Music Transposition Calculator

Transpose a note by a chosen musical interval and direction, and get the new pitch name, semitone shift, MIDI note number, and equal-temperament frequency.

Quick Facts

Tuning system
12-tone equal temperament (12-TET)
Each semitone multiplies frequency by the 12th root of 2, approximately 1.059463.
Reference pitch
A4 = 440 Hz (MIDI note 69)
Concert pitch standard defined by ISO 16.

Your Results

Calculated
Transposed note
-
New pitch name and octave
Semitone shift
-
Signed interval applied
Transposed frequency
-
12-TET pitch, A4 = 440 Hz
MIDI note number
-
0-127 scale, C4 = 60

Ready

Choose a starting note, octave, and interval, then press Transpose.

Understanding Music Transposition

Transposition means shifting every note of a melody, chord, or key by the same musical interval, so the piece sounds higher or lower while all the relationships between notes stay identical. This tool transposes a single starting pitch by a chosen interval and direction, using the same math that underlies transposing whole passages, key signatures, or parts for transposing instruments.

The formula

Every pitch is represented as a MIDI note number, the standard integer scale used by digital instruments and notation software: midi = (octave + 1) x 12 + chromatic index, where the chromatic index runs from 0 (C) to 11 (B) and C4 (middle C) equals MIDI 60. Transposing by N semitones simply adds N to the MIDI number (or subtracts N when moving down): new midi = midi ± N. The resulting note name and octave are recovered with index = new midi mod 12 and octave = floor(new midi / 12) − 1.

Frequency in 12-tone equal temperament (12-TET) follows directly from the MIDI number: f = 440 x 2^((midi − 69) / 12) Hz, since MIDI note 69 is defined as A4 at exactly 440 Hz and each semitone changes frequency by a constant ratio of the 12th root of 2 (≈1.059463).

Reading intervals

An interval is the distance between two pitches, commonly named by counting semitones: a major 2nd is 2 semitones, a perfect 5th is 7 semitones, and a full octave is 12 semitones. Because 12-TET spaces every semitone identically, transposing "up a major 3rd" always adds exactly 4 semitones no matter what note you start from - the interval's sound and shape are preserved, only the starting pitch changes.

Why frequency and MIDI numbers matter

The pitch name alone (like "D4") does not tell you how the note relates numerically to others, and note spelling can vary (D# and Eb are the same pitch). The MIDI number and frequency give an unambiguous, calculable answer: two notes with the same MIDI number always sound identical, and the frequency tells you exactly how fast the string, reed, or speaker cone needs to vibrate to produce that pitch.

Frequently Asked Questions

What formula does this transposer use?
It uses standard 12-tone equal temperament (12-TET). Each note gets a MIDI number: midi = (octave + 1) x 12 + chromatic index, with C4 (middle C) equal to 60. Transposing by an interval adds or subtracts that many semitones from the MIDI number, and frequency is computed as f = 440 x 2^((midi − 69) / 12), which fixes A4 at exactly 440 Hz.
How is the MIDI note number calculated?
Each of the 12 chromatic pitches (C through B) gets an index from 0 to 11. The MIDI number is (octave + 1) x 12 + index, so C4 = (4+1) x 12 + 0 = 60 and A4 = (4+1) x 12 + 9 = 69. This is the same numbering used by MIDI keyboards, DAWs, and notation software everywhere.
Why do sharps and flats sound identical?
In 12-tone equal temperament, an octave is split into 12 equal semitone steps, so C# and Db land on the exact same pitch (enharmonic equivalents). This calculator displays results with sharp spelling; the sounding pitch and frequency are the same no matter which spelling a score chooses.
What happens if a transposition goes out of range?
Standard MIDI numbering only covers 0 to 127 (about C-1 to G9). If a transposition pushes the result below 0 or above 127, the calculator marks the input invalid instead of returning a nonsensical pitch - try a smaller interval, the opposite direction, or an octave nearer the middle of the keyboard.

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