Consonance

A numerical ratio, not a matter of taste

Two notes sound the more fused together, the simpler the ratio of their frequencies. The octave has the ratio 2:1, the fifth 3:2, the fourth 4:3, the major third 5:4. The larger the numbers become, the less often the vibrations coincide, and the rougher the combined sound. That is not only convention and habit: at 3:2 the common pattern of the two waves repeats after every two and three vibrations respectively, a very short common period that the ear perceives as one sound. With the tritone there is no common period at all in equal temperament, which is why it stays floating and undecided.

Consonant and dissonant

In harmony some combinations of notes sounded together seem calm and coherent (consonant), others full of friction and demanding continuation (dissonant). Neither is “better”: music lives on the alternation, dissonance creates tension, consonance releases it. The fifth shows a paradox: after the octave it is the most consonant interval, and for that very reason it sounds empty. The classification can also change: in the Middle Ages the major third was at first treated as a dissonance, only gradually counted as an imperfect consonance, and in the Renaissance became firmly part of the musical texture. The fourth counts in classical counterpoint as a dissonance between bass and upper voice, although it sounds consonant between other voices.

Common mistakes

• Equating consonance with “beautiful”: Music lives on the alternation of consonance and dissonance.
• Taking the fifth for major: It is a consonance without a third and thus without colouring.
• Expecting purity on the piano: In equal temperament every fifth and third deviates a little.