Musical Interval Converter (Semitones, Cents, Frequency Ratio)
指导
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) 且 ratio = 2semitones / 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.
如何使用
- Type a value into Semitones, Cents， 或者 Frequency Ratio — the other two fields and the interval name update instantly.
- Click one of the 快速选择 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.
- 调整 十进制精度 if you need more or fewer digits.
特征
- 双向转换 – 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 2cents / 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.
- 复制全部 – export the full conversion plus detune result to your clipboard as plain text.
- 纯客户端运行 – no API calls, no rate limits, works offline once the page loads.
常问问题
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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.
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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.
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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.
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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.
