120edo
| ← 119edo | 120edo | 121edo → |
Theory
120edo is an excellent tuning in the 2.3.7.11.13.23.29 subgroup. In the no-5's 11-limit, it tempers out 243/242.
120edo shares the perfect fifth with 12edo, tempering out the Pythagorean comma. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit superpyth temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit surmarvelpyth temperament where it represents 675/448, which is marvel comma sharp of 3/2. It may be used as a de facto dual fifth in newcome temperament. In the patent val 120edo is also a tuning for the 7-limit decoid temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.96 | +3.69 | +1.17 | -1.32 | -0.53 | -4.96 | +2.49 | +1.73 | +0.42 | +4.96 |
| Relative (%) | +0.0 | -19.6 | +36.9 | +11.7 | -13.2 | -5.3 | -49.6 | +24.9 | +17.3 | +4.2 | +49.6 | |
| Steps (reduced) |
120 (0) |
190 (70) |
279 (39) |
337 (97) |
415 (55) |
444 (84) |
490 (10) |
510 (30) |
543 (63) |
583 (103) |
595 (115) | |
Subsets and supersets
120edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5).
Miscellaneous properties
Being the simplest division of the octave by the Germanic long hundred, it has a unit step which is the fine relative cent of 1edo.
120edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 10 | ^D, ^E♭♭ | |
| 2 | 20 | ^^D, ^^E♭♭ | |
| 3 | 30 | ^3D, ^3E♭♭ | |
| 4 | 40 | 42/41, 43/42, 44/43, 45/44, 46/45 | ^4D, ^4E♭♭ |
| 5 | 50 | 34/33 | ^5D, v5E♭ |
| 6 | 60 | 29/28, 30/29 | v4D♯, v4E♭ |
| 7 | 70 | v3D♯, v3E♭ | |
| 8 | 80 | 22/21, 45/43 | vvD♯, vvE♭ |
| 9 | 90 | 20/19, 39/37 | vD♯, vE♭ |
| 10 | 100 | 18/17 | D♯, E♭ |
| 11 | 110 | 16/15, 49/46 | ^D♯, ^E♭ |
| 12 | 120 | 15/14 | ^^D♯, ^^E♭ |
| 13 | 130 | 14/13, 41/38 | ^3D♯, ^3E♭ |
| 14 | 140 | 13/12 | ^4D♯, ^4E♭ |
| 15 | 150 | 12/11 | ^5D♯, v5E |
| 16 | 160 | 45/41 | v4D𝄪, v4E |
| 17 | 170 | 32/29, 43/39 | v3D𝄪, v3E |
| 18 | 180 | vvD𝄪, vvE | |
| 19 | 190 | 29/26, 48/43 | vD𝄪, vE |
| 20 | 200 | 37/33, 46/41 | E |
| 21 | 210 | 35/31, 44/39 | ^E, ^F♭ |
| 22 | 220 | 42/37 | ^^E, ^^F♭ |
| 23 | 230 | 8/7 | ^3E, ^3F♭ |
| 24 | 240 | 23/20 | ^4E, ^4F♭ |
| 25 | 250 | 37/32 | ^5E, v5F |
| 26 | 260 | 43/37 | v4E♯, v4F |
| 27 | 270 | v3E♯, v3F | |
| 28 | 280 | 47/40 | vvE♯, vvF |
| 29 | 290 | 13/11 | vE♯, vF |
| 30 | 300 | 44/37 | F |
| 31 | 310 | 49/41 | ^F, ^G♭♭ |
| 32 | 320 | ^^F, ^^G♭♭ | |
| 33 | 330 | 23/19 | ^3F, ^3G♭♭ |
| 34 | 340 | 28/23, 45/37 | ^4F, ^4G♭♭ |
| 35 | 350 | 49/40 | ^5F, v5G♭ |
| 36 | 360 | 16/13 | v4F♯, v4G♭ |
| 37 | 370 | 26/21 | v3F♯, v3G♭ |
| 38 | 380 | vvF♯, vvG♭ | |
| 39 | 390 | vF♯, vG♭ | |
| 40 | 400 | 29/23, 34/27 | F♯, G♭ |
| 41 | 410 | 19/15 | ^F♯, ^G♭ |
| 42 | 420 | 37/29 | ^^F♯, ^^G♭ |
| 43 | 430 | 41/32 | ^3F♯, ^3G♭ |
| 44 | 440 | 40/31, 49/38 | ^4F♯, ^4G♭ |
| 45 | 450 | 48/37 | ^5F♯, v5G |
| 46 | 460 | 30/23, 43/33 | v4F𝄪, v4G |
| 47 | 470 | 21/16 | v3F𝄪, v3G |
| 48 | 480 | 29/22 | vvF𝄪, vvG |
| 49 | 490 | vF𝄪, vG | |
| 50 | 500 | 4/3 | G |
| 51 | 510 | 43/32, 47/35 | ^G, ^A♭♭ |
| 52 | 520 | ^^G, ^^A♭♭ | |
| 53 | 530 | 19/14 | ^3G, ^3A♭♭ |
| 54 | 540 | 41/30 | ^4G, ^4A♭♭ |
| 55 | 550 | 11/8 | ^5G, v5A♭ |
| 56 | 560 | 29/21 | v4G♯, v4A♭ |
| 57 | 570 | 32/23 | v3G♯, v3A♭ |
| 58 | 580 | vvG♯, vvA♭ | |
| 59 | 590 | 45/32 | vG♯, vA♭ |
| 60 | 600 | 41/29 | G♯, A♭ |
| 61 | 610 | 37/26 | ^G♯, ^A♭ |
| 62 | 620 | ^^G♯, ^^A♭ | |
| 63 | 630 | 23/16 | ^3G♯, ^3A♭ |
| 64 | 640 | 42/29 | ^4G♯, ^4A♭ |
| 65 | 650 | 16/11 | ^5G♯, v5A |
| 66 | 660 | 41/28 | v4G𝄪, v4A |
| 67 | 670 | 28/19 | v3G𝄪, v3A |
| 68 | 680 | 43/29 | vvG𝄪, vvA |
| 69 | 690 | vG𝄪, vA | |
| 70 | 700 | 3/2 | A |
| 71 | 710 | ^A, ^B♭♭ | |
| 72 | 720 | 44/29, 47/31 | ^^A, ^^B♭♭ |
| 73 | 730 | 32/21 | ^3A, ^3B♭♭ |
| 74 | 740 | 23/15 | ^4A, ^4B♭♭ |
| 75 | 750 | 37/24 | ^5A, v5B♭ |
| 76 | 760 | 31/20, 45/29 | v4A♯, v4B♭ |
| 77 | 770 | v3A♯, v3B♭ | |
| 78 | 780 | vvA♯, vvB♭ | |
| 79 | 790 | 30/19, 41/26 | vA♯, vB♭ |
| 80 | 800 | 27/17, 46/29 | A♯, B♭ |
| 81 | 810 | ^A♯, ^B♭ | |
| 82 | 820 | 45/28 | ^^A♯, ^^B♭ |
| 83 | 830 | 21/13 | ^3A♯, ^3B♭ |
| 84 | 840 | 13/8 | ^4A♯, ^4B♭ |
| 85 | 850 | 49/30 | ^5A♯, v5B |
| 86 | 860 | 23/14 | v4A𝄪, v4B |
| 87 | 870 | 38/23, 43/26 | v3A𝄪, v3B |
| 88 | 880 | vvA𝄪, vvB | |
| 89 | 890 | vA𝄪, vB | |
| 90 | 900 | 37/22 | B |
| 91 | 910 | 22/13, 49/29 | ^B, ^C♭ |
| 92 | 920 | ^^B, ^^C♭ | |
| 93 | 930 | ^3B, ^3C♭ | |
| 94 | 940 | ^4B, ^4C♭ | |
| 95 | 950 | 45/26 | ^5B, v5C |
| 96 | 960 | 40/23 | v4B♯, v4C |
| 97 | 970 | 7/4 | v3B♯, v3C |
| 98 | 980 | 37/21 | vvB♯, vvC |
| 99 | 990 | 39/22 | vB♯, vC |
| 100 | 1000 | 41/23 | C |
| 101 | 1010 | 43/24 | ^C, ^D♭♭ |
| 102 | 1020 | ^^C, ^^D♭♭ | |
| 103 | 1030 | 29/16 | ^3C, ^3D♭♭ |
| 104 | 1040 | ^4C, ^4D♭♭ | |
| 105 | 1050 | 11/6 | ^5C, v5D♭ |
| 106 | 1060 | 24/13 | v4C♯, v4D♭ |
| 107 | 1070 | 13/7 | v3C♯, v3D♭ |
| 108 | 1080 | 28/15 | vvC♯, vvD♭ |
| 109 | 1090 | 15/8 | vC♯, vD♭ |
| 110 | 1100 | 17/9 | C♯, D♭ |
| 111 | 1110 | 19/10 | ^C♯, ^D♭ |
| 112 | 1120 | 21/11 | ^^C♯, ^^D♭ |
| 113 | 1130 | ^3C♯, ^3D♭ | |
| 114 | 1140 | 29/15 | ^4C♯, ^4D♭ |
| 115 | 1150 | 33/17 | ^5C♯, v5D |
| 116 | 1160 | 41/21, 43/22, 45/23 | v4C𝄪, v4D |
| 117 | 1170 | v3C𝄪, v3D | |
| 118 | 1180 | vvC𝄪, vvD | |
| 119 | 1190 | vC𝄪, vD | |
| 120 | 1200 | 2/1 | D |