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 whole-number ratios: the perfect fifth is exactly 3/2 = 1.5000, against 1.49831 in equal temperament.

So the gap runs from almost nothing up to about 16 cents. The fourth and the fifth are nearly identical in both systems, which is why they sound so stable on any instrument. The thirds and sixths are where equal temperament pays its price: a piano’s major third is 13.7 cents sharp of pure, and once you have heard a barbershop quartet or a brass ensemble lock a just major third, the tempered one sounds slightly sour forever.

That is the bargain equal temperament makes. Every key is equally usable and no key is perfectly in tune. Fretless strings, voices and trombones drift toward just intervals automatically when they play together, because the beating disappears when the ratio is simple, and the players hear it long before they can explain it.

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.”

Beats are how you actually hear a mistuning. Two notes close in pitch produce a slow throbbing at the difference of their frequencies. Two A strings at 440 and 442 Hz beat twice a second, plainly audible and impossible to ignore. That is the whole technique behind tuning by ear: you do not listen for the pitch, you listen for the beating to slow down and stop. The higher the pitch, the worse a given error sounds, because a fixed number of cents is a bigger frequency gap up there. Five cents at A440 is 1.3 Hz and a slow wobble; five cents two octaves up is 5 Hz and an obvious warble.

Reference pitch is not universal. A440 is the modern standard, but orchestras in continental Europe often tune to A442 or A443 for brightness, historically informed baroque ensembles use A415 (about a semitone flat), and older instruments sit anywhere from A392 to A465. Shifting the reference moves every note with it, so an A415 baroque group playing from modern parts is really sounding a semitone lower than written.