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)
“Learn to shrink yourself to the size of the company you are in. Take their tone, whatever it may be, and excell in it if you can; but never pretend to give the tone. A free conversation will no more bear a dictator than a free government will.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)