Interval Size in Equal Temperament
Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed by Alois Hába (neutral third, etc.) and Ivan Wyschnegradsky (major fourth, etc.):
interval name | size (steps) | size (cents) | midi | just ratio | just (cents) | midi | error |
---|---|---|---|---|---|---|---|
octave | 24 | 1200 | play | 2:1 | 1200.00 | play | 0.00 |
semidiminished octave | 23 | 1150 | play | 2:1 | 1200.00 | play | −50.00 |
supermajor seventh | 23 | 1150 | play | 35:18 | 1151.23 | −1.23 | |
major seventh | 22 | 1100 | play | 15:8 | 1088.27 | play | +11.73 |
neutral seventh | 21 | 1050 | play | 11:6 | 1049.36 | play | +0.64 |
minor seventh | 20 | 1000 | play | 16:9 | 996.09 | play | +3.91 |
supermajor sixth/subminor seventh | 19 | 950 | play | 7:4 | 968.83 | play | −18.83 |
major sixth | 18 | 900 | play | 5:3 | 884.36 | play | +15.64 |
neutral sixth | 17 | 850 | play | 18:11 | 852.59 | play | −2.59 |
minor sixth | 16 | 800 | play | 8:5 | 813.69 | play | −13.69 |
subminor sixth | 15 | 750 | play | 14:9 | 764.92 | play | −14.92 |
perfect fifth | 14 | 700 | play | 3:2 | 701.95 | play | −1.95 |
minor fifth | 13 | 650 | play | 16:11 | 648.68 | play | +1.32 |
lesser septimal tritone | 12 | 600 | play | 7:5 | 582.51 | play | +17.49 |
major fourth | 11 | 550 | play | 11:8 | 551.32 | play | −1.32 |
perfect fourth | 10 | 500 | play | 4:3 | 498.05 | play | +1.95 |
tridecimal major third | 9 | 450 | play | 13:10 | 454.21 | play | −4.21 |
septimal major third | 9 | 450 | play | 9:7 | 435.08 | play | +14.92 |
major third | 8 | 400 | play | 5:4 | 386.31 | play | +13.69 |
undecimal neutral third | 7 | 350 | play | 11:9 | 347.41 | play | +2.59 |
minor third | 6 | 300 | play | 6:5 | 315.64 | play | −15.64 |
septimal minor third | 5 | 250 | play | 7:6 | 266.88 | play | −16.88 |
tridecimal minor third | 5 | 250 | play | 15:13 | 247.74 | play | +2.26 |
septimal whole tone | 5 | 250 | play | 8:7 | 231.17 | play | +18.83 |
whole tone, major tone | 4 | 200 | play | 9:8 | 203.91 | play | −3.91 |
whole tone, minor tone | 4 | 200 | 10:9 | 182.40 | +17.60 | ||
neutral second, greater undecimal | 3 | 150 | play | 11:10 | 165.00 | play | −15.00 |
neutral second, lesser undecimal | 3 | 150 | play | 12:11 | 150.64 | play | −0.64 |
15:14 semitone | 2 | 100 | play | 15:14 | 119.44 | −19.44 | |
diatonic semitone, just | 2 | 100 | play | 16:15 | 111.73 | play | −11.73 |
21:20 semitone | 2 | 100 | play | 21:20 | 84.47 | play | +15.53 |
28:27 semitone | 1 | 50 | play | 28:27 | 62.96 | play | −12.96 |
septimal quarter tone | 1 | 50 | play | 36:35 | 48.77 | play | +1.23 |
Moving from 12-TET to 24-TET allows the better approximation of a number of intervals. Intervals matched particularly closely include the neutral second, neutral third, and (11:8) ratio, or the 11th harmonic. The septimal minor third and septimal major third are approximated rather poorly; the (13:10) and (15:13) ratios, involving the 13th harmonic, are matched very closely. Overall, 24-TET can be viewed as matching the 11th harmonic more closely than the 7th.
Read more about this topic: Quarter Tone
Famous quotes containing the words interval, size, equal and/or temperament:
“The yearning for an afterlife is the opposite of selfish: it is love and praise for the world that we are privileged, in this complex interval of light, to witness and experience.”
—John Updike (b. 1932)
“Delusions that shrink to the size of a womans glove,
Then sicken inclusively outwards:
. . . the incessant recital
Intoned by reality, larded with technical terms,
Each one double-yolked with meaning and meanings rebuttal:
For the skirl of that bulletin unpicks the world like a knot....”
—Philip Larkin (19221986)
“Both equal hurt, in this change sought our bliss:
My true love hath my heart and I have his.”
—Sir Philip Sidney (15541586)
“Although this garrulity of advising is born with us, I confess that life is rather a subject of wonder, than of didactics. So much fate, so much irresistible dictation from temperament and unknown inspiration enter into it, that we doubt we can say anything out of our own experience whereby to help each other.”
—Ralph Waldo Emerson (18031882)