A piano key number identifies a physical key on a particular keyboard; a MIDI note number identifies a numeric pitch; and frequency measures that pitch in hertz. On a standard 88-key A0–C8 piano numbered from A0 as key 1, pianoKey = midiNote - 20. For equal temperament with A4 set to 440 Hz, frequencyHz = 440 * 2 ** ((midiNote - 69) / 12).
What each number describes
| Value | What it represents | What to keep in mind |
|---|---|---|
| Piano key number | A physical key’s position counted from a specified end of a specified keyboard. | It only has a stable meaning when the instrument range and counting convention are known. |
| MIDI note number | A numeric pitch index used in MIDI. | MIDI note 60 is middle C. Its octave label can vary by software or naming convention. |
| Frequency | The pitch’s frequency, measured in hertz (Hz). | A calculated value depends on the tuning reference and temperament assumed. |
For an 88-key piano, the physical-key count and MIDI index happen to be related by a fixed offset when the instrument runs from A0 to C8 and A0 is counted as key 1. That relationship is not a general rule for every keyboard or controller.
Map MIDI notes to keys on a standard 88-key piano
On the standard A0–C8 range, A0 is physical key 1 and MIDI note 21. Each next semitone advances both numbers by one, so the mapping is:
pianoKey = midiNote - 20midiNote = pianoKey + 20
For example, MIDI note 21 maps to piano key 1, and MIDI note 108 maps to piano key 88. This mapping assumes the standard 88-key range and that black keys are counted as keys. A 61-key controller’s key count alone does not tell you its lowest note; use its actual pitch range and numbering convention instead. The 88-key mapping is described in Weiwei Yang’s JavaScript reference.
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Convert MIDI note number to frequency in JavaScript
With A4 (MIDI note 69) set to 440 Hz and twelve-tone equal temperament, each semitone is a frequency step by a factor of 2 ** (1 / 12). The frequency formula is:
frequencyHz = 440 * 2 ** ((midiNote - 69) / 12)
This follows the equal-temperament relationship described by the UNSW School of Physics: an octave has a 2:1 frequency ratio, divided into 12 equal semitone ratios. Here is a bounded function for the notes on a standard 88-key piano:
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function pianoReference(midiNote, a4Hz = 440) {
if (!Number.isInteger(midiNote) || midiNote < 21 || midiNote > 108) {
throw new RangeError("Expected an integer MIDI note from 21 to 108.");
}
if (!Number.isFinite(a4Hz) || a4Hz <= 0) {
throw new RangeError("A4 reference must be a positive finite number.");
}
return {
midiNote,
pianoKey: midiNote - 20,
frequencyHz: a4Hz * 2 ** ((midiNote - 69) / 12),
};
}For example, pianoReference(60) returns MIDI note 60, piano key 40, and a frequency of approximately 261.6255653005986 Hz. pianoReference(69) returns piano key 49 and 440 Hz. The function rejects numeric strings; if the value comes from a text field, parse and validate it before calling the function. Passing a different positive a4Hz re-anchors the equal-temperament calculation without changing the MIDI number or physical-key offset. Keep the full calculated precision for further calculations and round only when formatting a value for display.
Convert frequency back to an equal-tempered MIDI position
For a positive frequency f in hertz and the same A4 reference, the corresponding semitone position is:
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midiPosition = 12 * log2(f / 440) + 69
A fractional result means the frequency lies between equal-tempered semitone centers; it is not necessarily an integer MIDI note. Round or choose the nearest note only if the application needs a discrete note number. This inverse relationship uses the same A4 reference and equal-temperament assumptions as the forward calculation.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Why software labels MIDI 60 as C3, C4, or C5
The MIDI number is the reliable comparison point; the octave label is a naming convention layered on top. The MIDI Association states: “For MIDI, middle C is always note number 60 even though it may be another pitch or described by a different octave designation – C3, C4 or C5.” Its note-number, frequency, and octave-designation table shows those alternative labels side by side.
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Consequently, if two programs display different octave labels for the same MIDI note number, that difference alone does not show that one has transposed the note. When displaying note names in your own software, document which octave-label convention it uses; retain and compare the numeric MIDI value when matching notes across applications. The MIDI Association identifies the MIDI 1.0 Detailed Specification as a core specification document.
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