34 Equal Temperament - Interval Size

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

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