Note ↔ Frequency Converter (A440 Equal Temperament)
Any note to its frequency and back — MIDI numbers, cents offset, the 2^(1/12) math, and alternate concert pitches from 432 to 444.
Equal temperament's whole trick is one irrational number: 2^(1/12). Every interval is slightly impure (a major third runs 14 cents sharp of the harmonic 5:4) in exchange for every key being equally usable — the compromise Bach advertised and pianos institutionalized.
Formula
⚠️ Acoustic estimates from standard formulas — real rooms, drivers and ears vary. For hearing-safety decisions use a calibrated SPL meter and official occupational limits.
Any note to its frequency and back — MIDI numbers, cents offset, the 2^(1/12) math, and alternate concert pitches from 432 to 444.
About Note ↔ Frequency Converter (A440 Equal Temperament)
Western music is a logarithm with a history: twelve equal steps per octave, each multiplying frequency by the twelfth root of two, anchored — since 1939, by international treaty of sorts — at A4 = 440 Hz. This converter turns any note and octave into its exact frequency, MIDI number, wavelength and piano-key position, at standard or alternate concert pitches, with the equal-temperament math (and its deliberate impurities) laid open.
How to use Note ↔ Frequency Converter (A440 Equal Temperament)
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula f = A4 × 2^((n−69)/12), n = MIDI number — each semitone multiplies by 2^(1/12) ≈ 1.05946 substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Note ↔ Frequency Converter (A440 Equal Temperament)?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula f = A4 × 2^((n−69)/12), n = MIDI number — each semitone multiplies by 2^(1/12) ≈ 1.05946 with sources cited on the page
- ✓Equal temperament's whole trick is one irrational number: 2^(1/12). Every interval is slightly impure (a major third runs 14 cents sharp of the harmonic 5:4) in exchange for every key being equally usable — the compromise Bach advertised and pianos institutionalized.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
Why twelve notes per octave?+
A happy numerical accident exploited for a millennium: stacking twelve perfect fifths (3:2 ratios) lands almost exactly on seven octaves — 1.5¹² = 129.7 vs 2⁷ = 128, a 1.4% gap (the Pythagorean comma). Twelve equal divisions absorb that gap so well that fifths stay 98% pure (2 cents flat) while every key becomes identical. Other cultures divide differently (Arabic quarter-tones at 24, Indonesian slendro at 5); 12-TET won the West because keyboards demanded fixed, transposable tuning.
Is there anything to the 432 Hz claims?+
Historically, pitch wandered freely — surviving 17th–18th-century organs and tuning forks range from A≈390 to 480, and Verdi did once advocate 432 (as 'scientific pitch' making middle C = 256) — but the modern claims of healing properties or cosmic resonance have no measurable basis: 432 vs 440 is a 31-cent shift, every interval RATIO stays identical, and blind tests show no reliable preference. This tool's reference input exists for the legitimate uses: baroque ensembles at 415, European orchestras at 442–443, and historically-informed performance.
How do MIDI numbers and piano keys line up with notes?+
Three coexisting indexes: scientific pitch notation (C4 = middle C, octaves increment at every C), MIDI (C4 = 60, A4 = 69, range 0–127 covering ~8 Hz to 12.5 kHz), and piano keys (1–88 from A0 to C8, so key number = MIDI − 20). Off-by-one-octave bugs are an industry tradition — some software calls middle C 'C3' (Yamaha convention). When transcribing between systems, anchor on A4 = 440 Hz = MIDI 69 = key 49 and count from there; this tool shows all three simultaneously for that reason.
What are cents, and how small a pitch difference can people hear?+
The cent is the tuning world's millimetre: 1/100 of an equal-tempered semitone, i.e. a ratio of 2^(1/1200) ≈ 1.00058. Trained listeners detect ~3–5 cents in sequential tones (less in sustained unisons, where beats give it away physically); vibrato swings ±20–50 cents without anyone minding; the equal-temperament major third's 14-cent sharpness is audible as mild brightness against a pure choir third. Guitar intonation, piano stretch-tuning (octaves deliberately widened ~1–3 cents for string inharmonicity) and orchestral drift all live on this scale.
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