Note Frequency Calculator
Converts any MIDI note number into its precise pitch frequency in Hz using A4 = 440 Hz reference tuning. Essential for synthesizer tuning, audio programming, and understanding the physics of musical pitch.
Last updated: May 2026
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About this calculator
Every pitch in 12-tone equal temperament corresponds to a specific frequency measured in hertz. The international standard (ISO 16) fixes MIDI note 69 — concert A4 — at exactly 440 Hz. From that reference point, every semitone up or down multiplies or divides the frequency by 2^(1/12) ≈ 1.05946, the twelfth root of two. The formula is f = 440 × 2^((noteNumber − 69) / 12), where noteNumber is the MIDI integer (0 = C−1 at ~8.18 Hz, 60 = middle C at ~261.63 Hz, 127 = G9 at ~12,544 Hz). This logarithmic mapping guarantees that every octave is exactly a 2:1 frequency ratio. Edge cases worth knowing: the formula assumes equal temperament, so it does not match historic tunings like Pythagorean, just intonation, or meantone; some orchestras adopt A = 442 or 443 Hz, which scales every result proportionally; non-integer MIDI values (used for microtonal pitch bend) plug into the formula unchanged. The output is the fundamental frequency only — real instruments add harmonics at integer multiples.
How to use
Example 1: Find the frequency of middle C (MIDI note 60). Step 1: compute the offset from A4 — 60 − 69 = −9 semitones. Step 2: raise 2 to (−9 / 12) = −0.75, giving 2^(−0.75) ≈ 0.5946. Step 3: multiply 440 × 0.5946 ≈ 261.63 Hz. Verify by checking a tuner app — middle C reads 261.63 Hz. Example 2: Find A5, one octave above concert A. Note number 81 means offset 81 − 69 = 12, so 2^(12/12) = 2, and 440 × 2 = 880 Hz. Verify: an octave doubles frequency, so A5 must be exactly twice 440 Hz, which matches.
Frequently asked questions
How is the MIDI note number related to musical pitch?
MIDI assigns one integer per semitone across the keyboard range, from note 0 (C−1) up to note 127 (G9). A4 — the standard tuning reference — is note 69, and middle C (C4) is note 60. Each step up represents one semitone, so 12 MIDI numbers always equal one octave regardless of register. This integer encoding lets controllers, sequencers, and software exchange pitch information using compact whole numbers while the conversion formula maps each number back to a physically meaningful frequency. Pitch-bend data extends the resolution between integer notes for vibrato and microtonal effects.
Why is 440 Hz used as the tuning standard?
ISO 16 (1955, reaffirmed 1975) standardized A4 at 440 Hz so orchestras, instruments, electronic devices, and recordings worldwide could play in tune with one another. Before standardization tuning varied widely. Baroque ensembles often used A ≈ 415 Hz, French operas adopted A = 435 Hz in the 19th century, and German orchestras experimented with A = 446 Hz. Some modern symphonies still tune to A = 442 or 443 Hz for a slightly brighter, more brilliant string sound, and period-instrument groups choose tunings appropriate to the era of the music. Digital audio workstations, MIDI synthesizers, and tuner apps universally default to 440 Hz unless you change a preference. A movement called 'Verdi tuning' advocates A = 432 Hz on aesthetic grounds, but it lacks any acoustical or perceptual justification.
What is the frequency difference between two notes one semitone apart?
Two notes a semitone apart differ by a multiplicative factor of 2^(1/12) ≈ 1.05946, meaning the higher note is about 5.946% higher in frequency than the lower one. In absolute terms the gap grows as you climb. A4 to A#4 spans about 26 Hz (440 to 466.16 Hz), but one octave higher A5 to A#5 spans roughly 52 Hz (880 to 932.33 Hz). This logarithmic spacing matches how the human ear perceives pitch, where equal-sounding steps require exponentially larger frequency jumps as pitch rises. Cents (1/100 of a semitone) are used when sub-semitone precision matters for tuning instruments or analyzing intonation. A trained ear can detect pitch differences of about 5–10 cents, so frequency calculations should be accurate to at least three decimal places when targeting that resolution.
What are common mistakes when converting MIDI numbers to frequency?
The most frequent error is using log base 10 instead of base 2 in the exponent — the formula requires the twelfth root of 2, not 10. Confusing the A4 reference number (69) with middle C (60) shifts every result by nine semitones, producing pitches roughly 3/5 of the correct value. Some developers mistakenly assume integer MIDI numbers only, forgetting that pitch-bend data uses fractional values. Mixing up cents and semitones leads to a 100× error in offset (1 cent = 0.01 semitones). Finally, some calculators assume A = 442 Hz internally; always confirm the reference if you are tuning critical equipment.
When should I NOT use this calculator?
Music in historic tunings or non-Western scales does not follow equal temperament — Pythagorean tuning, just intonation, meantone, and Indian classical 22-shruti systems all produce different frequencies for the same nominal note. Microtonal music using divisions other than 12 per octave (19-EDO, 31-EDO, Bohlen-Pierce, etc.) requires its own formula. When tuning an orchestra to A = 442 Hz or a Baroque ensemble to A = 415 Hz, you must scale every output proportionally rather than using the 440 Hz reference. Stretch-tuned pianos slightly widen octaves at the extremes to compensate for inharmonicity, so concert tuners deviate intentionally from this formula. Finally, harmonic analysis of real instrument tones requires the partial series, not just the fundamental.