Interval Size
The following table outlines some of the intervals of this tuning system and their match to various ratios in the harmonic series.
| interval name | size (steps) | size (cents) | just ratio | just (cents) | error |
| perfect fifth | 20 | 705.88 | 3:2 | 701.95 | +3.93 |
| septendecimal tritone | 11 | 600 | 17:12 | 603.00 | −3.00 |
| lesser septimal tritone | 17 | 600 | 7:5 | 582.51 | +17.49 |
| tridecimal narrow tritone | 17 | 564.71 | 18:13 | 563.38 | +1.32 |
| 11:8 wide fourth | 16 | 564.71 | 11:8 | 551.32 | +13.39 |
| undecimal wide fourth | 15 | 529.41 | 15:11 | 536.95 | −7.54 |
| perfect fourth | 14 | 494.12 | 4:3 | 498.04 | −3.93 |
| tridecimal major third | 12 | 458.82 | 13:10 | 454.21 | +4.61 |
| septimal major third | 12 | 423.53 | 9:7 | 435.08 | −11.55 |
| undecimal major third | 12 | 423.53 | 14:11 | 417.51 | +6.02 |
| major third | 11 | 388.24 | 5:4 | 386.31 | +1.92 |
| tridecimal neutral third | 10 | 352.94 | 16:13 | 359.47 | −6.53 |
| undecimal neutral third | 10 | 352.94 | 11:9 | 347.41 | +5.53 |
| minor third | 9 | 317.65 | 6:5 | 315.64 | +2.01 |
| tridecimal minor third | 8 | 282.35 | 13:11 | 289.21 | −6.86 |
| septimal minor third | 8 | 282.35 | 7:6 | 266.87 | +15.48 |
| tridecimal semimajor second | 7 | 247.06 | 15:13 | 247.74 | −0.68 |
| septimal whole tone | 7 | 247.06 | 8:7 | 231.17 | +15.88 |
| whole tone, major tone | 6 | 211.76 | 9:8 | 203.91 | +7.85 |
| whole tone, minor tone | 5 | 176.47 | 10:9 | 182.40 | −5.93 |
| neutral second, greater undecimal | 5 | 176.47 | 11:10 | 165.00 | +11.47 |
| neutral second, lesser undecimal | 4 | 141.18 | 12:11 | 150.64 | −9.46 |
| greater tridecimal 2/3-tone | 2 | 141.18 | 13:12 | 138.57 | +2.60 |
| lesser tridecimal 2/3-tone | 2 | 141.18 | 14:13 | 128.30 | +12.88 |
| 15:14 semitone | 3 | 105.88 | 15:14 | 119.44 | −13.56 |
| diatonic semitone | 3 | 105.88 | 16:15 | 111.73 | −5.85 |
| 17th harmonic | 3 | 105.88 | 17:16 | 104.96 | +0.93 |
| 21:20 semitone | 2 | 70.59 | 21:20 | 84.47 | −13.88 |
| chromatic semitone | 2 | 70.59 | 25:24 | 70.67 | −0.08 |
| 28:27 semitone | 2 | 70.59 | 28:27 | 62.96 | +7.63 |
| septimal sixth-tone | 1 | 35.29 | 50:49 | 34.98 | +0.31 |
Read more about this topic: 34 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)
“One writes of scars healed, a loose parallel to the pathology of the skin, but there is no such thing in the life of an individual. There are open wounds, shrunk sometimes to the size of a pin-prick but wounds still. The marks of suffering are more comparable to the loss of a finger, or the sight of an eye. We may not miss them, either, for one minute in a year, but if we should there is nothing to be done about it.”
—F. Scott Fitzgerald (1896–1940)