Every note on a modern instrument is a frequency, and the exchange rate between the two is one of music’s few exact sciences. This Note Frequency Calculator converts any note and octave into its frequency in hertz under the A440 equal-temperament standard — and reports its MIDI number, wavelength and period alongside, because synthesizers, tuners and acousticians each speak a different one of those dialects.
The Formula: Twelve Equal Steps to the Octave
An octave is a doubling of frequency, and equal temperament divides that doubling into twelve equal ratios — so each semitone multiplies the frequency by the twelfth root of 2, about 1.059463. With A4 fixed at 440 Hz (MIDI note 69), any note’s frequency is f = 440 × 2^((m − 69) / 12), where m is its MIDI number. The worked anchors: A4 = 440.00 Hz exactly (by definition), middle C (C4, MIDI 60) = 261.63 Hz, and C5 (MIDI 72) = 523.25 Hz. The system’s elegance is that transposition becomes addition: move a note up k semitones and its MIDI number rises by k while its frequency multiplies by 2^(k/12) — which is why this page and the semitone arithmetic musicians do by ear are the same mathematics. The compromise inside the elegance deserves its fame: pure intervals are simple ratios (a perfect fifth is exactly 3:2 = 1.500), but the tempered fifth is 2^(7/12) = 1.49831 — about 2 cents flat — and the tempered major third (2^(4/12) = 1.25992) runs about 14 cents sharp of the pure 5:4. Equal temperament spreads these small errors evenly so that every key is equally (im)perfect and music can modulate freely; the cents column of a good tuner is precisely a report of these designed deviations plus your instrument’s own.
Wavelength, Period and the Physical Note
A frequency is also a physical wave in air, and the two companion figures translate it. The period is 1/f: A4 completes one cycle in 2.27 milliseconds — the number a synthesizer’s oscillator and a pitch-detection algorithm actually work with. The wavelength is the speed of sound divided by the frequency: at 343 m/s (air at 20°C), A4’s wave is 343 / 440 = 0.78 m long, middle C’s is 1.31 m, and the piano’s lowest A (A0, 27.5 Hz) stretches to 12.5 m — longer than the room most pianos sit in, which is the acoustical reason small rooms cannot reproduce deep bass faithfully and why the lowest notes are felt as much as heard. At the other end, the top piano C (C8, 4,186 Hz) has a wavelength of 8.2 cm. Two caveats keep the figures honest: the speed of sound rises about 0.6 m/s per degree Celsius, so wavelengths in a hot hall run slightly long (frequencies, set by the instrument, do not change); and the wavelength that matters for instrument design is the one inside the instrument — a stopped organ pipe sounds a note whose wavelength is about four times the pipe’s length, a flute’s about twice — because the air column’s boundary conditions, not the free-air wave, set the pitch. The calculator’s wavelength is the free-air figure: the right one for room acoustics, speaker placement and microphone technique.
Tuning Standards and the Moving A
The 440 in A440 is a convention with a passport, not a law of nature — ISO 16 standardized A4 = 440 Hz in 1955, and most of the world’s instruments, tuners and synthesizers default to it, which is why this calculator does. But orchestras have drifted sharp for brilliance (many European ensembles tune A = 442–444 Hz), period-instrument performance deliberately tunes flat (Baroque pitch is commonly A = 415 Hz, a full semitone below modern), and some historical standards sit at 432 Hz or lower still. The calculator’s arithmetic absorbs any standard gracefully: a frequency computed at A440 scales by the ratio of the standards, so Baroque A is our A4 result × 415/440. What changes is only the anchor; the twelfth-root-of-2 ladder between notes is the temperament’s, and it is invariant. Practical translation: if you are tuning to a recording, a house piano or a period ensemble, measure or ask for their A first, scale accordingly, and every figure on this page follows. If you are programming a synthesizer or setting a sample library, 440 is home. And if a discussion of 432 Hz healing properties finds you, the physics on this page is the polite ground truth: the ladder of ratios is identical, the anchor is a choice, and no frequency in the audible range has properties beyond the ones acoustics assigns it.
The Piano’s Range and the Guitar’s Open Strings
The calculator’s ladder, walked to its ends: the piano’s 88 keys run from A0 at 27.50 Hz through middle C to C8 at 4,186 Hz — five and a quarter octaves of the same twelfth-root rule, and a frequency ratio of about 152:1 between the instrument’s extremes. The guitar’s open strings are the ladder’s most-touched rungs, worth memorizing beside the tuner’s display: low E (E2) 82.41 Hz, A2 110.00, D3 146.83, G3 196.00, B3 246.94, high E (E4) 329.63. Notice the tuning system’s fingerprints in the numbers: the guitar’s fourths are tempered fourths (the A-to-D step multiplies by 1.3348 rather than the pure 4:3 = 1.3333), and the G-to-B major third is the temperament’s widest compromise, which is why guitars are famously tuned by compromise — a third string sweetened flat against the tuner pleases the ear in some keys by borrowing the error the system assigned elsewhere. A tuner reading in cents is reporting exactly these designed deviations: one cent is a frequency ratio of 2^(1/1200) ≈ 1.000578, so a string 5 cents sharp at A2 is running about 0.3 Hz high — small numbers with audible consequences when two strings share a pitch class.
Beats: Hearing Frequency Differences Directly
Two notes close in pitch produce a phenomenon that turns frequency differences into something countable with a stopwatch: beats. Sound a 440 Hz string beside a 442 Hz string and the combined tone pulses exactly 2 times per second — the beat rate equals the frequency difference, |f₁ − f₂| — because the waves drift in and out of phase at that rate, reinforcing and cancelling in turn. Piano tuners built a craft on this: they tune not to frequencies but to beat rates between coincident harmonics, counting pulses per second against a mental table (the A3–A4 pair’s shared partials, the tempered fifth’s slow ~1-per-second wander at certain registers). The beat method is this calculator’s arithmetic made audible — subtract two frequencies from the table, and the result is a rhythm. It also explains the shimmer of a twelve-string guitar or a chorus effect: pairs of strings or voices deliberately offset by a few hertz, beating gently forever, the ensemble’s warmth expressed as a frequency difference you can now compute. And it sets a practical floor on tuning by ear: differences under about half a hertz beat slower than attention holds, which is where the strobe tuner — cycles counted by machine, this page’s formula in hardware — takes over.
Common Mistakes
Octave-numbering confusion: middle C is C4 in scientific pitch notation (used here and by MIDI), but some manufacturers label it C3 — a one-octave error that doubles or halves the frequency. Treating note frequencies as evenly spaced (they are geometric: the gap between adjacent notes grows with pitch). Assuming A is always 440 (see the standards section — ensembles differ). Using the tempered frequency where a just-intonation ratio is required, or vice versa, in instrument building. And forgetting that harmonics are separate frequencies: a note’s pitch is its fundamental, the number this page returns, while its timbre lives in the integer multiples above it.
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Frequently Asked Questions
What is the frequency of middle C?
261.63 Hz in equal temperament at A440 (MIDI note 60). Its period is 3.82 ms and its wavelength in air about 1.31 m.
How are note frequencies calculated?
f = 440 × 2^((m − 69)/12), where m is the MIDI note number and 69 is A4 at 440 Hz. Each semitone is one MIDI step and multiplies frequency by the twelfth root of 2 (≈ 1.059463).
What does A440 mean?
The tuning standard that fixes A above middle C at exactly 440 Hz (ISO 16). Some orchestras tune to 442–444 Hz and historical performance to 415 Hz; the ratios between notes stay the same, only the anchor moves.
Why is a tempered fifth slightly flat?
Equal temperament divides the octave into 12 identical ratios, so the fifth is 2^(7/12) = 1.49831 against the pure 3:2 = 1.500 — about 2 cents flat, the small, evenly spread compromise that lets all keys work.
What is the wavelength of A4?
About 0.78 m in air at 20°C (343 m/s ÷ 440 Hz). Wavelengths shrink as pitch rises — the top piano C is about 8.2 cm — and grow slightly in warmer air as sound speeds up.
Do harmonics change the note’s frequency?
No — the note’s frequency (its pitch) is the fundamental. Harmonics at 2f, 3f, 4f… ride above it and create timbre; they are why a violin and a flute playing the same 440 Hz sound different while sharing a pitch.