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
Famous quotes containing the words interval and/or size:
“[I have] been in love with one princess or another almost all my life, and I hope I shall go on so, till I die, being firmly persuaded, that if ever I do a mean action, it must be in some interval betwixt one passion and another.”
—Laurence Sterne (1713–1768)
“Delusions that shrink to the size of a woman’s glove,
Then sicken inclusively outwards:
. . . the incessant recital
Intoned by reality, larded with technical terms,
Each one double-yolked with meaning and meaning’s rebuttal:
For the skirl of that bulletin unpicks the world like a knot....”
—Philip Larkin (1922–1986)