Interval Size
Here are the sizes of some common intervals (shaded rows mark relatively poor matches):
| interval name | size (steps) | size (cents) | midi | just ratio | just (cents) | midi | error |
| perfect fifth | 24 | 702.44 | Play | 3:2 | 701.96 | Play | +0.48 |
| septimal tritone | 20 | 585.37 | Play | 7:5 | 582.51 | Play | +2.85 |
| 11:8 wide fourth | 19 | 556.10 | Play | 11:8 | 551.32 | Play | +4.78 |
| 15:11 wide fourth | 18 | 526.83 | Play | 15:11 | 536.95 | −10.12 | |
| 27:20 wide fourth | 18 | 526.83 | Play | 27:20 | 519.55 | +7.28 | |
| perfect fourth | 17 | 497.56 | Play | 4:3 | 498.04 | Play | −0.48 |
| septimal narrow fourth | 16 | 468.29 | Play | 21:16 | 470.78 | −2.48 | |
| septimal major third | 15 | 439.02 | Play | 9:7 | 435.08 | Play | +3.94 |
| undecimal major third | 14 | 409.76 | Play | 14:11 | 417.51 | Play | −7.75 |
| major third | 13 | 380.49 | Play | 5:4 | 386.31 | Play | −5.83 |
| inverted 13th harmonic | 12 | 351.22 | Play | 16:13 | 359.47 | Play | −8.25 |
| undecimal neutral third | 12 | 351.22 | Play | 11:9 | 347.41 | Play | +3.81 |
| minor third | 11 | 321.95 | Play | 6:5 | 315.64 | Play | +6.31 |
| tridecimal minor third | 10 | 292.68 | Play | 13:11 | 289.21 | Play | +3.47 |
| septimal minor third | 9 | 263.41 | Play | 7:6 | 266.87 | Play | −3.46 |
| septimal whole tone | 8 | 234.15 | Play | 8:7 | 231.17 | Play | +2.97 |
| whole tone, major tone | 7 | 204.88 | Play | 9:8 | 203.91 | Play | +0.97 |
| whole tone, minor tone | 6 | 175.61 | Play | 10:9 | 182.40 | Play | −6.79 |
| lesser undecimal neutral second | 5 | 146.34 | Play | 12:11 | 150.64 | Play | −4.30 |
| septimal diatonic semitone | 4 | 117.07 | Play | 15:14 | 119.44 | Play | −2.37 |
| diatonic semitone | 4 | 117.07 | Play | 16:15 | 111.73 | +5.34 | |
| septimal chromatic semitone | 3 | 87.80 | Play | 21:20 | 84.47 | Play | +3.34 |
| chromatic semitone | 2 | 58.54 | 25:24 | 70.67 | −12.14 | ||
| 28:27 semitone | 2 | 58.54 | 28:27 | 62.96 | −4.42 | ||
| septimal comma | 1 | 29.27 | Play | 64:63 | 27.26 | Play | +2.00 |
As the table above shows, the 41-ET both distinguishes between and closely matches all intervals involving the ratios in the harmonic series up to and including the 10th overtone. This includes the distinction between the major tone and minor tone (thus 41-ET is not a meantone tuning). These close fits make 41-ET a good approximation for 5-, 7- and 9-limit music.
41-ET also closely matches a number of other intervals involving higher harmonics. It distinguishes between and closely matches all intervals involving up through the 12th overtones, with the exception of the greater undecimal neutral second (11:10).
Read more about this topic: 41 Equal Temperament
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