Semitone: the smallest interval in Western tonal music

Physical and mathematical meaning

In the widely used system called 12-tone equal temperament the octave is divided into twelve equal parts. Each semitone therefore represents a constant frequency ratio of the twelfth root of two. In numeric terms that ratio is approximately 2^(1/12) ≈ 1.05946, so two notes a semitone apart differ in frequency by about 5.946%. Intervals are also measured in cents, a logarithmic unit: one equal-tempered semitone equals 100 cents and an octave equals 1200 cents.

Tuning systems and ratios

Although equal temperament is the most common tuning for modern Western instruments, other historical or theoretical systems treat the semitone differently. In just intonation a small-step interval can be approximated by simple integer ratios such as 16:15, while in Pythagorean tuning a semitone appears as the limma with ratio 256:243. These variants produce semitones of slightly different sizes, so enharmonically equivalent notes (for example C# and D flat) may not be identical outside equal temperament.

Notation, keyboard layout, and terminology

On a piano keyboard a semitone occurs between any adjacent keys. Where a black key lies between two whites (for example C and D) each white–black or black–white step is a semitone; where two white keys are adjacent (for example E and F or B and C) that white–white step is also a semitone. Musicians distinguish chromatic semitones (same letter, altered by a sharp or flat) from diatonic semitones (different letter names); the distinction matters in classical voice-leading and theoretical analysis.

Musical role and examples

Semitones are fundamental to melody and harmony in tonal music. The chromatic scale is formed by a sequence of twelve semitones and underlies modulation, chromaticism, and full chromatic harmony. Many expressive effects—such as the leading tone resolving to the tonic, or short, dissonant appoggiaturas—depend on semitone relationships. Instruments and singers use semitones when tuning, adjusting intonation, or ornamenting lines.

Related concepts and distinctions

• Whole tone: an interval of two semitones (e.g., C to D).
• Enharmonic equivalence: in equal temperament C# and Db are the same pitch; in other tunings they can differ.
• Microtones: many musical cultures use intervals smaller than a semitone; such divisions are outside the standard Western semitone framework.

For concise reference about language or regional terminology see British English usage and other English variants. Background on how semitones function in Western music contexts and the idea of adjacent pitch are useful for practical study. Visual learners often consult a piano keyboard diagram. The semitone's relation to the octave, to mathematical frequency ratios, and to raw frequency values (via the twelfth root of two) is central; see notes on equal temperament and the factor 2^(1/12) for technical detail.

Understanding the semitone clarifies how scales are built, why tuning matters, and how small pitch differences produce large musical effects.