Piano Frequency Table

261.63 Hz - the C4 row of the table, sitting four octaves above the lowest C on the piano. The name middle C comes from position: it is near the middle of the 88-key keyboard, close to the physical center of the instrument, which is why virtually every music-reading tradition uses it as the anchor between the treble and bass clefs (written one ledger line below the treble staff, one above the bass). Two footnotes explain most confusion around it: scientific pitch notation numbers octaves differently in some older European systems (where the middle C is called c1 rather than C4), and organs sometimes transpose whole ranks an octave - but in the equal-tempered, A-440 world the piano lives in, middle C is 261.63 Hz and every reference above or below it is a power of two away.

Because the ear hears ratios, not differences: two frequencies an octave apart excite the same note-quality in hearing, and the octave happens to be the simplest ratio there is - two to one. Multiply any frequency by two and the waveform repeats itself exactly twice per cycle where the lower note did once, which hearing collapses into sameness-of-letter with a sense of height. Equal temperament then splits that doubling into twelve geometrically equal semitones (each by the twelfth root of two, about 1.059 times), so all twelve major keys share one tuning - the compromise pianos have lived with since the Well-Tempered Clavier era. The doubling rule also explains the layout of the second table: C8 at 4186 Hz is not tuned to anything special, it is simply C0 (16.35 Hz) doubled eight times.

Two lookups and one multiplication. First, find the note letter in the octave-4 table (for example G4 at 392.00 Hz). Second, count octaves from 4 to your target - up or down. Third, multiply by 2 once per octave up (or divide per octave down): G5 is 392.00 times 2 = 784 Hz; G2 is 392.00 divided by 4 = 98 Hz. For in-octave moves, use the semitone ratio: each step up multiplies by about 1.0595. The two tables together therefore cover all 88 keys without listing them: any key is a letter row from table one plus an octave power from table two. The only caveat is tuning standard - the numbers assume A4 = 440 Hz; a historical-performance ensemble at 415 Hz or a rock band a quarter-step down shifts every number by a small constant factor that the same ratios still describe.

The 88-key standard runs from A0 at 27.5 Hz (three octaves below the octave-4 A) up to C8 at 4186.01 Hz - and both extremes sit at the edges of human hearing for different reasons: 27.5 Hz is felt in the chest almost as much as heard, which is why the lowest strings are single, long and copper-wound, while 4186 Hz is crisp and small, which is why the top strings are short, bare steel and struck by hammers that barely weigh anything. Extensions exist: some concert instruments add keys down to F0 or C0 (16.35 Hz, in the table) for organ-transcription repertoire, and digital keyboards stretch further without acoustic excuse. Anything below about 20 Hz or above about 20,000 Hz leaves the range of hearing entirely - the piano stops well inside both limits, which is exactly why its extremes sound like piano and not like rumble or air.