2L 5s: Difference between revisions

Revision as of 07:18, 27 May 2023

2L 5s, named antidiatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 5 small steps, repeating every octave. Generators that produce this scale range from 514.3 ¢ to 600 ¢, or from 600 ¢ to 685.7 ¢.

↖ 1L 4s	↑ 2L 4s	3L 4s ↗
← 1L 5s	2L 5s	3L 5s →
↙ 1L 6s	↓ 2L 6s	3L 6s ↘

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

Scale structure

Step pattern

LssLsss
sssLssL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

3\7 to 1\2 (514.3 ¢ to 600.0 ¢)

Dark

1\2 to 4\7 (600.0 ¢ to 685.7 ¢)

TAMNAMS information

Name

antidiatonic

Prefix

pel-

Abbrev.

pel

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

3\7 (514.3 ¢)

Supersoft (L:s = 4:3)

10\23 (521.7 ¢)

7\16 (525.0 ¢)

11\25 (528.0 ¢)

4\9 (533.3 ¢)

9\20 (540.0 ¢)

5\11 (545.5 ¢)

Superhard (L:s = 4:1)

6\13 (553.8 ¢)

Collapsed (L:s = 1:0)

1\2 (600.0 ¢)

While antidiatonic is closely associated with mavila temperament and 7L 2s, not every 2L 5s scale is an instance of "mavila", since some of them extend to 2L 7s scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament score, which is not intended to be treated as having any kind of fifth, flat or otherwise.)

In terms of harmonic entropy, the most significant minimum is at Liese/Triton, in which the generator is about 7/5 and three of them make a 3/1.

The antidiatonic scale is similar to the normal diatonic scale except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and the antilocrian scale has an augmented fifth instead of a diminished fifth. The flatter the "fifth" gets, the less the scale resembles the diatonic scale, with mavila scales generated by flat fifths appearing like a flipped diatonic, but casablanca and triton scales generated by subfifths or even tritones much less so.

Names

It is often called antidiatonic, because it has the step pattern of diatonic (5L 2s), but with the large and small steps switched. TAMNAMS uses this name as well.

Notation

We'll use the convention DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz, &/@ = raise and lower by one chroma. The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up flattens a note by a chroma, rather than sharpening it as in diatonic (5L 2s).

Intervals

Note: In TAMNAMS, a k-step interval class in antidiatonic may be called a "k-step", "k-mosstep", or "k-pelstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.

Modes

Modes of the antidiatonic scale are usually named as "anti-" combined with the opposite mode of the diatonic scale, e.g. 4|2 being called "antiaeolian". CompactStar also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.

Modes of 2L 5s
UDP	Cyclic order	Step pattern
6\|0	1	LssLsss
5\|1	4	LsssLss
4\|2	7	sLssLss
3\|3	3	sLsssLs
2\|4	6	ssLssLs
1\|5	2	ssLsssL
0\|6	5	sssLssL

Scale tree

Generator ranges:

Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)

Generator						Cents	L	s	L/s	Comments
3\7						514.286	1	1	1.000
					16\37	518.919	6	5	1.200	Gravity↑
				13\30		520.000	5	4	1.250
					23\53	520.755	9	7	1.286
			10\23			521.739	4	3	1.333
					27\62	522.581	11	8	1.375
				17\39		523.077	7	5	1.400
					24\55	523.636	10	7	1.428
		7\16				525.000	3	2	1.500	Mavila is in this region
					25\57	526.316	11	7	1.571
				18\41		526.829	8	5	1.600
					29\66	527.273	13	8	1.625	Golden mavila (527.1497¢)
			11\25			528.000	5	3	1.667
					26\59	528.814	12	7	1.714
				15\34		529.412	7	4	1.750
					19\43	530.233	9	5	1.800	Mabila / Amavil
	4\9					533.333	2	1	2.000	Basic antidiatonic (Generators smaller than this are proper)
					17\38	536.842	9	4	2.250
				13\29		537.931	7	3	2.333
					22\49	538.776	12	5	2.400
			9\20			540.000	5	2	2.500	Score
					23\51	541.176	13	5	2.600	Unnamed golden tuning (541.3837¢)
				14\31		541.935	8	3	2.667	Casablanca is around here
					19\42	542.857	11	4	2.750
		5\11				545.455	3	1	3.000
					16\35	548.571	10	3	3.333
				11\24		550.000	7	2	3.500
					17\37	551.351	11	3	3.667	Freivald / emka
			6\13			553.846	4	1	4.000
					13\28	557.143	9	2	4.500
				7\15		560.000	5	1	5.000	Thuja is around here
					8\17	564.706	6	1	6.000	Liese↓, triton↓
1\2						600.000	1	0	→ inf

@@ Line 1: / Line 1: @@
-{{Infobox MOS
+{{MOS intro}}{{Infobox MOS
 | Name = antidiatonic
 | Periods = 1
@@ Line 10: / Line 10: @@
 }}
-'''2L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 3\7 (3 degrees of [[7edo]] = 514.29¢) to 1\2 (one degree of [[2edo]] = 600¢). In the case of 7edo, L and s are the same size; in the case of 2edo, s becomes so small it disappears (and all that remains are the two equal L's).
+While antidiatonic is closely associated with [[mavila temperament]] and [[7L 2s]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic pairs #Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.)
-While '''antidiatonic''' is closely associated with [[mavila temperament]] and [[7L 2s]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic pairs #Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.)
 In terms of harmonic entropy, the most significant minimum is at [[Meantone family #Liese|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
@@ Line 28: / Line 26: @@
 == Modes ==
 Modes of the antidiatonic scale are usually named as "anti-" combined with the opposite mode of the diatonic scale, e.g. 4|2 being called "antiaeolian". [[User:CompactStar|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.
-* 6|0 LssLsss (anti-locrian, corsican)
-* 5|1 LsssLss (anti-phrygian, breton)
+{{MOS modes|Mode Names=Anti-locrian; Anti-phrygian; Anti-aeolian; Anti-dorian; Anti-mixolydian; Anti-ionian; Anti-lydian|Table Headers=CompactStar's names|Table Entries=Corsican; Breton; Burgundian; Picardian; Norman; Provencal; Alsatian}}
-* 4|2 sLssLss (anti-aeolian, burgundian)
-* 3|3 sLsssLs (anti-dorian, picardian)
-* 2|4 ssLssLs (anti-mixolydian, norman)
-* 1|5 ssLsssL (anti-ionian, provencal)
-* 0|6 sssLssL (anti-lydian, alsatian)
 == Scale tree ==

2L 5s: Difference between revisions

Revision as of 07:18, 27 May 2023

Contents

Names

Notation

Intervals

Modes

Scale tree

Navigation menu

2L 5s: Difference between revisions

Revision as of 07:18, 27 May 2023

Names

Notation

Intervals

Modes

Scale tree

Navigation menu

Search