98edo: Difference between revisions
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{{EDO intro|98}} | {{EDO intro|98}} | ||
The [[patent val]] has a flat 3, a sharp 5 and a slightly flat 7, and tempers out 81/80 in the 5-limit, making it a system of [[meantone family]] with a 4-cent-flat fifth. In the 7-limit it tempers out 1029/1024, 1728/1715, | == Theory == | ||
The [[patent val]] of 98edo has a flat [[3/1|3]], a sharp [[5/1|5]] and a slightly flat [[7/1|7]], and [[tempering out|tempers out]] [[81/80]] in the 5-limit, making it a system of [[meantone family]] with a 4-cent-flat fifth. In the 7-limit it tempers out [[1029/1024]], [[1728/1715]], [[support]]ing [[mothra]] temperament, in the 11-limit [[176/175]] and [[540/539]], supporting [[mosura]], and in the 13-limit [[144/143]] and [[196/195]]. It provides the optimal patent val for 13-limit mosura temperament. | |||
== | === Odd harmonics === | ||
{{Harmonics in equal|98}} | {{Harmonics in equal|98}} | ||
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* [https://www.youtube.com/watch?v=pR4li7aIUZE ''microtonal improvisation in 98edo''] (2023) | * [https://www.youtube.com/watch?v=pR4li7aIUZE ''microtonal improvisation in 98edo''] (2023) | ||
[[Category: | [[Category:Mothra]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 11:52, 11 June 2024
| ← 97edo | 98edo | 99edo → |
Theory
The patent val of 98edo has a flat 3, a sharp 5 and a slightly flat 7, and tempers out 81/80 in the 5-limit, making it a system of meantone family with a 4-cent-flat fifth. In the 7-limit it tempers out 1029/1024, 1728/1715, supporting mothra temperament, in the 11-limit 176/175 and 540/539, supporting mosura, and in the 13-limit 144/143 and 196/195. It provides the optimal patent val for 13-limit mosura temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.00 | +5.52 | -1.48 | +4.25 | -0.30 | +4.37 | +1.53 | +5.25 | -3.64 | -5.47 | -3.78 |
| Relative (%) | -32.6 | +45.1 | -12.1 | +34.7 | -2.4 | +35.7 | +12.5 | +42.9 | -29.7 | -44.7 | -30.9 | |
| Steps (reduced) |
155 (57) |
228 (32) |
275 (79) |
311 (17) |
339 (45) |
363 (69) |
383 (89) |
401 (9) |
416 (24) |
430 (38) |
443 (51) | |
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 12.2 | ^D, vE♭♭ | |
| 2 | 24.5 | ^^D, E♭♭ | |
| 3 | 36.7 | ^3D, ^E♭♭ | |
| 4 | 49 | 35/34 | v3D♯, ^^E♭♭ |
| 5 | 61.2 | 29/28, 30/29 | vvD♯, ^3E♭♭ |
| 6 | 73.5 | 24/23 | vD♯, v3E♭ |
| 7 | 85.7 | 41/39 | D♯, vvE♭ |
| 8 | 98 | 37/35 | ^D♯, vE♭ |
| 9 | 110.2 | 16/15 | ^^D♯, E♭ |
| 10 | 122.4 | 44/41 | ^3D♯, ^E♭ |
| 11 | 134.7 | 40/37 | v3D𝄪, ^^E♭ |
| 12 | 146.9 | 37/34 | vvD𝄪, ^3E♭ |
| 13 | 159.2 | 23/21, 34/31 | vD𝄪, v3E |
| 14 | 171.4 | 21/19, 32/29, 43/39 | D𝄪, vvE |
| 15 | 183.7 | ^D𝄪, vE | |
| 16 | 195.9 | E | |
| 17 | 208.2 | 35/31, 44/39 | ^E, vF♭ |
| 18 | 220.4 | ^^E, F♭ | |
| 19 | 232.7 | 8/7 | ^3E, ^F♭ |
| 20 | 244.9 | 38/33 | v3E♯, ^^F♭ |
| 21 | 257.1 | vvE♯, ^3F♭ | |
| 22 | 269.4 | 7/6 | vE♯, v3F |
| 23 | 281.6 | 20/17 | E♯, vvF |
| 24 | 293.9 | ^E♯, vF | |
| 25 | 306.1 | 31/26, 37/31 | F |
| 26 | 318.4 | ^F, vG♭♭ | |
| 27 | 330.6 | 23/19 | ^^F, G♭♭ |
| 28 | 342.9 | 28/23, 39/32 | ^3F, ^G♭♭ |
| 29 | 355.1 | 43/35 | v3F♯, ^^G♭♭ |
| 30 | 367.3 | vvF♯, ^3G♭♭ | |
| 31 | 379.6 | vF♯, v3G♭ | |
| 32 | 391.8 | F♯, vvG♭ | |
| 33 | 404.1 | 24/19, 43/34 | ^F♯, vG♭ |
| 34 | 416.3 | 14/11 | ^^F♯, G♭ |
| 35 | 428.6 | 41/32 | ^3F♯, ^G♭ |
| 36 | 440.8 | 40/31 | v3F𝄪, ^^G♭ |
| 37 | 453.1 | 13/10 | vvF𝄪, ^3G♭ |
| 38 | 465.3 | 17/13 | vF𝄪, v3G |
| 39 | 477.6 | 29/22 | F𝄪, vvG |
| 40 | 489.8 | ^F𝄪, vG | |
| 41 | 502 | G | |
| 42 | 514.3 | 35/26, 39/29 | ^G, vA♭♭ |
| 43 | 526.5 | 19/14 | ^^G, A♭♭ |
| 44 | 538.8 | 15/11, 41/30 | ^3G, ^A♭♭ |
| 45 | 551 | 11/8 | v3G♯, ^^A♭♭ |
| 46 | 563.3 | vvG♯, ^3A♭♭ | |
| 47 | 575.5 | 39/28 | vG♯, v3A♭ |
| 48 | 587.8 | G♯, vvA♭ | |
| 49 | 600 | 41/29 | ^G♯, vA♭ |
| 50 | 612.2 | 37/26 | ^^G♯, A♭ |
| 51 | 624.5 | 33/23, 43/30 | ^3G♯, ^A♭ |
| 52 | 636.7 | v3G𝄪, ^^A♭ | |
| 53 | 649 | 16/11 | vvG𝄪, ^3A♭ |
| 54 | 661.2 | 22/15, 41/28 | vG𝄪, v3A |
| 55 | 673.5 | 28/19 | G𝄪, vvA |
| 56 | 685.7 | ^G𝄪, vA | |
| 57 | 698 | A | |
| 58 | 710.2 | ^A, vB♭♭ | |
| 59 | 722.4 | 44/29 | ^^A, B♭♭ |
| 60 | 734.7 | 26/17 | ^3A, ^B♭♭ |
| 61 | 746.9 | 20/13 | v3A♯, ^^B♭♭ |
| 62 | 759.2 | 31/20 | vvA♯, ^3B♭♭ |
| 63 | 771.4 | vA♯, v3B♭ | |
| 64 | 783.7 | 11/7 | A♯, vvB♭ |
| 65 | 795.9 | 19/12 | ^A♯, vB♭ |
| 66 | 808.2 | ^^A♯, B♭ | |
| 67 | 820.4 | ^3A♯, ^B♭ | |
| 68 | 832.7 | v3A𝄪, ^^B♭ | |
| 69 | 844.9 | vvA𝄪, ^3B♭ | |
| 70 | 857.1 | 23/14 | vA𝄪, v3B |
| 71 | 869.4 | 38/23, 43/26 | A𝄪, vvB |
| 72 | 881.6 | ^A𝄪, vB | |
| 73 | 893.9 | B | |
| 74 | 906.1 | ^B, vC♭ | |
| 75 | 918.4 | 17/10 | ^^B, C♭ |
| 76 | 930.6 | 12/7 | ^3B, ^C♭ |
| 77 | 942.9 | v3B♯, ^^C♭ | |
| 78 | 955.1 | 33/19 | vvB♯, ^3C♭ |
| 79 | 967.3 | 7/4 | vB♯, v3C |
| 80 | 979.6 | B♯, vvC | |
| 81 | 991.8 | 39/22 | ^B♯, vC |
| 82 | 1004.1 | C | |
| 83 | 1016.3 | ^C, vD♭♭ | |
| 84 | 1028.6 | 29/16, 38/21 | ^^C, D♭♭ |
| 85 | 1040.8 | 31/17, 42/23 | ^3C, ^D♭♭ |
| 86 | 1053.1 | v3C♯, ^^D♭♭ | |
| 87 | 1065.3 | 37/20 | vvC♯, ^3D♭♭ |
| 88 | 1077.6 | 41/22 | vC♯, v3D♭ |
| 89 | 1089.8 | 15/8 | C♯, vvD♭ |
| 90 | 1102 | ^C♯, vD♭ | |
| 91 | 1114.3 | ^^C♯, D♭ | |
| 92 | 1126.5 | 23/12 | ^3C♯, ^D♭ |
| 93 | 1138.8 | 29/15 | v3C𝄪, ^^D♭ |
| 94 | 1151 | vvC𝄪, ^3D♭ | |
| 95 | 1163.3 | vC𝄪, v3D | |
| 96 | 1175.5 | C𝄪, vvD | |
| 97 | 1187.8 | ^C𝄪, vD | |
| 98 | 1200 | 2/1 | D |