4L 5s: Difference between revisions

Revision as of 07:45, 28 March 2021

↖ 3L 4s	↑ 4L 4s	5L 4s ↗
← 3L 5s	4L 5s	5L 5s →
↙ 3L 6s	↓ 4L 6s	5L 6s ↘

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│║│║│║│║│││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LsLsLsLss
ssLsLsLsL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

2\9 to 1\4 (266.7 ¢ to 300.0 ¢)

Dark

3\4 to 7\9 (900.0 ¢ to 933.3 ¢)

TAMNAMS information

Name

gramitonic

Prefix

gram-

Abbrev.

gm

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

2\9 (266.7 ¢)

Supersoft (L:s = 4:3)

7\31 (271.0 ¢)

5\22 (272.7 ¢)

8\35 (274.3 ¢)

3\13 (276.9 ¢)

7\30 (280.0 ¢)

4\17 (282.4 ¢)

Superhard (L:s = 4:1)

5\21 (285.7 ¢)

Collapsed (L:s = 1:0)

1\4 (300.0 ¢)

4L 5s refers to the structure of MOS scales whose generator falls between 2\9 (two degrees of 9edo = approx. 266.667¢) and 1\4 (one degree of 4edo = 300¢). In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:

Generator					Scale	Generator in cents	Comments
2\9					1 1 1 1 1 1 1 1 1	266.667
				9\40	4 5 4 5 4 5 4 5 4	270
			7\31		3 4 3 4 3 4 3 4 3	270.968
				12\53	5 7 5 7 5 7 5 7 5	271.698
		5\22			2 3 2 3 2 3 2 3 2	272.727
					2 pi 2 pi 2 pi 2 pi 2	273.412
				13\57	5 8 5 8 5 8 5 8 5	273.684
			8\35		3 5 3 5 3 5 3 5 3	274.286
					1 √3 1 √3 1 √3 1 √3 1	274.85
				11\48	4 7 4 7 4 7 4 7 4	275
	3\13				1 2 1 2 1 2 1 2 1	276.923	Boundary of propriety: generators smaller than this are proper
				10\43	3 7 3 7 3 7 3 7 3	279.07
			7\30		2 5 2 5 2 5 2 5 2	280.000
				11\47	3 8 3 8 3 8 3 8 3	280.851
					1 e 1 e 1 e 1 e 1	281.100	L/s = e
		4\17			1 3 1 3 1 3 1 3 1	282.353	L/s = 3
					1 pi 1 pi 1 pi 1 pi 1	282.922	L/s = pi
				9\38	2 7 2 7 2 7 2 7 2	284.2105
			5\21		1 4 1 4 1 4 1 4 1	285.714	L/s = 4
				6\25	1 5 1 5 1 5 1 5 1	288
1\4					0 1 0 1 0 1 0 1 0	300.000

@@ Line 52: / Line 52: @@
 | style="text-align:center;" | 5 7 5 7 5 7 5 7 5
 | | 271.698
-| style="text-align:center;" | Orwell is around here
+| style="text-align:center;" | <!--Orwell is around here-->
 |-
 | |
@@ Line 61: / Line 61: @@
 | style="text-align:center;" | 2 3 2 3 2 3 2 3 2
 | | 272.727
-| style="text-align:center;" | Optimum rank range (L/s=3/2) orwell
+| style="text-align:center;" | <!--Optimum rank range (L/s=3/2) orwell-->
 |-
 | |
@@ Line 79: / Line 79: @@
 | style="text-align:center;" | 5 8 5 8 5 8 5 8 5
 | | 273.684
-| style="text-align:center;" | Golden orwell (bad tuning)
+| style="text-align:center;" | <!--Golden orwell (bad tuning)-->
 |-
 | |
@@ Line 208: / Line 208: @@
 | | 300.000
 | style="text-align:center;" |
-|}
+|}<!--
-Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.
+Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.-->
 [[Category:Abstract MOS patterns]]
 [[Category:scales]]

4L 5s: Difference between revisions

Revision as of 07:45, 28 March 2021

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