lecture16 - Consonance and Dissonance Consonance - sounds...

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Consonance and Dissonance Consonance - sounds that are pleasant Consonant intervals in descending order of consonance: λ f i f f : f i example # of half steps 1:1 1:1 unison (C,C) 0 1:2 2:1 octave (C,C) 12 2:3 3:2 perfect fifth (C,G) or (F,C) 7 3:4 4:3 perfect fourth (C,F) or (G,C) 5 3:5 5:3 major six (C,A) or (Eb,C) 9 4:5 5:4 major third (C,E) or (Ab,C) 4 5:8 8:5 minor six (C,Ab) or (E,C) 8 5:6 6:5 minor third (C,Eb) or (A,C) 3
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Octave (C/C) 1 1:2 Perfect fifth (C:G) 2:3 1 Perfect fourth (C:F ) 1 3:4 λ / v f = 2 : 3 : 3 : 2 : = = C G C G f f 3 : 4 : 4 : 3 : = = C F C F f f 1 : 2 : 2 : 1 : ' ' = = C C C C f f 2 3 4 2 3 = = C F C G f f f f
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Helmholtz Theory (1877) Dissonance occurs when partials of the two tones produce 30-40 beats per second The more partials of a tone coincide with the partials of another, the less chance that beats in the range will produce roughness This explains why simply frequency windows define most of the consonant intervals
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lecture16 - Consonance and Dissonance Consonance - sounds...

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