BPM and Semitone Calculator: Convert Tempo and Pitch

A BPM and semitone calculator converts a tempo change into the pitch shift it would cause when audio is sped up or slowed down, or converts a pitch shift into the corresponding tempo change. Enter the original and new BPM, or the semitone change, to see the matching result and the relationship between tempo and pitch.

Formula

For audio whose playback speed changes without independent pitch correction, tempo and pitch move together. The semitone shift is:

n = 12 × log₂(B_new / B_original)

• n is the pitch change in semitones. A positive value means higher; a negative value means lower.
• B_original is the starting tempo in beats per minute (BPM).
• B_new is the destination tempo in BPM.
• The speed ratio is r = B_new / B_original. A ratio above 1 speeds playback up; below 1 slows it down.

The inverse formula is r = 2^n/12, so B_new = B_original × 2^n/12. These formulas use the equal-tempered musical semitone, in which each semitone has a frequency ratio of 2^1/12. BPM is a rate, not a physical distance or duration, so no US customary or metric conversion applies.

Worked Example

Using the calculator’s default values, the tempo changes from 120 BPM to 126 BPM.

1. Calculate the speed ratio: 126 ÷ 120 = 1.05.
2. Find the semitone change: 12 × log₂(1.05) ≈ 0.844.
3. Round to the calculator’s two decimal places: +0.84 semitones.

The positive sign indicates that ordinary speed-up playback raises the pitch. The ratio, shown to four decimal places, is 1.0500×.

What the Calculator Tells You

Tempo and pitch are linked when a recording is played faster or slower as a whole. If a track rises from 120 to 126 BPM, it is 5% faster, but its pitch change is not 5% of a semitone: the relationship is logarithmic. The calculator translates that speed ratio into semitones, a standard way musicians describe musical pitch intervals.

The result can be fractional. A shift of +0.84 semitones falls between the starting pitch and one semitone above it; it is not automatically rounded to a whole note. If you need to match a musical key, the fractional result matters, because rounding it to +1 semitone changes the target. For a desired whole-semitone shift, use the inverse formula to find the exact corresponding tempo.

When to Use It

• Matching a tempo by changing playback speed: Estimate how much the track’s pitch will rise or fall when you set a new BPM.
• Planning a pitch shift: Find the tempo that would result from speeding up or slowing down by a chosen number of semitones.
• Comparing samples: Check whether a sample’s original tempo is close enough to a project tempo to work with a simple speed change.
• Understanding time changes: A faster playback rate shortens the duration by the same ratio. For example, a 1.05× speed makes the audio duration the original duration divided by 1.05.

When entering values, use the actual BPM figures rather than a percentage difference. The calculator accepts positive tempos; a zero or negative BPM has no useful meaning in this ratio-based calculation. If the source tempo is uncertain or detected at half-time or double-time, verify the beat interpretation first.

Speed Change Versus Pitch Correction

The calculator describes a linked speed-and-pitch change, sometimes called varispeed or tape-style speed change. It does not predict the result of time-stretching software that changes tempo while attempting to preserve pitch, or pitch-shifting software that changes pitch while attempting to preserve duration. Those tools deliberately separate the two quantities, and their sound quality depends on the audio and processing method.

For instance, a producer can move a 120 BPM loop to 126 BPM with time stretching and keep its notes at their original pitches. In that case the actual pitch shift is approximately zero, even though this calculator’s linked-speed result is +0.84 semitones. Use the calculation when playback speed itself changes, not when a processor independently corrects pitch.

Common Mistakes and Limits

• Confusing percent with semitones: A 5% tempo increase is not a 5% pitch increase measured in semitones. Apply the logarithmic formula.
• Reversing the ratio: Put new BPM over original BPM. Reversing the order flips the sign and describes the opposite change.
• Assuming every BPM label is unambiguous: A beat can be counted at half or double the perceived pulse. The math is correct for the numbers supplied, but it cannot decide which pulse best describes the music.
• Over-interpreting decimal precision: A displayed value such as 0.84 semitones is rounded. It is a mathematical estimate, not a guarantee of a particular musical note or processing result.
• Ignoring independent processing: Pitch correction, time stretching, resampling, or tempo maps can break the simple link between measured BPM and pitch.

The model assumes a single, constant speed ratio and a stable tempo. It does not analyze audio, identify beats, account for tempo changes within a song, or account for audio artifacts from resampling. Its pitch result is an equal-tempered interval; tuning systems or musical contexts that use other pitch relationships may describe intervals differently.

Frequently Asked Questions

How many semitones is a 10% tempo increase?
Use 12 × log₂(1.10). The result is about +1.65 semitones, assuming playback speed changes together with pitch.

How much does tempo change for one semitone?
One semitone corresponds to a speed ratio of 2^1/12, approximately 1.0595. That is about a 5.95% increase in tempo for a rise of one semitone, or the reciprocal ratio for a drop of one semitone.

Does changing BPM always change pitch?
No. It changes pitch when the audio is simply played faster or slower. Time-stretching can alter tempo while preserving pitch, and pitch-shifting can alter pitch without changing tempo.

Why is the semitone answer not a whole number?
Most tempo ratios do not line up exactly with whole-semitone intervals. A fractional answer gives the size and direction of the interval without rounding it to a nearby note.

Can I enter a negative semitone shift?
This calculator takes two positive BPM values and calculates the signed shift between them. A lower destination BPM automatically produces a negative semitone result.

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in bpm | Original tempo | BPM | 120 | 0
in new_bpm | New tempo | BPM | 126 | 0
out semitones | Pitch shift | semitones | 12 * log2(new_bpm / bpm) | 2
out ratio | Speed ratio | x | new_bpm / bpm | 4