3L 5s: Difference between revisions

Revision as of 20:36, 26 March 2021

↖ 2L 4s	↑ 3L 4s	4L 4s ↗
← 2L 5s	3L 5s	4L 5s →
↙ 2L 6s	↓ 3L 6s	4L 6s ↘

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└┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LsLssLss
ssLssLsL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

5\8 to 2\3 (750.0 ¢ to 800.0 ¢)

Dark

1\3 to 3\8 (400.0 ¢ to 450.0 ¢)

TAMNAMS information

Name

checkertonic

Prefix

check-

Abbrev.

chk

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

5\8 (750.0 ¢)

Supersoft (L:s = 4:3)

17\27 (755.6 ¢)

12\19 (757.9 ¢)

19\30 (760.0 ¢)

7\11 (763.6 ¢)

16\25 (768.0 ¢)

9\14 (771.4 ¢)

Superhard (L:s = 4:1)

11\17 (776.5 ¢)

Collapsed (L:s = 1:0)

2\3 (800.0 ¢)

3L 5s or sensoid refers to the structure of octave-equivalent MOS scales with generators ranging from 1\3 (one degrees of 3edo = 400¢) to 3\8 (three degrees of 8edo = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is named antioneirotonic because it is the oneirotonic (5L 3s) MOS pattern with large and small steps switched.

There are two significant harmonic entropy minima with this MOS pattern. Sensi, in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. Squares, in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.

Generator						Cents	Comments
1\3						400
					8\23	417.39
				7\20		420
			6\17			423.53	L/s = 4
					17\48	425	Squares is around here
				11\31		425.81
						427.73	L/s = pi
		5\14				428.57	L/s = 3
						430.41	L/s = e
				14\39		430.77
					23\64	431.25
			9\25			432
	4\11					436.36	Boundary of propriety: generators larger than this are proper
						439.23
			11\30			440
					29\79	440.51	Golden antioneirotonic
				18\49		440.82
						441.185
		7\19				442.11	Optimum rank range (L/s=3/2) sensi
				17\46		443.48	Sensi is around here
			10\27			444.44
				13\35		445.71
					16\43	446.51
3\8						450

@@ Line 1: / Line 1: @@
 {{Infobox MOS
-| Name = antioneirotonic
+| Name = sensoid
 | Periods = 1
 | nLargeSteps = 3
@@ Line 9: / Line 9: @@
 }}
-'''3L 5s''' or '''antioneirotonic''' (/oʊnaɪrəˈtɒnɪk/ ''oh-ny-rə-TON-ik'' or /ənaɪrə-/ ''ə-ny-rə-'') refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degrees of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched.
+'''3L 5s''' or '''sensoid''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degrees of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched.
 There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent_family|Sensi]], in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. [[Meantone_family#Squares|Squares]], in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.

3L 5s: Difference between revisions

Revision as of 20:36, 26 March 2021

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