdegree	m20md
−6	Minor 24-mosdegree	m24md
−7	Minor 28-mosdegree	m28md
−8	Minor 32-mosdegree	m32md
−9	Minor 3-mosdegree	m3md
−10	Minor 7-mosdegree	m7md
−11	Minor 11-mosdegree	m11md
−12	Minor 15-mosdegree	m15md
−13	Minor 19-mosdegree	m19md
−14	Minor 23-mosdegree	m23md
−15	Minor 27-mosdegree	m27md
−16	Minor 31-mosdegree	m31md
−17	Minor 2-mosdegree	m2md
−18	Minor 6-mosdegree	m6md
−19	Minor 10-mosdegree	m10md
−20	Minor 14-mosdegree	m14md
−21	Minor 18-mosdegree	m18md
−22	Minor 22-mosdegree	m22md
−23	Minor 26-mosdegree	m26md
−24	Minor 30-mosdegree	m30md
−25	Minor 1-mosdegree	m1md
−26	Minor 5-mosdegree	m5md
−27	Minor 9-mosdegree	m9md
−28	Minor 13-mosdegree	m13md
−29	Minor 17-mosdegree	m17md
−30	Minor 21-mosdegree	m21md
−31	Minor 25-mosdegree	m25md
−32	Diminished 29-mosdegree	d29md
−33	Diminished 33-mosdegree	d33md
−34	Diminished 4-mosdegree	d4md
−35	Diminished 8-mosdegree	d8md
−36	Diminished 12-mosdegree	d12md
−37	Diminished 16-mosdegree	d16md
−38	Diminished 20-mosdegree	d20md
−39	Diminished 24-mosdegree	d24md
−40	Diminished 28-mosdegree	d28md
−41	Diminished 32-mosdegree	d32md
−42	Diminished 3-mosdegree	d3md
−43	Diminished 7-mosdegree	d7md
−44	Diminished 11-mosdegree	d11md
−45	Diminished 15-mosdegree	d15md
−46	Diminished 19-mosdegree	d19md
−47	Diminished 23-mosdegree	d23md
−48	Diminished 27-mosdegree	d27md
−49	Diminished 31-mosdegree	d31md
−50	Diminished 2-mosdegree	d2md
−51	Diminished 6-mosdegree	d6md
−52	Diminished 10-mosdegree	d10md
−53	Diminished 14-mosdegree	d14md
−54	Diminished 18-mosdegree	d18md
−55	Diminished 22-mosdegree	d22md
−56	Diminished 26-mosdegree	d26md
−57	Diminished 30-mosdegree	d30md

Modes of 25L 8s

UDP	Cyclic order	Step pattern
32|0	1	LLLLsLLLsLLLsLLLsLLLsLLLsLLLsLLLs
31|1	30	LLLsLLLLsLLLsLLLsLLLsLLLsLLLsLLLs
30|2	26	LLLsLLLsLLLLsLLLsLLLsLLLsLLLsLLLs
29|3	22	LLLsLLLsLLLsLLLLsLLLsLLLsLLLsLLLs
28|4	18	LLLsLLLsLLLsLLLsLLLLsLLLsLLLsLLLs
27|5	14	LLLsLLLsLLLsLLLsLLLsLLLLsLLLsLLLs
26|6	10	LLLsLLLsLLLsLLLsLLLsLLLsLLLLsLLLs
25|7	6	LLLsLLLsLLLsLLLsLLLsLLLsLLLsLLLLs
24|8	2	LLLsLLLsLLLsLLLsLLLsLLLsLLLsLLLsL
23|9	31	LLsLLLLsLLLsLLLsLLLsLLLsLLLsLLLsL
22|10	27	LLsLLLsLLLLsLLLsLLLsLLLsLLLsLLLsL
21|11	23	LLsLLLsLLLsLLLLsLLLsLLLsLLLsLLLsL
20|12	19	LLsLLLsLLLsLLLsLLLLsLLLsLLLsLLLsL
19|13	15	LLsLLLsLLLsLLLsLLLsLLLLsLLLsLLLsL
18|14	11	LLsLLLsLLLsLLLsLLLsLLLsLLLLsLLLsL
17|15	7	LLsLLLsLLLsLLLsLLLsLLLsLLLsLLLLsL
16|16	3	LLsLLLsLLLsLLLsLLLsLLLsLLLsLLLsLL
15|17	32	LsLLLLsLLLsLLLsLLLsLLLsLLLsLLLsLL
14|18	28	LsLLLsLLLLsLLLsLLLsLLLsLLLsLLLsLL
13|19	24	LsLLLsLLLsLLLLsLLLsLLLsLLLsLLLsLL
12|20	20	LsLLLsLLLsLLLsLLLLsLLLsLLLsLLLsLL
11|21	16	LsLLLsLLLsLLLsLLLsLLLLsLLLsLLLsLL
10|22	12	LsLLLsLLLsLLLsLLLsLLLsLLLLsLLLsLL
9|23	8	LsLLLsLLLsLLLsLLLsLLLsLLLsLLLLsLL
8|24	4	LsLLLsLLLsLLLsLLLsLLLsLLLsLLLsLLL
7|25	33	sLLLLsLLLsLLLsLLLsLLLsLLLsLLLsLLL
6|26	29	sLLLsLLLLsLLLsLLLsLLLsLLLsLLLsLLL
5|27	25	sLLLsLLLsLLLLsLLLsLLLsLLLsLLLsLLL
4|28	21	sLLLsLLLsLLLsLLLLsLLLsLLLsLLLsLLL
3|29	17	sLLLsLLLsLLLsLLLsLLLLsLLLsLLLsLLL
2|30	13	sLLLsLLLsLLLsLLLsLLLsLLLLsLLLsLLL
1|31	9	sLLLsLLLsLLLsLLLsLLLsLLLsLLLLsLLL
0|32	5	sLLLsLLLsLLLsLLLsLLLsLLLsLLLsLLLL

Scale tree

Scale tree and tuning spectrum of 25L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
29\33						1054.545	145.455	1:1	1.000	Equalized 25L 8s
					167\190	1054.737	145.263	6:5	1.200
				138\157		1054.777	145.223	5:4	1.250
					247\281	1054.804	145.196	9:7	1.286
			109\124			1054.839	145.161	4:3	1.333	Supersoft 25L 8s
					298\339	1054.867	145.133	11:8	1.375
				189\215		1054.884	145.116	7:5	1.400
					269\306	1054.902	145.098	10:7	1.429
		80\91				1054.945	145.055	3:2	1.500	Soft 25L 8s
					291\331	1054.985	145.015	11:7	1.571
				211\240		1055.000	145.000	8:5	1.600
					342\389	1055.013	144.987	13:8	1.625
			131\149			1055.034	144.966	5:3	1.667	Semisoft 25L 8s
					313\356	1055.056	144.944	12:7	1.714
				182\207		1055.072	144.928	7:4	1.750
					233\265	1055.094	144.906	9:5	1.800
	51\58					1055.172	144.828	2:1	2.000	Basic 25L 8s Scales with tunings softer than this are proper
					226\257	1055.253	144.747	9:4	2.250
				175\199		1055.276	144.724	7:3	2.333
					299\340	1055.294	144.706	12:5	2.400
			124\141			1055.319	144.681	5:2	2.500	Semihard 25L 8s
					321\365	1055.342	144.658	13:5	2.600
				197\224		1055.357	144.643	8:3	2.667
					270\307	1055.375	144.625	11:4	2.750
		73\83				1055.422	144.578	3:1	3.000	Hard 25L 8s
					241\274	1055.474	144.526	10:3	3.333
				168\191		1055.497	144.503	7:2	3.500
					263\299	1055.518	144.482	11:3	3.667
			95\108			1055.556	144.444	4:1	4.000	Superhard 25L 8s
					212\241	1055.602	144.398	9:2	4.500
				117\133		1055.639	144.361	5:1	5.000
					139\158	1055.696	144.304	6:1	6.000
22\25						1056.000	144.000	1:0	→ ∞	Collapsed 25L 8s