20edo: Difference between revisions

Revision as of 02:28, 28 March 2019

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cents each. It contains smaller edos 2, 4, 5, and 10 and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from 5edo), 11, 13 & 15 (from 10edo), 19 & 27 (from 4edo), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.

Compositions

Underwater Spontaniety (lo-fi ambient) by Stephen Weigel
God's Favorite Tuning (xen-pop) by Stephen Weigel
You Lied, and I'm not Mentioning your Name (xen-pop) by Stephen Weigel
Etude in 20-tone equal tuning play by Herman Miller
20ET — Prelude & Fugue a3 by Aaron Hunt
We Call It Sharing Breath play by Andrew Heathwaite
The Walrus and the Carpenter byChris Vaisvil and Bethan Mathis
20 edo Electric Guitar Improvisation byChris Vaisvil
Göbekli Tepe (20 edo guitar solo) by Chris Vaisvil
A Paradigm Shift (20 edo) by Chris Vaisvil
Composition for unconventional tempered clavier by Pyotr Chernobrivets
5 compositions for violin and clavier in 20-EDO by Pyotr Chernobrivets
Composition for cello and clavier in 20-tone equal temperament by Pyotr Chernobrivets
5 compositions for violin and clavier in 20-tone equal temperament by Pyotr Chernobrivets

Intervals

Like 15edo, every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th.

Degree	Cents	pions	7mus	Approximate Ratios	Ups and Downs Notation			Nearest Harmonic
0	0			1/1	unison	P1	D	1
1	60	63.6	76.8 (4C.D₁₆)	29/28	upminor 2nd	^m2	D^	33
2	120	127.2	153.6 (99.A₁₆)	14/13, 15/14	mid 2nd	~2	D^^, Evv	69
3	180	190.8	230.4 (EA.6₁₆)	10/9	downmajor 2nd	vM2	Ev	71
4	240	254.4	307.2 (133.3₁₆)	8/7, 15/13	major 2nd, minor 3rd	M2, m3	E, F	37
5	300	318	384 (180₁₆)	13/11, 19/16	upminor 3rd	^m3	F^	19
6	360	381.6	460.8 (1CC.D₁₆)	16/13, 5/4	mid 3rd	~3	F^^	79
7	420	445.2	537.6 (219.A₁₆)	14/11, 51/40	downmajor 3rd	vM3	F#v	41
8	480	508.8	614.4 (266.6₁₆)	25/19, 4/3	major 3rd, perfect fourth	M3, P4	F#, G	21
9	540	572.4	691.2 (2AA.3₁₆)	15/11, 11/8	up-fourth	^4	G^	11
10	600	636	768 (300₁₆)	7/5	double-up fourth, double-down fifth	^^4, vv5	G^^, Avv	91
11	660	699.6	844.8 (34C.D₁₆)	22/15, 16/11	down-fifth	v5	Av	47
12	720	763.2	921.6 (399.A₁₆)	38/25, 3/2	fifth	P5, m6	A	97
13	780	826.8	998.4 (3EA.6₁₆)	11/7, 25/16	upminor 6th	^m6	A^	25
14	840	890.4	1095.2 (433.3₁₆)	13/8, 8/5	mid 6th	~6	A^^, Bvv	13
15	900	954	1152 (480₁₆)	22/13, 32/19	downmajor 6th	vM6	Bv	27
16	960	1017.6	1228.8 (4CC.D₁₆)	7/4, 26/15	major 6th, minor 7th	M6, m7	B, C	7
17	1020	1081.2	1305.6 (519.A₁₆)1208.4	9/5	upminor 7th	^m7	C^	115
18	1080	1144.8	1382.4 (566.6₁₆)	15/8, 13/7	mid 7th	~7	C^^, Dvv	15
19	1140	1208.4	1459.2 (5AA.3₁₆)	56/29	downmajor 7th	vM7	Dv	31
20	1200	1272	1536 (600₁₆)	2/1	octave	P8	D	2

Chord Names

20edo chord names using ups and downs:

0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
0-5-12 = D F^ A = D.^m = "D upminor"
0-6-12 = D F^^ A = D.~ = "D mid"
0-7-12 = D F#v A = D.v = "D dot down" or "D downmajor"
0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
0-5-12-16 = D F^ A C = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three"
0-6-12-16 = D F^^ A C = D7(~3) = "D seven mid-three", or D F^ A B = D6(~3) = "D six mid-three"
0-7-12-16 = D F#v A C = D7(v3) = "D seven down-three", or D F#v A B = D6(v3) = "D six down-three"
0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
0-7-12-19 = D F#v A C#v = D.vM7 = "D downmajor seven"
0-5-12-17 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six"

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs. Because many intervals have several names, many chords do too.

Modes

20 tone equal modes:

3 1 3 1 3 1 3 1 3 1	Blackwood Major Decatonic (bi-equal decatonic, according to the MOS naming scheme)
1 3 1 3 1 3 1 3 1 3	Blackwood Minor Decatonic (also bi-equal decatonic)
2 3 2 2 2 3 2 2 2	Balzano Nine-tone (fair mavila, score9)
2 2 2 2 1 2 2 2 2 2 1	Balzano Eleven-tone, Agmon Diatonic DS4, score11
2 2 2 3 2 2 2 3 2	Balzano Nine-tone inverse (also fair mavila, score9)
1 2 2 2 2 2 1 2 2 2 2	Balzano Eleven-tone inverse (also score11)
2 3 2 3 2 3 2 3	Octatonic (diminished, according to the MOS naming scheme)
3 2 3 2 3 2 3 2	Diminished
4 3 1 4 3 4 1	Twenty-tone "Major"
4 1 3 4 1 4 3	Twenty-tone "Minor"
2 2 1 2 1 2 2 1 2 2 2 1	Twelve-tone Chromatic
2 2 2 2 1 2 2 2 2 1 2	Zweifel Major
2 1 2 2 2 2 2 1 2 2 2	Zweifel Natural Minor
3 3 3 3 3 3 2	Major quasi-equal Heptatonic (Grumpy heptatonic)
3 2 3 3 3 3 3	Minor quasi-equal Heptatonic (also Grumpy heptatonic)
3 2 2 2 2 3 2 2 2	Rothenberg Generalized Diatonic (also score9)
3 4 1 4 3 3 2	Stearns Major
7 2 7 2 2	score5 (classic pentatonic)
5 2 2 5 2 2 2	score7 (mavila, anti-diatonic)

Commas

20 EDO tempers out the following commas. (Note: This assumes the val < 20 32 46 56 69 74 |.)

Rational	Monzo	Size (Cents)	Name 1	Name 2	Name 3
256/243	[8 -5⟩	90.22	Limma	Pythagorean Minor 2nd
16875/16384	[-14 3 4⟩	51.12	Negri Comma	Double Augmentation Diesis
9931568/9752117	[-25 7 6⟩	31.57	Ampersand's Comma
2048/2025	[11 -4 -2⟩	19.55	Diaschisma
525/512	[-9 1 2 1⟩	43.41	Avicennma	Avicenna's Enharmonic Diesis
49/48	[-4 -1 0 2⟩	35.70	Slendro Diesis
50/49	[1 0 2 -2⟩	34.98	Tritonic Diesis	Jubilisma
686/675	[1 -3 -2 3⟩	27.99	Senga
64/63	[6 -2 0 -1⟩	27.26	Septimal Comma	Archytas' Comma	Leipziger Komma
9859966/9733137	[-10 7 8 -7⟩	22.41	Blackjackisma
1029/1024	[-10 1 0 3⟩	8.43	Gamelisma
225/224	[-5 2 2 -1⟩	7.71	Septimal Kleisma	Marvel Comma
16875/16807	[0 3 4 -5⟩	6.99	Mirkwai
6772805/6751042	[11 -10 -10 10⟩	5.57	Linus
121/120	[-3 -1 -1 0 2⟩	14.37	Biyatisma
91/90	[-1 -2 -1 1 0 1⟩	19.13	Superleap
2401/2400	[-5 -1 2 4⟩	0.72	Breedsma
676/675	[2 -3 -2 0 0 2⟩	2.56	Parizeksma

Books

External image: http://ronsword.com/images/20_tet_Coversm.jpg ^{[dead link]}

WARNING: MediaWiki doesn't have very good support for external images.

Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.

"Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more by Ron Sword ^{[dead link]}

@@ Line 6: / Line 6: @@
 }}
 -tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 &amp; 15 (from [[10edo]]), 19 &amp; 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
 __FORCETOC__
 -----
@@ Line 34: / Line 35: @@
 ! Degree
 ! Cents
+! pions
+!7mus
 ! Approximate Ratios
 ! colspan="3" | [[Ups and Downs Notation]]
@@ Line 39: / Line 42: @@
 |-
 | 0
-| style="text-align:right;" | 0
+| colspan="3" style="text-align:right;" | 0
 | 1/1
 | unison
@@ Line 48: / Line 51: @@
 | 1
 | style="text-align:right;" | 60
+|63.6
+|76.8 (4C.D<sub>16</sub>)
 | 29/28
 | upminor 2nd
@@ Line 56: / Line 61: @@
 | 2
 | style="text-align:right;" | 120
+|127.2
+|153.6 (99.A<sub>16</sub>)
 | 14/13, 15/14
 | mid 2nd
@@ Line 64: / Line 71: @@
 | 3
 | style="text-align:right;" | 180
+|190.8
+|230.4 (EA.6<sub>16</sub>)
 | 10/9
 | downmajor 2nd
@@ Line 72: / Line 81: @@
 | 4
 | style="text-align:right;" | 240
+|254.4
+|307.2 (133.3<sub>16</sub>)
 | 8/7, 15/13
 | major 2nd, minor 3rd
@@ Line 80: / Line 91: @@
 | 5
 | style="text-align:right;" | 300
+|318
+|384 (180<sub>16</sub>)
 | 13/11, 19/16
 | upminor 3rd
@@ Line 88: / Line 101: @@
 | 6
 | style="text-align:right;" | 360
+|381.6
+|460.8 (1CC.D<sub>16</sub>)
 | 16/13, 5/4
 | mid 3rd
@@ Line 96: / Line 111: @@
 | 7
 | style="text-align:right;" | 420
+|445.2
+|537.6 (219.A<sub>16</sub>)
 | [[14/11]], [[51/40]]
 | downmajor 3rd
@@ Line 104: / Line 121: @@
 | 8
 | style="text-align:right;" | 480
+|508.8
+|614.4 (266.6<sub>16</sub>)
 | 25/19, 4/3
 | major 3rd, perfect fourth
@@ Line 112: / Line 131: @@
 | 9
 | style="text-align:right;" | 540
+|572.4
+|691.2 (2AA.3<sub>16</sub>)
 | 15/11, 11/8
 | up-fourth
@@ Line 120: / Line 141: @@
 | 10
 | style="text-align:right;" | 600
+|636
+|768 (300<sub>16</sub>)
 | 7/5
 | double-up fourth, double-down fifth
@@ Line 128: / Line 151: @@
 | 11
 | style="text-align:right;" | 660
+|699.6
+|844.8 (34C.D<sub>16</sub>)
 | 22/15, 16/11
 | down-fifth
@@ Line 136: / Line 161: @@
 | 12
 | style="text-align:right;" | 720
+|763.2
+|921.6 (399.A<sub>16</sub>)
 | 38/25, 3/2
 | fifth
@@ Line 144: / Line 171: @@
 | 13
 | style="text-align:right;" | 780
+|826.8
+|998.4 (3EA.6<sub>16</sub>)
 | 11/7, 25/16
 | upminor 6th
@@ Line 152: / Line 181: @@
 | 14
 | style="text-align:right;" | 840
+|890.4
+|1095.2 (433.3<sub>16</sub>)
 | 13/8, 8/5
 | mid 6th
@@ Line 160: / Line 191: @@
 | 15
 | style="text-align:right;" | 900
+|954
+|1152 (480<sub>16</sub>)
 | 22/13, 32/19
 | downmajor 6th
@@ Line 168: / Line 201: @@
 | 16
 | style="text-align:right;" | 960
+|1017.6
+|1228.8 (4CC.D<sub>16</sub>)
 | 7/4, 26/15
 | major 6th, minor 7th
@@ Line 176: / Line 211: @@
 | 17
 | style="text-align:right;" | 1020
+|1081.2
+|1305.6 (519.A<sub>16</sub>)1208.4
 | 9/5
 | upminor 7th
@@ Line 184: / Line 221: @@
 | 18
 | style="text-align:right;" | 1080
+|1144.8
+|1382.4 (566.6<sub>16</sub>)
 | 15/8, 13/7
 | mid 7th
@@ Line 192: / Line 231: @@
 | 19
 | style="text-align:right;" | 1140
+|1208.4
+|1459.2 (5AA.3<sub>16</sub>)
 | 56/29
 | downmajor 7th
@@ Line 200: / Line 241: @@
 | 20
 | style="text-align:right;" | 1200
+|1272
+|1536 (600<sub>16</sub>)
 | 2/1
 | octave

20edo: Difference between revisions

Revision as of 02:28, 28 March 2019

Contents

Compositions

Intervals

Chord Names

Modes

Commas

Books

Navigation menu

20edo: Difference between revisions

Revision as of 02:28, 28 March 2019

Compositions

Intervals

Chord Names

Modes

Commas

Books

Navigation menu

Search