43edo

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← 42edo43edo44edo →
Prime factorization 43 (prime)
Step size 27.907¢ 
Fifth 25\43 (697.674¢)
Semitones (A1:m2) 3:4 (83.72¢ : 111.6¢)
Consistency limit 7
Distinct consistency limit 7

43 equal divisions of the octave (abbreviated 43edo or 43ed2), also called 43-tone equal temperament (43tet) or 43 equal temperament (43et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 43 equal parts of about 27.9 ¢ each. Each step represents a frequency ratio of 21/43, or the 43rd root of 2.

History

The French Baroque acoustician Joseph Sauveur, who was ironically hearing and speech impaired, based his tuning system on 43 equal tones to the octave, calling one step a méride. Sauveur favoured 43-tone equal temperament because the small intervals are well represented in it.[1]

The composer Juhan Puhm uses 43edo in some of his fortepiano suites and prefers it to 31edo.

Theory

43edo tempers out 81/80 in the 5-limit, and as such it is strongly associated with meantone. Specifically, it is (for all practical purposes) equivalent to 1/5-comma meantone, as it tunes the major third sharp of 5/4 and perfect fifth flat of 3/2 by slightly more than four cents on both of them. It also tempers out the hypovishnuzma and the escapade comma, so that six chromatic semitones make a perfect fourth and eight minor seconds make a major sixth.

Except for 9/7, 11/9, 14/9, and 18/11, all 15-odd-limit intervals have consistent approximations in 43edo, making it an excellent tuning in the 7-, 11-, and 13-limit. In the 7-limit, it supports septimal meantone, as it tempers out 126/125, 225/224, and 3136/3125. The version of 11-limit meantone is the one tempering out 99/98, 176/175, and 441/440, sometimes called Huygens. In the 13-limit it supports meridetone, which tempers out 78/77, and grosstone, which tempers out 144/143. Meridetone has generator map 0 1 4 10 18 27], for which 43 supplies the optimal patent val for, and grosstone 0 1 4 10 18 -16].

43edo's patent val 43 68 100 121 149 159] maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to the jerome temperament, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7-, 11-, 13-, 17-, 19-, and even 23-limit. It also provides the optimal patent val for the 11- and 13-limit amavil temperament, which is not meantone. Thuja is also a possibility, whose 11-limit extension makes five 11/8s stack to a major third (i.e. (11/8)5 → 5/1), with moses of 15 and 28.

Prime harmonics

Approximation of prime harmonics in 43edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37
Error Absolute (¢) +0.0 -4.3 +4.4 +7.9 +6.8 -3.3 +6.7 +9.5 +13.6 +3.0 -0.8 -0.2
Relative (%) +0.0 -15.3 +15.7 +28.4 +24.4 -11.9 +23.9 +33.9 +48.7 +10.7 -3.0 -0.6
Steps
(reduced)
43
(0)
68
(25)
100
(14)
121
(35)
149
(20)
159
(30)
176
(4)
183
(11)
195
(23)
209
(37)
213
(41)
224
(9)
Approximation of prime harmonics in 43edo (continued)
Harmonic 41 43 47 53 59 61 67 71 73 79 83 89
Error Absolute (¢) -10.5 -9.2 +4.3 -8.4 +1.3 -0.6 +4.4 -12.3 -4.5 -1.7 -3.5 -12.7
Relative (%) -37.5 -32.9 +15.3 -30.1 +4.6 -2.2 +15.8 -43.9 -16.2 -6.3 -12.7 -45.7
Steps
(reduced)
230
(15)
233
(18)
239
(24)
246
(31)
253
(38)
255
(40)
261
(3)
264
(6)
266
(8)
271
(13)
274
(16)
278
(20)
Approximation of prime harmonics in 43edo (continued even further)
Harmonic 97 101 103 107 109 113 127 131 137 139 149 151
Error Absolute (¢) +5.7 -8.5 +13.4 +3.3 -0.9 -7.5 +13.6 -12.2 -6.0 -3.2 -11.8 -7.0
Relative (%) +20.4 -30.3 +48.0 +11.7 -3.2 -26.8 +48.7 -43.7 -21.5 -11.4 -42.4 -25.1
Steps
(reduced)
284
(26)
286
(28)
288
(30)
290
(32)
291
(33)
293
(35)
301
(0)
302
(1)
305
(4)
306
(5)
310
(9)
311
(10)

Although not consistent, 43edo performs quite well in very high prime limits. It has unambiguous mappings for all prime harmonics up to 113 (after which the demands on its pitch resolution finally become too great), with the sole exceptions of 23, 71, 89, and 103, making a great Ringer scale. Mappings for ratios between these prime harmonics can then be derived from those for the primes themselves, allowing for a complete set of approximations to the first 16 harmonics in the harmonic series and an almost-complete approximation of the first 32 harmonics, although the limited consistency will give some unusual results. Indeed, one step of 43edo is very close to the septimal comma (64/63); similarly, two steps is close to 32/31, and four steps tunes 16/15 almost perfectly.

43edo has less than 35% relative error (less than 10 cents error) on an impressive 17 of the 19 prime harmonics in the 67-limit. The only ones it misses are 23 and 41. So it can be used as a solid full 19-limit tuning, or as a solid no-23-or-41 67-limit tuning.

It approximates harmonics 31, 37 and 61 close to exactly - within less than a cent (less than 3% relative error). It approximates 3, 13, 43, 53 and 61 slightly flat. It approximates 5, 7, 11, 17, 19, 29, 47, 59 and 67 slightly sharp. Overall this gives 43edo a slightly sharp tendency/feeling, though with the major exception of harmonic 3 (the perfect fifth).

Divisors

43edo is the 14th prime edo, following 41edo and coming before 47edo.

Intervals

The distance from C to C♯ is 3 edosteps (or keys, frets). Thus one edostep equals one third of a sharp.

# Cents Approximate 17-limit Ratios Ups and Downs Notation
0 0.000 1/1 P1 perfect unison D
1 27.907 36/35, 50/49, 64/63, 65/64, 66/65 ^1, d2 up unison, dim 2nd ^D, Ebb
2 55.814 49/48, 33/32 vA1, ^d2 downaug unison, updim 2nd vD#, ^Ebb
3 83.721 25/24, 21/20, 28/27, 22/21, 18/17 A1, vm2 aug 1sn, downminor 2nd D#, vEb
4 111.628 16/15, 15/14, 17/16 m2 minor 2nd Eb
5 139.535 12/11, 13/12, 14/13 ^m2 upminor 2nd ^Eb
6 167.442 11/10 vM2 downmajor 2nd vE
7 195.349 9/8, 10/9 M2 major 2nd E
8 223.256 8/7 ^M2, d3 upmajor 2nd, dim 3rd ^E, Fb
9 251.163 15/13 vA2, ^d3 downaug 2nd, updim 3rd vE#, ^Fb
10 279.070 7/6, 13/11 A2, vm3 aug 2nd, downminor 3rd E#, vF
11 306.977 6/5 m3 minor 3rd F
12 334.884 39/32, 17/14 ^m3 upminor 3rd ^F
13 362.791 16/13, 21/17, 11/9 vM3 downmajor 3rd vF#
14 390.698 5/4 M3 major 3rd F#
15 418.605 9/7, 14/11 ^M3, d4 upmajor 3rd, dim 4th ^F#, Gb
16 446.512 13/10 vA3, ^d4 downaug 3rd, updim 4th vFx, ^Gb
17 474.419 21/16 v4 down 4th vG
18 502.326 4/3 P4 perfect 4th G
19 530.233 15/11 ^4 up 4th ^G
20 558.140 11/8, 18/13 vA4 downaug 4th vG#
21 586.047 45/32, 7/5, 24/17 A4, vd5 aug 4th, downdim 5th G#, ^Ab
22 613.953 64/45, 10/7, 17/12 ^A4, d5 upaug 4th, dim 5th ^G#, Ab
23 641.860 16/11, 13/9 ^d5 updim 5th ^Ab
24 669.767 22/15 v5 down 5th vA
25 697.674 3/2 P5 perfect 5th A
26 725.581 32/21 ^5 up 5th ^A
27 753.488 20/13 vA5, ^d6 downaug 5th, updim 6th vA#, ^Bbb
28 781.395 14/9, 11/7 A5, vm6 aug 5th, downminor 6th A#, vBb
29 809.302 8/5 m6 minor 6th Bb
30 837.209 13/8, 34/21, 18/11 ^m6 upminor 6th ^Bb
31 865.116 64/39, 28/17 vM6 downmajor 6th vB
32 893.023 5/3 M6 major 6th B
33 920.930 12/7, 22/13 ^M6, d7 upmajor 6th, dim 7th ^B, Cb
34 948.837 26/15 vA6, ^d7 downaug 6th, updim 7th vB#, ^Cb
35 976.744 7/4 A6, vm7 aug 6th, downminor 7th B#, vC
36 1004.651 16/9, 9/5 m7 minor 7th C
37 1032.558 20/11 ^m7 upminor 7th ^C
38 1060.465 11/6, 24/13, 13/7 vM7 downmajor 7th vC#
39 1088.372 15/8, 28/15, 32/17 M7 major 7th C#
40 1116.279 48/25, 40/21, 27/14, 21/11, 17/9 ^M7, d8 upmajor 7th, dim 8ve ^C#, Db
41 1144.186 96/49, 64/33 vA7, ^d8 downaug 7th, updim 8ve vCx, ^Db
42 1172.093 35/18, 49/25, 63/32, 65/33, 128/65 A7, v8 aug 7th, down 8ve Cx, vD
43 1200.000 2/1 P8 perfect 8ve D

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See Ups and Downs Notation #Chords and Chord Progressions.

JI approximation

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Selected 19-limit intervals approximated in 43edo

Interval mappings

The following tables show how 15-odd-limit intervals are represented in 43edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 43edo (direct approximation, even if inconsistent)
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
15/8, 16/15 0.103 0.4
13/12, 24/13 0.962 3.4
11/7, 14/11 1.097 3.9
11/10, 20/11 2.438 8.7
13/8, 16/13 3.318 11.9
15/13, 26/15 3.422 12.3
7/5, 10/7 3.534 12.7
3/2, 4/3 4.281 15.3
5/4, 8/5 4.384 15.7
13/9, 18/13 5.243 18.8
15/11, 22/15 6.718 24.1
11/8, 16/11 6.822 24.4
13/10, 20/13 7.702 27.6
15/14, 28/15 7.815 28.0
7/4, 8/7 7.918 28.4
9/8, 16/9 8.561 30.7
5/3, 6/5 8.665 31.0
13/11, 22/13 10.140 36.3
11/6, 12/11 11.102 39.8
13/7, 14/13 11.237 40.3
9/7, 14/9 11.428 40.9
7/6, 12/7 12.199 43.7
11/9, 18/11 12.524 44.9
9/5, 10/9 12.945 46.4
15-odd-limit intervals in 43edo (patent val mapping)
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
15/8, 16/15 0.103 0.4
13/12, 24/13 0.962 3.4
11/7, 14/11 1.097 3.9
11/10, 20/11 2.438 8.7
13/8, 16/13 3.318 11.9
15/13, 26/15 3.422 12.3
7/5, 10/7 3.534 12.7
3/2, 4/3 4.281 15.3
5/4, 8/5 4.384 15.7
13/9, 18/13 5.243 18.8
15/11, 22/15 6.718 24.1
11/8, 16/11 6.822 24.4
13/10, 20/13 7.702 27.6
15/14, 28/15 7.815 28.0
7/4, 8/7 7.918 28.4
9/8, 16/9 8.561 30.7
5/3, 6/5 8.665 31.0
13/11, 22/13 10.140 36.3
11/6, 12/11 11.102 39.8
13/7, 14/13 11.237 40.3
7/6, 12/7 12.199 43.7
9/5, 10/9 12.945 46.4
11/9, 18/11 15.383 55.1
9/7, 14/9 16.479 59.1

Notation

Red-Blue Notation

Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A♯ and B♭ are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.

For people who aren't colorblind, a red-note/blue-note system (similar to that proposed for 36edo) can be used. (Note that this is different than Kite's color notation.) Now we have the following sequence of notes, each separated by one meride:  A ,  A ,  A♯ ,  A♯ ,  B♭ ,  B♭ ,  B ,  B . (Note that red sharps or blue flats are enharmonically equivalent to simpler notes:  A♯  is enharmonic to B♭, and  B♭  is actually just A♯).

The diatonic semitone is four steps, so for the region between B and C, we can use:  B ,  C♭ ,  B♯  /  C♭  (they are enharmonic equivalents),  B♯ , and  C . All of the notes in 43edo therefore have unambiguous names except for  B♯  /  C♭ , and  E♯  /  F♭ . It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).

If  C♭  and  B♯  (and  F♭  /  E♯ ) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a completely unambiguous red-note/blue-note notation for 45edo, which is another meantone (actually, a flattone) system.

Ups and downs notation

The third-sharps and third-flats can also be notated using ups and downs notation and extended Helmholtz–Ellis accidentals:

Step Offset 0 1 2 3 4 5 6 7
Sharp Symbol
Heji18.svg
Heji19.svg
Heji24.svg
Heji25.svg
Heji26.svg
Heji31.svg
Heji32.svg
Heji33.svg
Flat Symbol
Heji17.svg
Heji12.svg
Heji11.svg
Heji10.svg
Heji5.svg
Heji4.svg
Heji3.svg

The notes between A and B can then be notated as A, AHeji19.svg, AHeji24.svg, A♯, B♭, BHeji12.svg, BHeji17.svg, B. Note that A♯ is enharmonic to BHeji10.svg, and B♭ is enharmonic to AHeji26.svg.

The notes from B to C are B, C♭, BHeji24.svg / CHeji12.svg, B♯, and C. Similarily, the notes from E to F are E, F♭, EHeji24.svg / FHeji12.svg, E♯, and F. As with the red/blue note system described above, all notes in 43edo therefore have unambiguous names except for BHeji24.svg / CHeji12.svg and EHeji24.svg / FHeji12.svg.

Double or even triple arrows may arise if the arrows are taken to have their own layer of enharmonic spellings.

Sagittal

The following table shows sagittal notation accidentals in one apotome for 43do.

Steps 0 1 2 3
Symbol Sagittal natural.png Sagittal tai.png Sagittal sharp tao.png Sagittal sharp.png

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢)
Tuning error
Absolute (¢) Relative (%)
2.3 [-68 43 [43 68]] +1.35 1.35 4.84
2.3.5 81/80, 50331648/48828125 [43 68 100]] +0.27 1.88 6.75
2.3.5.7 81/80, 126/125, 17280/16807 [43 68 100 121]] −0.51 2.11 7.56
2.3.5.7.11 81/80, 99/98, 126/125, 864/847 [43 68 100 121 149]] −0.80 1.98 7.08
2.3.5.7.11.13 78/77, 81/80, 99/98, 126/125, 144/143 [43 68 100 121 149 159]] −0.52 1.91 6.85
2.3.5.7.11.13.17 78/77, 81/80, 99/98, 120/119, 126/125, 144/143 [43 68 100 121 149 159 176]] −0.52 1.81 6.49
2.3.5.7.11.13.17.19 78/77, 81/80, 99/98, 120/119, 126/125, 135/133, 144/143 [43 68 100 121 149 159 176 183]] −0.87 1.77 6.34

Commas

This is a partial list of the 19-limit commas that 43edo tempers out with its patent val, 43 68 100 121 149 159 176 183].

Prime
Limit
Ratio[note 1] Monzo Cents Color name Name(s)
3 (42 digits) [-68 43 184.07 Tribilawa 43-comma
5 (18 digits) [20 5 -12 74.01 Saquadtrigu Hypovishnuzma
5 (16 digits) [24 1 -11 52.50 Salegu Magus comma
5 81/80 [-4 4 -1 21.51 Gu Syntonic comma, Didymus comma, meantone comma
5 (20 digits) [32 -7 -9 9.49 Sasa-tritrigu Escapade comma
5 (42 digits) [-68 18 17 2.52 Quinla-seyo Vavoom comma
7 59049/57344 [-13 10 0 -1 50.72 Laru Harrison's comma
7 3645/3584 [-9 6 1 -1 29.22 Laruyo Schismean comma
7 (14 digits) [5 -1 7 -7 20.46 Sepruyo Mermisma
7 126/125 [1 2 -3 1 13.80 Zotrigu Starling comma
7 (14 digits) [21 -5 -2 -3 11.12 Satriru-agugu Bronzisma
7 (18 digits) [-14 7 -6 6 8.76 Latribizogu Historisma
7 225/224 [-5 2 2 -1 7.71 Ruyoyo Septimal kleisma, Marvel comma
7 3136/3125 [6 0 -5 2 6.08 Zozoquingu Hemimean comma
7 (12 digits) [-11 2 7 -3 1.63 Latriru-asepyo Meter comma
11 1350/1331 [1 3 2 0 -3 24.54 Trilu-ayoyo Large Tetracot diesis
11 99/98 [-1 2 0 -2 1 17.58 Loruru Mothwellsma
11 176/175 [4 0 -2 -1 1 9.86 Lorugugu Valinorsma
11 441/440 [-3 2 -1 2 -1 3.93 Luzozogu Werckisma
11 4000/3993 [5 -1 3 0 -3 3.03 Triluyo Wizardharry comma, pine comma
11 (12 digits) [17 -5 0 -2 -1 1.26 Salururu Olympic comma
11 (18 digits) [24 -6 0 1 -5 0.51 Saquinlu-azo Quartisma
13 78/77 [1 1 0 -1 -1 1 22.34 Tholuru Negustma
13 144/143 [4 2 0 0 -1 -1 12.06 Thulu Grossma
13 169/168 [-3 -1 0 -1 0 2 10.27 Thothoru Buzurgisma, dhanvantarisma
13 (12 digits) [9 6 0 0 0 -5 9.09 Quinthu Glacier comma
13 364/363 [2 -1 0 1 -2 1 4.76 Tholuluzo Minor minthma
13 1001/1000 [-3 0 -3 1 1 1 1.73 Tholozotrigu Fairytale comma, sinbadma
13 2080/2079 [5 -3 1 -1 -1 1 0.83 Tholuruyo Ibnsinma, sinaisma
13 4096/4095 [12 -2 -1 -1 0 -1 0.42 Sathurugu Schismina
17 120/119 [3 1 1 -1 0 0 -1 14.49 Suruyo Lynchisma
17 221/220 [-2 0 -1 0 -1 1 1 7.85 Sotholugu Minor naiadma
17 256/255 [8 -1 -1 0 0 0 -1 6.78 Sugu Charisma, septendecimal kleisma
17 273/272 [5 1 -1 0 0 0 0 -1 6.35 Suthozo Tannisma
17 715/714 [-1 -1 1 -1 1 1 -1 2.42 Sutholoruyo September comma
19 96/95 [5 1 -1 0 0 0 0 -1 18.13 Nugu 19th Partial chroma
19 153/152 [-3 2 0 0 0 0 1 -1 11.35 Nuso Ganassisma
19 171/170 [-1 2 -1 0 0 0 -1 1 10.15 Nosugu Malcolmisma
19 209/208 [-4 0 0 0 1 -1 0 1 8.30 Nothulo Yama comma
19 210/209 [1 1 1 1 -1 0 0 -1 8.26 Nuluzoyo Spleen comma
  1. Ratios longer than 10 digits are presented by placeholders with informative hints

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
ratio*
Temperaments
1 1\43 27.91 64/63 Arch
1 2\43 55.81 33/32 Escapade
1 4\43 111.63 16/15 Vavoom
1 5\43 139.53 13/12 Jerome
1 6\43 167.44 11/10 Superpine
1 7\43 195.35 28/25 Didacus
1 8\43 223.26 8/7 Kumonga
1 9\43 251.16 15/13 Hemimeantone
1 10\43 279.07 75/64 Decipentic
1 11\43 334.88 17/14 Cohemimabila
1 13\43 362.79 16/13 Submajor (43e) / interpental (43)
1 14\43 390.70 5/4 Amigo
1 16\43 446.51 13/10 Supersensi
1 18\43 502.33 4/3 Meantone
1 19\43 530.23 15/11 Amavil
1 20\43 558.14 11/8 Thuja
1 21\43 586.05 7/5 Merman

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Detemperaments

Ringer 43

The metaphorical color palette that the intervals of 43edo present can be quite appealing for various reasons such as being meantone and splitting 4/3 into 6 equal parts and 3/2 into 5 equal parts, but the accuracy leaves one wanting in many cases, which is why an excellent alternative (given the unambiguity of mappings of all primes in the 109-limit except 71 and 89) is Ringer 43, a Ringer scale with 43 notes per octave period:

55:56:57:58:59:60:61:62:63:64:65:66:67:68:69:70:72:73:74:75:76:78:79:80:82:83:84:86:87:88:90:91:92:94:96:97:98:100:102:104:106:108:109:110

Or equivalently in the form of reduced, rooted intervals:

65/64, 33/32, 67/64, 17/16, 69/64, 35/32, 9/8, 73/64, 37/32, 75/64, 19/16, 39/32, 79/64, 5/4, 41/32, 83/64, 21/16, 43/32, 87/64, 11/8, 45/32, 91/64, 23/16, 47/32, 3/2, 97/64, 49/32, 25/16, 51/64, 13/8, 53/32, 27/16, 109/64, 55/32, 7/4, 57/32, 29/16, 59/32, 15/8, 61/32, 31/16, 63/32, 2/1

Scales

MOS scales

Harmonic scales

43edo represents the first 16 overtones of the harmonic series well (written as a ratio of 8:9:10:11:12:13:14:15:16 in just intonation) with degrees 0, 7, 14, 20, 25, 30, 35, 39, and 43, and scale steps of 7, 7, 6, 5, 5, 5, 4, and 4.

  • 7\43 (195.349¢) stands in for frequency ratio 9/8 (203.910¢) and 10/9 (182.404¢).
  • 6\43 (156.522¢) stands in for 11/10 (165.004¢)
  • 5\46 (130.435¢) stands in for 12/11 (150.637¢), 13/12 (138.573¢), and 14/13 (128.298¢).
  • 4\43 (111.628¢) stands in for 15/14 (119.443¢) and 16/15 (111.731¢).
Harmonic Note (starting from C)
1 C
3 G
5 E
7 A♯, BHeji10.svg
9 D
11 E𝄪, FHeji24.svg, FHeji20.svg
13 B♭♭♭, AHeji12.svg
15 B

Subsets of Meantone

Major scales

  • Ionian Pentatonic: 14 4 7 14 4
  • Major: 7 7 4 7 7 7 4
  • Major Pentatonic: 7 7 11 7 11


Minor scales

  • Minor: 7 4 7 7 4 7 7
  • Minor Harmonic: 7 4 7 7 4 10 4
  • Minor Harmonic Pentatonic: 7 4 14 14 4
  • Minor Hexatonic: 7 4 7 7 11 7
  • Minor Melodic: 7 4 7 7 7 7 4
  • Minor Pentatonic: 11 7 7 11 7


Modal scales

  • Dorian: 7 4 7 7 7 4 7
  • Locrian: 4 7 7 4 7 7 7
  • Lydian: 7 7 7 4 7 7 4
  • Mixolydian: 7 7 4 7 7 4 7
  • Mixolydian Harmonic: 14 4 7 4 7 7
  • Mixolydian Pentatonic: 14 4 7 11 7
  • Phrygian: 4 7 7 7 4 7 7
  • Phrygian Dominant: 4 10 4 7 4 7 7
  • Phrygian Dominant Hexatonic: 4 10 4 7 11 7
  • Phrygian Dominant Pentatonic: 14 4 7 4 14
  • Phrygian Pentatonic: 4 7 14 4 14


Blues scales

  • Blues Aeolian Hexatonic: 11 7 4 3 4 14
  • Blues Aeolian Pentatonic I: 11 7 7 4 14
  • Blues Aeolian Pentatonic II: 11 14 4 7 7
  • Blues Bright Double Harmonic: 4 10 4 7 4 7 3 4
  • Blues Dark Double Harmonic: 7 4 7 4 3 4 10 4
  • Blues Dorian Hexatonic: 11 7 7 7 4 7
  • Blues Dorian Pentatonic: 11 14 7 4 7
  • Blues Dorian Septatonic: 11 7 4 3 7 4 7
  • Blues Harmonic Hexatonic: 7 4 7 7 14 4
  • Blues Harmonic Septatonic: 11 7 4 3 4 10 4
  • Blues Leading: 11 7 4 3 11 3 4
  • Blues Minor: 11 7 4 3 11 7
  • Blues Minor Maj7: 11 7 4 3 14 4
  • Blues Pentachordal: 7 4 7 4 3 18
  • Hyperblue Dorian: 11 7 2 5 9 2 7
  • Hyperblue Harmonic: 11 7 2 5 3 12 3


Others

  • Akebono I: 7 4 14 7 11
  • Dominant Pentatonic: 7 7 11 11 7
  • Double Harmonic: 4 10 4 7 4 10 4
  • Hirajoshi: 7 4 14 4 14
  • Javanese Pentachordal: 4 7 11 3 18
  • Picardy Hexatonic: 7 7 4 7 4 14
  • Picardy Pentatonic: 7 7 11 4 14

Other notable scales

Music

Modern renderings

Johann Sebastian Bach
Nicolaus Bruhns
George Frideric Handel
Scott Joplin
  • Maple Leaf Rag (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
Shirō Sagisu

21st century

Claudi Meneghin
Bryan Deister
Peter Kosmorsky
Budjarn Lambeth
  • Gamelan-Inspired Improvisation in 43edo, Fossa Scale (Nov 2024) - YouTube
Juhan Puhm (site)
Randy Wells
Xotla

Instruments

Keyboards

A possible isomorphic keyboard layout for 43edo:

Fifth Comma Meantone Keyboard Layout.svg

References

External links

Articles

Diagrams