How frequencies work

What frequency actually measures

Frequency is a rate, not a substance. It measures how many cycles of vibration happen each second, expressed in hertz (Hz). When a guitar string vibrates 444 times per second, it compresses the air 444 times per second, and your ear reports that rate as the pitch A4.

Sound itself is a travelling pressure wave. A vibrating object squeezes the air beside it; that squeeze pushes the air beyond it; and the disturbance moves outward at roughly 343 metres per second in room-temperature air. What we call “a note” is simply our brain’s map of how fast those pressure cycles arrive.

The maths: pitch is logarithmic

One of the most useful facts in tuning is that pitch perception is logarithmic. Equal musical intervals are equal ratios, not equal differences. An octave is a doubling: 220 Hz to 440 Hz is the same interval as 440 Hz to 880 Hz. A semitone is 2^(1/12), about 1.05946. That is why retuning a song means multiplying every frequency by one factor, not adding a fixed number of hertz to each note.

In equal temperament every note is A4 × 2^(n/12), where n counts semitones from A4. A cent is one hundredth of a semitone — a ratio of 2^(1/1200) — and around 5 cents is the smallest difference most trained listeners reliably detect on a sustained tone. These two formulas are all the arithmetic tuning requires.

Frequency and matter: resonance

Every physical object has natural frequencies at which it vibrates most easily, set by its size, stiffness and mass. Drive it at one of those frequencies and each new push arrives in step with the motion already there, so the amplitude grows. This is resonance, and it is measurable, repeatable physics.

• Chladni figures. Ernst Chladni showed in the 1780s that sand on a bowed metal plate collects into precise geometric patterns — and that the pattern changes with every change of frequency. Sound literally organises matter into visible order.
• Resonant failure. A glass sung at its own resonant pitch, loudly enough, will flex past its limit and break.
• Medical ultrasound. Focused sound in the megahertz range images soft tissue, and at higher intensity breaks up kidney stones without an incision.
• Hearing itself. The cochlea is a mechanical frequency analyser: different positions along its membrane respond to different frequencies, which is how you hear pitch at all.

What follows from all this is real but bounded. Frequency demonstrably shapes matter and demonstrably shapes perception. It does not follow that one particular musical reference pitch cures anything, and this app makes no such claim.

Why 440 Hz is a convention, not a law of nature

A4 = 440 Hz was adopted in the 20th century for a practical reason: orchestras, instrument makers and broadcasters needed one agreed number, and pitch had drifted widely by country, era and even by concert hall. It was a committee decision about interoperability. Nothing about 440 was derived from acoustics, mathematics or the human body.

The consequences are mostly aesthetic and numerical. At 440 Hz the equal-tempered scale produces awkward numbers — C5 = 523.25 Hz, G4 = 391.995 Hz — so no round value and no clean power of two falls on a note. Some singers and choirs also find that older repertoire written when reference pitch was lower sits slightly high in the voice at 440.

Claims that 440 Hz is harmful, or was imposed to disturb people, circulate widely and have no supporting evidence. The fair criticism is narrower and still worth making: 440 is arbitrary, and if the anchor is arbitrary anyway, you are free to choose one whose numbers mean something to you.

How retuning is done without stretching time

Because a tuning change is one constant ratio, the converter resamples the audio by that exact factor rather than editing individual notes. Every partial in the recording moves by the same proportion, so chords, intervals and timbre stay intact. WAV and FLAC are retuned losslessly; MP3, AAC and M4A must be re-encoded because those formats permit only fixed sample rates.

The app then re-analyses the output with an FFT-based detector and reports the measured A4 to three decimal places, iterating until the result falls inside your chosen tolerance. The claim on screen is always a measurement, never an assumption.

Frequently asked questions

What is a frequency, in simple terms?

Frequency is how many times per second something vibrates, measured in hertz (Hz). A guitar string vibrating 440 times per second pushes the air 440 times per second, and your ear reads that rate as the pitch we call A above middle C.

Can sound frequencies really affect physical matter?

Yes, and this part is ordinary physics. Every object has natural frequencies at which it vibrates most easily. Drive it at one of those and the motion builds — sand on a vibrating plate gathers into geometric patterns, a wine glass can shatter at its resonant pitch, and medical ultrasound uses focused sound to image and even break up tissue. What is not established is that a specific musical tuning produces a specific health outcome.

Why is A4 = 440 Hz the standard?

It was a 20th-century committee decision about interoperability. Orchestras, instrument makers and broadcasters needed one agreed number after centuries of pitch drift. Nothing about 440 was derived from acoustics, mathematics or the human body.

Why is retuning a multiplication rather than an addition?

Pitch perception is logarithmic, so equal musical intervals are equal ratios. An octave is a doubling and a semitone is 2^(1/12) ≈ 1.05946. Retuning a song therefore means multiplying every frequency by one constant factor, not adding a fixed number of hertz to each note.

Does retuning damage the recording?

No. The converter multiplies every frequency in the file by one exact ratio, so the internal harmony is untouched and nothing is time-stretched. WAV and FLAC are retuned losslessly; MP3, AAC and M4A are re-encoded because those formats only allow fixed sample rates.