Quarter Tone - Interval Size in Equal Temperament

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)

    “To believe her limited in range because she was harmonious in method is as sensible as to imagine that when the Atlantic Ocean is as smooth as a mill-pond it shrinks to the size of a mill-pond.”
    —Rebecca West (1892–1983)

    “A great many will find fault in the resolution that the negro shall be free and equal, because our equal not every human being can be; but free every human being has a right to be. He can only be equal in his rights.”
    —Mrs. Chalkstone, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 2, ch. 16, by Elizabeth Cady Stanton, Susan B. Anthony, and Matilda Joslyn Gage (1882)

    “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 (1803–1882)