What makes an interval consonant?

Consonant intervals tend to have simple frequency ratios whose partials beat little against one another, but the category is also shaped by stylistic convention that has shifted over centuries.

Why does inverting an interval change its name?

Inverting moves the lower note up an octave, so a third becomes a sixth, a fifth becomes a fourth, and so on; the qualities also flip (major to minor, perfect staying perfect).

Intervals and Consonance

How the distance between two pitches is measured and why some combinations sound stable and others unstable.

Definition

An interval is the pitch distance between two notes; consonance and dissonance are the perceived qualities of relative stability or instability that different intervals carry.

Scope

Covers the measurement of intervals by size and quality, simple versus compound intervals, interval inversion, and the categorization of intervals as consonant or dissonant — including the acoustic and perceptual bases of consonance and the historically shifting boundary between the two. Excludes the syntactic treatment of dissonance in voice leading, treated under counterpoint.

Core questions

How are intervals classified by size and quality?
What happens to an interval when it is inverted?
Why do certain intervals sound consonant and others dissonant?
What is the acoustic basis of consonance in the harmonic series and beating?
How has the consonance-dissonance boundary changed across music history?

Key theories

Acoustic theory of consonance: Helmholtz proposed that the relative roughness of an interval depends on beating between the upper partials of its tones, giving a physiological basis for the long-standing intuition that simple frequency ratios sound more consonant — though later work stresses that consonance is also culturally conditioned.

History

From the Pythagorean identification of consonance with simple string-length ratios, through the Renaissance acceptance of thirds and sixths as consonances, to Helmholtz's nineteenth-century physiological account, the explanation of consonance has moved between mathematics, acoustics, and perception.

Debates

Is consonance acoustic or cultural?: Helmholtz's beating account roots consonance in the physics of the ear, but the historical migration of the third and seventh across the consonance-dissonance line, and cross-cultural variation, suggest that learned convention also shapes the judgment.

Key figures

Hermann von Helmholtz
Pythagoras
Gioseffo Zarlino

Seminal works

helmholtz1885
clendinning2021

Frequently asked questions

What makes an interval consonant?: Consonant intervals tend to have simple frequency ratios whose partials beat little against one another, but the category is also shaped by stylistic convention that has shifted over centuries.
Why does inverting an interval change its name?: Inverting moves the lower note up an octave, so a third becomes a sixth, a fifth becomes a fourth, and so on; the qualities also flip (major to minor, perfect staying perfect).