74edo: Difference between revisions
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CompactStar (talk | contribs) Adding interval list auto-generated by a program I wrote |
m Added to category "historical" |
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[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Historical]] | |||
Revision as of 01:14, 27 April 2023
| ← 73edo | 74edo | 75edo → |
74edo divides the octave into 74 equal parts of size 16.216 cents each. It is most notable as a meantone tuning, tempering out 81/80 in the 5-limit; 81/80 and 126/125 (and hence 225/224) in the 7-limit; 99/98, 176/175 and 441/440 in the 11-limit; and 144/143 and 847/845 in the 13-limit. Discarding 847/845 from that gives 13-limit meantone, aka 13-limit huygens, for which 74edo gives the optimal patent val; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone. Script error: No such module "primes_in_edo".
74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
Intervals
| # | Cents | Diatonic interval category |
|---|---|---|
| 0 | 0.0 | perfect unison |
| 1 | 16.2 | superunison |
| 2 | 32.4 | superunison |
| 3 | 48.6 | subminor second |
| 4 | 64.9 | subminor second |
| 5 | 81.1 | minor second |
| 6 | 97.3 | minor second |
| 7 | 113.5 | minor second |
| 8 | 129.7 | supraminor second |
| 9 | 145.9 | neutral second |
| 10 | 162.2 | submajor second |
| 11 | 178.4 | submajor second |
| 12 | 194.6 | major second |
| 13 | 210.8 | major second |
| 14 | 227.0 | supermajor second |
| 15 | 243.2 | ultramajor second |
| 16 | 259.5 | ultramajor second |
| 17 | 275.7 | subminor third |
| 18 | 291.9 | minor third |
| 19 | 308.1 | minor third |
| 20 | 324.3 | supraminor third |
| 21 | 340.5 | neutral third |
| 22 | 356.8 | neutral third |
| 23 | 373.0 | submajor third |
| 24 | 389.2 | major third |
| 25 | 405.4 | major third |
| 26 | 421.6 | supermajor third |
| 27 | 437.8 | supermajor third |
| 28 | 454.1 | ultramajor third |
| 29 | 470.3 | subfourth |
| 30 | 486.5 | perfect fourth |
| 31 | 502.7 | perfect fourth |
| 32 | 518.9 | perfect fourth |
| 33 | 535.1 | superfourth |
| 34 | 551.4 | superfourth |
| 35 | 567.6 | low tritone |
| 36 | 583.8 | low tritone |
| 37 | 600.0 | high tritone |
| 38 | 616.2 | high tritone |
| 39 | 632.4 | high tritone |
| 40 | 648.6 | subfifth |
| 41 | 664.9 | subfifth |
| 42 | 681.1 | perfect fifth |
| 43 | 697.3 | perfect fifth |
| 44 | 713.5 | perfect fifth |
| 45 | 729.7 | superfifth |
| 46 | 745.9 | ultrafifth |
| 47 | 762.2 | subminor sixth |
| 48 | 778.4 | subminor sixth |
| 49 | 794.6 | minor sixth |
| 50 | 810.8 | minor sixth |
| 51 | 827.0 | supraminor sixth |
| 52 | 843.2 | neutral sixth |
| 53 | 859.5 | neutral sixth |
| 54 | 875.7 | submajor sixth |
| 55 | 891.9 | major sixth |
| 56 | 908.1 | major sixth |
| 57 | 924.3 | supermajor sixth |
| 58 | 940.5 | ultramajor sixth |
| 59 | 956.8 | ultramajor sixth |
| 60 | 973.0 | subminor seventh |
| 61 | 989.2 | minor seventh |
| 62 | 1005.4 | minor seventh |
| 63 | 1021.6 | supraminor seventh |
| 64 | 1037.8 | supraminor seventh |
| 65 | 1054.1 | neutral seventh |
| 66 | 1070.3 | submajor seventh |
| 67 | 1086.5 | major seventh |
| 68 | 1102.7 | major seventh |
| 69 | 1118.9 | major seventh |
| 70 | 1135.1 | supermajor seventh |
| 71 | 1151.4 | ultramajor seventh |
| 72 | 1167.6 | suboctave |
| 73 | 1183.8 | suboctave |
| 74 | 1200.0 | perfect octave |