A piano key number identifies a physical key on a particular keyboard; a MIDI note number identifies a pitch in MIDI’s numeric system; frequency describes that pitch in hertz. For a standard 88-key piano, A0 is physical key 1 and MIDI note 21, so pianoKey = midiNote - 20. With A4 tuned to 440 Hz in twelve-tone equal temperament, calculate frequency with 440 * 2 ** ((midiNote - 69) / 12).
What each number means
| Value | What it identifies | What to keep in mind |
|---|---|---|
| Piano key number | A physical key counted from a specified end of a specified keyboard. | Its meaning depends on the instrument’s range and the counting convention. Key 1 is not universally the same pitch. |
| MIDI note number | A numeric pitch index used in MIDI. | Middle C is note 60. The octave label shown for that note can differ between software and naming systems. |
| Frequency | The pitch’s rate of vibration, measured in hertz (Hz). | A frequency calculation requires a tuning reference and a tuning model, such as A4 = 440 Hz in twelve-tone equal temperament. |
These values are related, but they are not interchangeable: a piano key number is a position on an instrument, a MIDI note number is a pitch index, and frequency is a physical measurement.
Why MIDI 60 may appear as C3, C4, or C5
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.” The numeric note number is the dependable way to compare MIDI pitches across applications; the written octave label is a display convention. An octave-label difference alone does not show that notes have been transposed.
The MIDI Association’s technical table presents note number, frequency, and multiple octave-designation systems side by side, illustrating that note names and octave labels are layered onto the numeric index. When displaying a name in software, use the application’s stated convention rather than assuming every program numbers octaves identically.
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Convert between a standard 88-key piano key and MIDI note
For a standard 88-key A0–C8 piano, with A0 counted as physical key 1 and black keys included in the count, MIDI note 21 maps to key 1. Each next semitone advances both counts by one, yielding:
pianoKey = midiNote - 20midiNote = pianoKey + 20
This offset applies only to that specified range and counting convention. It does not automatically apply to a 61-key controller or another keyboard. Key count alone does not identify an instrument’s lowest note; use the instrument’s actual starting pitch and numbering convention to determine its mapping.
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Convert MIDI note number to frequency
In twelve-tone equal temperament, each semitone is separated by a frequency ratio of 2 ** (1 / 12), and an octave doubles frequency. Using A4 = 440 Hz as the reference, MIDI note 69 is A4 and the frequency for MIDI note m is:
frequencyHz = 440 * 2 ** ((midiNote - 69) / 12)
For example, MIDI 60 (middle C) is approximately 261.6255653005986 Hz under this reference. Keep the full calculated value for further computation; round only when formatting a value for display.
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To calculate the equal-tempered semitone position for a frequency f relative to A4, use midiNote = 12 * log2(f / 440) + 69. A non-integer result indicates a position between equal-tempered semitone centers rather than a whole-number MIDI note.
JavaScript reference implementation
This function is deliberately bounded to the 88 physical keys of the standard A0–C8 piano. It rejects values outside MIDI 21–108 and numeric strings; parse and validate text input in the user interface before calling it.
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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 instance, pianoReference(60) returns MIDI note 60, piano key 40, and a frequency of approximately 261.6255653005986 Hz. The optional a4Hz parameter changes the tuning reference for the equal-temperament frequency calculation; it does not change the MIDI index or the standard-piano key offset.
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Sources
- The MIDI Association: The naming of MIDI notes (2017 discussion).
- UNSW School of Physics: Musical notes.
- The MIDI Association: MIDI note number and frequency table.
- The MIDI Association: MIDI specifications.
- Weiwei Yang: Piano key number vs. MIDI note number vs. frequency.
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