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Musical Interval Converter (Semitones, Cents, Frequency Ratio)

DeveloperMath

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INPUT

Auto Process

Interval Conversion

Semitones

Cents

Frequency Ratio

Interval Name

Decimal Precision

Quick Select Intervals

Detune Calculator

Apply a cent offset to a base frequency to find the detuned result frequency.

Base Frequency (Hz)

Detune (cents)

Result Frequency (Hz)

OUTPUT

Client Side

Equal Temperament vs Just Intonation

Comparison for the nearest named interval to your current input.

System	Cents	Ratio
Equal Temperament
Just Intonation
Difference

Interval Reference Chart

Semitones	Cents	Ratio (ET)	Interval
0	0	1.0000	Perfect Unison (P1)
1	100	1.0595	Minor 2nd (m2)
2	200	1.1225	Major 2nd (M2)
3	300	1.1892	Minor 3rd (m3)
4	400	1.2599	Major 3rd (M3)
5	500	1.3348	Perfect 4th (P4)
6	600	1.4142	Tritone (TT)
7	700	1.4983	Perfect 5th (P5)
8	800	1.5874	Minor 6th (m6)
9	900	1.6818	Major 6th (M6)
10	1000	1.7818	Minor 7th (m7)
11	1100	1.8877	Major 7th (M7)
12	1200	2.0000	Perfect Octave (P8)

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Guide

Musical Interval Converter

Convert any musical interval between three universal units — semitones, cents, and frequency ratios — and instantly see the matching interval name (minor 3rd, tritone, perfect 5th, octave, and beyond). The tool is built for music theory students, instrument builders, audio engineers, and electronic-music producers who work with pitch in precise units rather than note names alone.

Every conversion is performed client-side with the standard logarithmic formulas: cents = 1200 × log₂(ratio) and ratio = 2^{semitones / 12}. A built-in detune calculator multiplies any base frequency by a cents offset so you can find the resulting pitch of a sample slowed, sped up, or pitch-shifted by an arbitrary amount.

How to Use

Type a value into Semitones, Cents, or Frequency Ratio — the other two fields and the interval name update instantly.
Click one of the Quick Select chips (P5, M3, Octave…) to load a common interval with one click.
Read the Equal Temperament vs Just Intonation table to see how the equal-tempered interval differs from the pure integer-ratio version in cents.
To find the result of a pitch shift, enter a base frequency (e.g. 440 Hz) and a cent offset (positive = up, negative = down) under Detune Calculator.
Adjust Decimal Precision if you need more or fewer digits.

Features

Bidirectional conversion – edit any of semitones, cents, or frequency ratio and the other units update automatically with full precision.
Interval name lookup – instantly identifies named intervals from unison through double-octave, including non-integer inputs flagged with their cent deviation.
Quick-select chips – one-click access to the thirteen most common intervals from Perfect Unison (P1) to Perfect Octave (P8).
Equal Temperament vs Just Intonation table – side-by-side comparison of the equal-tempered ratio versus the small-integer just-intonation ratio for the current interval, with cent difference.
Detune frequency calculator – multiplies a base frequency by 2^{cents / 1200} to compute the result of any pitch shift.
Interval Reference Chart – always-visible table of semitones, cents, ratios, and names from 0 to 12 with the active row highlighted.
Copy All – export the full conversion plus detune result to your clipboard as plain text.
Pure client-side – no API calls, no rate limits, works offline once the page loads.

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 FAQ

What is the difference between cents and semitones?

A semitone is the smallest interval used in Western music's 12-tone equal temperament system, equivalent to 100 cents. Cents provide a finer-grained logarithmic unit: 1200 cents span exactly one octave, so a cent is 1/1200 of an octave. Cents are essential when describing micro-tonal pitches, instrument detuning, or comparing tuning systems where pitches do not land on integer semitones.
How does equal temperament differ from just intonation?

Equal temperament divides the octave into 12 mathematically identical semitones (each ratio = 2^(1/12) ≈ 1.0595), so every key sounds equally in-tune. Just intonation uses small integer ratios (3/2, 5/4, 6/5…) so individual intervals sound purer because their frequencies share harmonic overtones, but transposing to a distant key introduces noticeable beating. Equal temperament is the compromise that lets a single tuning serve every key.
What is a frequency ratio in music theory?

A frequency ratio expresses how two pitches relate in their fundamental frequencies. An octave is 2:1 — the higher note vibrates twice as fast as the lower. A perfect fifth is 3:2, a perfect fourth is 4:3, and a major third in just intonation is 5:4. Ratios with small integers tend to sound consonant because their overtones align, which is why ancient musical systems were built around them.
Why are intervals counted in twelfths of an octave?

The 12-tone division of the octave emerged because it produces close approximations of the most consonant just-intonation ratios (perfect fifth, fourth, major third) using a single repeating step size. Twelve semitones per octave is small enough to remember and notate, yet large enough that the equal-tempered fifth deviates from the pure 3:2 ratio by only about two cents — an error most listeners cannot detect.