Music Tools

Chord finders, tuners, and a metronome.

About these music tools

Every note you have ever heard on a piano is out of tune, and it has to be. Stack twelve pure fifths and you should arrive back where you started, seven octaves up. You do not. Twelve pure fifths come to 8,423.46 cents while seven octaves come to exactly 8,400, so the circle of fifths overshoots by 23.46 cents — the Pythagorean comma, about a quarter of a semitone and plainly audible. No tuning makes every interval pure, because the arithmetic forbids it. Equal temperament resolves this by spreading the error evenly: every semitone becomes exactly the twelfth root of two, so every key is equally usable and every interval except the octave is slightly wrong. A tempered fifth is 700 cents against a pure 701.955, close enough to pass. The major third is the real casualty — 400 cents against a pure 386.31, nearly fourteen cents sharp, which is why a piano chord has a faint beating that a barbershop quartet singing the same chord does not. Singers and string players drift away from the tempered pitches without being taught to, which is also why a choir accompanied by piano sounds subtly different from one singing unaccompanied. The other thing worth carrying is that pitch is logarithmic while frequency is not. A4 is 440 Hz and A5 is 880, so that octave adds 440 Hz; the next adds 880. Equal steps in pitch are equal RATIOS in frequency, never equal differences. It is why guitar frets crowd together up the neck, why tuners report cents rather than hertz, and why being ten hertz flat is serious on a low string and inaudible on a high one.

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