How many semitones are in an octave?

Exactly 12. In Western 12-tone equal temperament (12-TET) the octave is divided into 12 equal semitones, each 100 cents wide. Two notes an octave apart have a 2:1 frequency ratio.

What is a cent in music?

A cent is 1/100th of a semitone — so one octave = 1,200 cents. Cents give a fine-grained way to describe tuning differences. The human ear can typically detect deviations of about 5-10 cents, and string or wind players regularly adjust by 10-20 cents when tuning to just intonation or historical temperaments.

What is the formula for equal-temperament frequency ratio?

For n semitones, the ratio is 2^(n/12). One semitone = 2^(1/12) ≈ 1.059463. A perfect fifth (7 semitones) = 2^(7/12) ≈ 1.498307. Compare that to the just-intonation pure fifth of 3:2 = 1.5 — a difference of about 1.96 cents.

What is just intonation and how does it differ from equal temperament?

Just intonation uses pure integer frequency ratios derived from the harmonic series (e.g., a perfect fifth is exactly 3:2 = 1.5). Equal temperament compromises by making all semitones identical, so every interval except the octave is slightly mistuned relative to the pure ratio. The biggest deviation is the major third (ET 400 cents vs just 386.31 cents — a 13.69-cent gap that is clearly audible). Orchestras and choirs often bend toward just intonation when playing sustained chords.

How do I calculate the frequency of any note?

The formula is f = A4_ref × 2^((MIDI − 69) / 12). The MIDI number of a note is (octave + 1) × 12 + pitch-class-index, where C = 0, C# = 1, D = 2 … B = 11. For example, middle C (C4) has MIDI 60, so f = 440 × 2^((60−69)/12) = 440 × 2^(−0.75) ≈ 261.63 Hz.

What is the tritone and why is it special?

The tritone is 6 semitones — exactly half an octave. Its equal-temperament ratio is 2^(1/2) ≈ 1.4142, and it divides the octave symmetrically. It sounds maximally ambiguous and tense, which is why medieval theorists called it 'diabolus in musica'. In jazz it is the defining dissonance of a dominant seventh chord, and tritone substitution is a core harmonic technique.

Semitone Interval Calculator

The semitone interval calculator tells you everything about the relationship between any two pitches: how many semitones and cents separate them, the equal-temperament frequency ratio, both note frequencies in Hz, the classical interval name (Perfect 5th, Major 3rd, Tritone, etc.), and exactly how far the equal-temperament tuning deviates from a pure just-intonation ratio.

How it works

Every note in Western 12-tone equal temperament (12-TET) is assigned a MIDI note number. The formula is straightforward:

MIDI = (octave + 1) × 12 + pitch-class-index

where C = 0, C# = 1, D = 2, D# = 3, E = 4, F = 5, F# = 6, G = 7, G# = 8, A = 9, A# = 10, B = 11. A4 (concert A) = MIDI 69.

The semitone distance is simply MIDI2 − MIDI1. Multiply by 100 to get cents. The equal-temperament frequency ratio for n semitones is:

ratio = 2^(n / 12)

And the frequency of any note is:

f = A4_ref × 2^((MIDI − 69) / 12)

The default A4 reference is 440 Hz (ISO 16), but you can enter 432 Hz (popular alternative tuning), 415 Hz (Baroque pitch), 443 Hz (some European orchestras), or anything else.

Worked example

C4 to G4 (Perfect 5th)

MIDI(C4) = (4 + 1) × 12 + 0 = 60
MIDI(G4) = (4 + 1) × 12 + 7 = 67
Semitones = 67 − 60 = 7
Cents = 7 × 100 = 700 ¢
ET ratio = 2^(7/12) = 1.498307
f(C4) = 440 × 2^((60−69)/12) = 261.63 Hz
f(G4) = 440 × 2^((67−69)/12) = 392.00 Hz
Just ratio: 3:2 = 1.5 (pure fifth)
ET vs just: 700 − 701.96 = −1.96 ¢ (ET is 1.96 cents flat of pure)

Understanding the ET vs Just deviation

The ‘ET vs Just intonation’ readout shows how many cents the equal-temperament version of the interval differs from the nearest pure harmonic ratio. Key figures:

Perfect 5th: −1.96 ¢ (barely noticeable)
Major 3rd: +13.69 ¢ (clearly audible — ET thirds sound noticeably wide)
Minor 3rd: −15.64 ¢ (also significant)
Perfect 4th: +1.96 ¢ (almost pure)
Tritone: +9.78 ¢ relative to 45:32

Differences below about 5 cents are generally imperceptible to untrained listeners; above 10 cents, they are audible even to casual listeners. Choir directors, string-quartet coaches, and early-music performers regularly ask players to adjust by these amounts when tuning sustained chords.

Interval quality and consonance

The calculator colour-codes intervals by consonance:

Green (perfect): unison, octave, perfect 4th, perfect 5th — the most stable, used as resolution points in harmony.
Blue (consonant): major/minor 3rds and 6ths — the building blocks of triads and rich chords.
Amber (dissonant): major/minor 2nds and 7ths, tritone — create tension that resolves to consonances.

This classification derives from Western common-practice harmony; in jazz and contemporary music, dissonances are often left unresolved deliberately.