Music Interval Converter

Music intervals describe the distance between two pitches. They can be expressed as semitones, cents, or frequency ratios.

Core conversion formulas:

• Cents from semitones: cents = semitones x 100
• Frequency ratio from semitones: ratio = 2^(semitones / 12)
• Semitones from frequency ratio: semitones = 12 x log2(ratio)
• Cents from frequency ratio: cents = 1200 x log2(ratio)

What each unit means:

• Semitone: The smallest interval in standard Western music (e.g., C to C#). One fret on a guitar, one key on a piano (including black keys).
• Cent: One hundredth of a semitone. There are 1,200 cents in an octave. Cents are used for fine tuning comparisons and measuring how far a note is from a standard pitch.
• Frequency ratio: The mathematical ratio between two frequencies. An octave is 2:1, a perfect fifth is approximately 3:2.

Standard equal temperament intervals:

Just intonation vs equal temperament: In equal temperament (used on pianos), each semitone has the exact ratio of 2^(1/12) = 1.05946. In just intonation, intervals use simple ratios: the perfect fifth is exactly 3/2 = 1.5000 (compared to 1.4983 in equal temperament). The difference between just and equal temperament intervals is typically 2-14 cents.

Practical applications:

• Guitar tuners display pitch deviation in cents. A reading of +5 cents means the note is 5 cents sharp.
• When tuning instruments together, differences of less than 5 cents are generally not noticeable to most listeners.
• Differences of 10-15 cents are clearly audible and make music sound “out of tune.”