Acoustic theory and algorithm

1. Why turning a peg changes the pitch

By Mersenne's Laws, the fundamental frequency of a vibrating string f is determined by three physical quantities:

• T (tension): tightening the peg → more tension → higher pitch
• L (string length): fretting a note → shorter speaking length → higher pitch
• μ (linear density): thicker strings → heavier → lower pitch (which is why bass strings are always thicker)

2. What a cent is

A cent is a logarithmic unit for measuring tiny pitch differences. In equal temperament one octave = 1200 cents, and adjacent semitones differ by 100 cents:

Measured in practice, the human ear resolves pitch differences of roughly 5–10 cents, while professional recording usually demands ±3 cents. This tuner defaults to a ±5 cent tolerance, adjustable in the settings.

3. The harmonic series and timbre

When you pluck a string it does not only vibrate as a whole (fundamental f₁) but also in segments at 1/2, 1/3, 1/4 … of its length, producing integer multiples of that frequency:

On the spectrum page the strong peak furthest to the left is usually the fundamental, and the smaller peaks at equal spacing after it are the harmonics. The balance among them is what gives each instrument its character, which is also why a tuner cannot simply take "the strongest peak" as the pitch: on some instruments the second harmonic is even stronger than the fundamental.

4. What algorithm this tuner uses

It uses McLeod Pitch Method (MPM): first computes autocorrelation with an FFT, normalises it into an NSDF, takes "the first peak reaching 88% of the global maximum" as the pitch period, then refines it by parabolic interpolation so the resolution is far finer than one sample.

• Unlike plain autocorrelation, MPM tells the fundamental apart from its octave, so bass strings no longer jump an octave up
• A 22 Hz high-pass and a 2.2 kHz low-pass are chained at the input, filtering out ambient rumble and high-frequency noise
• Accuracy reaches the ±0.1 cent range; real stability depends on the microphone and room noise

5. Temperaments: why there are so many

Equal temperament splits the octave into 12 equal parts, so every key is equally "slightly off but usable"; the price is that no interval other than the octave is pure. Just intonation uses simple integer ratios (3:2, 5:4) to make chords extremely clean, but it goes out of tune the moment you modulate. Historical meantone, Werckmeister, Kirnberger and other "well temperaments" are compromises between the two.

• Fretless instruments (violins, erhu, voice, choir) often drift towards just intonation in practice
• When playing Baroque repertoire, try Werckmeister III with A4 = 415 Hz
• China's traditional three-part sanfen yihe is closely related to the Western Pythagorean algorithm

6. Octave stretch (piano tuning)

Real strings have stiffness, so their harmonics sit slightly above exact integer multiples (string inharmonicity). Piano tuners therefore tune the treble slightly sharp and the bass slightly flat so the harmonics line up across octaves; that is the Railsback curve. The "Octave stretch" setting in the panel simulates this behaviour.

7. Keyboard shortcuts

• 7. Keyboard shortcuts Space
• 1–6 Start / pause the microphone
• 0 Lock string N (in string order)
• A Unlock and return to automatic detection

Play the long A4 reference note

• 8. Practical tips
• In a quiet room, tap "Sample the ambient noise floor" first — readings get noticeably steadier
• After plucking, wait about 0.3 s before reading: the harmonics are confused while the note is still startingWhen tuning,always work upwards from below the target
• so the strings settle in a consistent direction and hold their pitch better
• New strings need 2–3 rounds of tuning because they keep stretching