Music Theory/Consonance and Dissonance

Consonance and dissonance are subjective qualities of relationship that we assign to music intervals. A quick review of intervals might be helpful if you're approaching the subject for the first time. A dissonant interval can be described as being "unstable" or demanding treatment by resolving to a consonant interval. A consonant interval is one that is stable and does not demand treatment. However, dissonance in itself is not an undesirable thing; we use dissonance to provide the "spice" to music. Thus, there is a hierarchy of consonant and dissonant intervals. (Chords having dissonant intervals are themselves considered dissonant).

Note that this distinction depends entirely on musical context. As such, a sonority which is consonant in one context where it does not seem to demand resolution (say, major 2nds in a Debussy prelude) may sound harsh or out-of-place in a different context where it must be resolved (the same major 2nds in a Bach fugue). In this article, we will be using the terms "consonant" and "dissonant" as they are understood in common-practice tonal music, as is the tacit convention when speaking of consonance and dissonance in general.

Consonant intervals in tonal music

The perfect fifth and the perfect octave are considered perfect consonances. The unison is a consonance insofar as it can be considered an interval at all (many say it cannot).
The major third and sixth, as well as the minor third, sixth, are considered to be imperfect consonances.
The perfect fourth is dissonant in some contexts but consonant in others (see below). Specifically, the perfect fourth is dissonant when it is formed with the bass note of any sonority.

Dissonant intervals

The perfect fourth is considered dissonant in common practice music when not supported by a lower third or fifth (but see below).
Major and minor seconds, sevenths, and ninths are dissonant. Composer/theorist Vincent Persichetti, in his book Twentieth-Century Harmony, classifies major 2nds, minor 7ths, and major 9ths as "soft dissonances," whereas minor 2nds, major 7ths, and minor 9ths are "sharp dissonances."
The tritone (an augmented fourth or diminished fifth) is dissonant. In the Middle Ages and Renaissance, it was known as diabolus in musica because the perfect fifth was considered to be a reflection of the divine, and the tritone falls just short of a perfect fifth. [Note for the advanced: Technically, it is not proper to refer to the diminished fifth as a "tritone." The word "tritone" refers to "three whole-tones," the distance represented by the tritone. This means that the augmented fourth, which comprises three whole-tones, is a true tritone, while the diminished fifth, because of its accidental-spelling, is not made up of three whole-tones and is therefore not a tritone. However, it is acceptable as an informal convention to refer to the diminished fifth as a "tritone."]
In Jazz, the minor 9th is often considered too dissonant for practical use. This is the basis for some notes being called "avoid notes", typically the 4th of a major scale - it sounds dissonant because it forms a minor 9th with the 3rd. Other "avoid notes" are the minor 6th in aeolian mode, or the minor 2nd in phrygian mode. Some chords are typically voiced to avoid a minor 9th (musicians invert the interval and play a major 7th instead). For example, in a Cadd11 chord (see Complete List of Chord Patterns), there is a minor ninth between the third, E and the eleventh F. If the F is played below the E, the interval becomes a major seventh, which is less dissonant.

The perfect fourth

The perfect fourth is the inversion of the perfect fifth. In common practice music, it can be both consonant and dissonant: in this case, it has a need for resolution when unsupported by lower notes, in which case it is dissonant even though it sounds as "good" as the fifth. The fourth is always consonant when supported by a lower third or perfect fifth, for example, E-G-C-E is consonant, but G-C-E is dissonant. In more contemporary music, many consider the fourth to always be as consonant as the fifth.

The perfect fourth is often considered a perfect consonance, as the perfect fifth and the octave.