Note to Frequency Calculator

Equal temperament divides the octave into twelve equal steps. Equal here means equal in ratio rather than equal in Hertz: each semitone multiplies the frequency by the twelfth root of two, roughly $1.0595$. Twelve of those multiplications land exactly on double the starting frequency, which is why an octave up is always twice the Hz and an octave down always half.

That multiplicative behaviour is what makes the arithmetic feel strange at first. Between A3 at 220 Hz and A4 at 440 Hz there are 220 Hz of room. Between A4 and A5 there are 440 Hz. The musical distance is identical, but the frequency distance doubles every time you climb.

To turn a note name into a number, the whole keyboard needs a single index. MIDI numbering provides it: every semitone gets one integer, with A4 fixed at 69 and middle C, C4, at 60. Once a note has a MIDI number, one formula produces its frequency:

The exponent counts semitones away from the reference. Feed it 69 and the exponent is zero, so the answer is the reference itself. Feed it 81, twelve semitones higher, and the exponent is one, so the answer doubles.

The same formula runs in reverse when you have a frequency and want the note, which is exactly what a tuner does several times per second.

Every frequency above depends on one chosen anchor. Since 1,955 the international standard has put A4 at 440 Hz, formalised as ISO 16. It is a convention rather than a law of physics, and orchestras have never treated it as untouchable.

Many European orchestras tune to 442 or 443 Hz, and a few push to 444 Hz. The stated reason is usually brightness: a slightly higher reference makes strings feel more present. Historical pitch runs the other way, with baroque ensembles commonly at 415 Hz, roughly a semitone below modern pitch.

Then there is 432 Hz, which generates more search traffic than the rest combined. What it does is straightforward: it lowers every note by about 1.8% of a semitone, which is 31.8 cents. Middle C moves from 261.63 Hz to 256.87 Hz. A guitar tuned to it sounds very slightly flatter and, to most listeners, slightly warmer.

What it does not do is anything measurable beyond that. Claims that 432 Hz aligns with natural or bodily frequencies, reduces stress or improves healing have no verified evidence behind them. The audible effect is the same effect any small downward reference shift produces, and a listener comparing the two without knowing which is which generally cannot tell them apart reliably.

The practical consequence is compatibility. Anything tuned to a non-standard reference will clash with recordings, backing tracks and other instruments at 440 Hz, and the mismatch grows with the interval.

Frequency is one way to describe a vibration. The calculator shows two more, and each answers a different practical question.

Period is the time for one complete cycle, in milliseconds:

A4 at 440 Hz has a period of about 2.27 ms. Period matters when you are working in the time domain rather than the frequency domain: setting an oscilloscope sweep, choosing a delay short enough to act as comb filtering, or understanding why a 5 ms attack cannot possibly catch the first cycle of a bass note.

Wavelength is the physical length of the wave in air, using the speed of sound at 20°C:

A4 comes out around 0.78 m. Low notes are enormous by comparison. E2, the bottom string of a guitar at 82.41 Hz, stretches to about 4.16 m. A1 at 55 Hz is over 6 m long.

That number explains a great deal of studio frustration. A wave longer than the room cannot form properly inside it, which is why small rooms struggle with bass and why a subwoofer that measures flat in one corner measures terrible in another. It also explains driver size: moving enough air to sustain a six metre wave needs a large cone, and no amount of processing substitutes for it.

A cent is one hundredth of a semitone, which makes 1,200 cents to the octave. Because pitch perception is ratio based, cents give a unit that means the same thing at every register: 10 cents sounds like the same amount of wrong on a low E as on a high E, even though the Hertz differences are wildly apart.

Deviation is measured against the exact note frequency:

A positive result means sharp, negative means flat. Feed the formula 445 Hz against A4 at 440 and it returns 19.6 cents sharp, which a trained ear hears immediately as out of tune.

The threshold where people start noticing sits somewhere between 5 and 10 cents for most listeners on sustained tones, and closer to 3 cents for trained musicians listening to two notes at once. Beating between simultaneous notes is far easier to detect than absolute pitch error on a single note.

In practice, ±3 cents on every string of a guitar is more than clean enough that a full chord sounds in tune. Chasing zero is usually wasted effort, because a plucked string drifts more than that as it decays and pushing hard on a fret bends it further. A chromatic tuner reading in cents shows exactly that drift while the note rings out.

Instruments with fixed frequency ratios add their own deviations. Piano tuners deliberately stretch octaves at the extremes, so a well-tuned piano reads several cents off equal temperament at both ends.

Octave numbering causes the most confusion. Scientific pitch notation, which this calculator uses, calls middle C by the name C4 and puts A4 at 440 Hz. Several DAWs and samplers label the same key C3, shifting every octave number by one. When a frequency looks like it is out by exactly a factor of two, the numbering convention is almost always the reason.

Sharps and flats trip people up next. C# and Db are the same pitch in equal temperament and produce identical frequencies, even though they are different notes musically and appear in different keys. A calculator that reports one when you expected the other is not wrong.

The 432 Hz reference is often described as ancient or natural tuning. It is neither. Historical pitch varied enormously by city and century, and 432 Hz is a modern proposal, not a recovered tradition. Describing it accurately as a lower reference avoids a lot of pointless argument.

Hz and BPM get mixed up more often than seems likely, because both count events per unit time. Hertz counts cycles per second and describes pitch; BPM counts beats per minute and describes tempo. A 2 Hz LFO and a 120 BPM tempo happen to coincide, which makes the confusion easy to fall into.

Finally, a tuner disagreeing with a calculator usually has a different reference or a different temperament. Check the A4 setting first, and check whether the tuner applies stretch or a preset instrument curve.