Piano Tuning Interval Calculator
Frequency for any note from any reference pitch, in equal temperament or just intonation.
https://calculators.nirajiitr.com/hobbies/piano-tuning-calculator
How it works
Equal temperament divides the octave into twelve steps that are equal as ratios rather than as differences, because pitch is perceived logarithmically. Each semitone multiplies the frequency by the twelfth root of two, roughly 1.05946, and twelve of those multiplications double it — which is exactly one octave. Just intonation instead uses small whole-number ratios, which sound purer for a single chord but drift badly as soon as you change key, and that compromise is the whole reason equal temperament won.
f = reference × 2^(n/12)- reference
- Pitch of A4, usually 440 Hz
- n
- Semitones above or below A4
- cents
- A hundredth of a semitone; around 3 cents is just audible
- beats
- The pulsing when two close pitches interfere, per second
Worked example
Finding C5, three semitones above A4, at standard pitch.
- 1n = 3 semitones above A4
- 22^(3/12) = 2^0.25 = 1.18921
- 3440 × 1.18921 = 523.25 Hz
- 4Just intonation would use the 6/5 minor third: 440 × 1.2 = 528 Hz
523.25 Hz in equal temperament — about 16 cents flat of the pure minor third, which is why that interval audibly beats on a piano.
Frequently asked questions
Why is a perfectly tuned piano still slightly out of tune?
Because equal temperament is a deliberate compromise. Pure intervals come from simple ratios such as 3/2 for a fifth, but you cannot stack twelve pure fifths and land back on an octave — the leftover gap is the Pythagorean comma. Equal temperament spreads that error evenly across all twelve keys, so every interval except the octave is very slightly impure and every key is equally usable. Piano fifths beat around once a second, and that is correct rather than a fault.
What is stretch tuning?
Real strings are stiff, so their overtones land slightly sharp of exact multiples of the fundamental — an effect called inharmonicity. Tune a piano to exact mathematical frequencies and the octaves sound flat, because the ear matches overtones rather than fundamentals. Tuners therefore stretch: the treble is tuned progressively sharp and the bass progressively flat. Short pianos have far more inharmonicity and need more stretch than a concert grand.
Why do some people tune to 432 Hz?
It is a preference rather than a standard. A440 was fixed by international agreement in 1955, and before that pitch varied widely by country and era — baroque ensembles commonly use 415 Hz, a semitone below modern pitch, to suit period instruments. Claims that 432 Hz has special physical or physiological properties do not hold up, but if you prefer how it sounds, set the reference here and the whole scale follows.
What are beats, and how do tuners use them?
When two notes are close but not identical, the sound pulses at a rate equal to the difference in frequency — two tones 2 Hz apart beat twice a second. Tuners count those beats rather than trying to judge absolute pitch, because counting is far more precise than listening for sharpness. Setting the temperament octave is largely a matter of getting the beat rates of the fifths and thirds to progress smoothly up the scale.
Can I tune my piano with this?
It gives you the target frequencies, but tuning a piano needs a lever, mutes and a great deal of practice at setting pins so they hold. Each note has up to three strings that must be perfect unisons, the pin has to be left without torsion or it will drift within days, and the instrument as a whole is under roughly twenty tons of tension. This is genuinely useful for understanding intervals and for simpler instruments; for a piano it complements a technician rather than replacing one.