Hertz is an absolute frequency
At A4 = 440 Hz, a standard fifth-string A2 is 110 Hz and the A one octave above it is 220 Hz. An octave doubles frequency; it does not add a fixed number of hertz. This is why a one-hertz error matters more on a low note than a high one. For example, 111 Hz is approximately 15.7 cents above 110 Hz, whereas 441 Hz is about 3.9 cents above 440 Hz. The same frequency difference is not the same musical interval.
Cents describe a ratio
An equal-tempered semitone contains 100 cents, and an octave 1,200. TuneGuitar compares a detected frequency with a target using 1200 × log₂(detected ÷ target). A negative result means below target; positive means above. A string at 220 Hz is exactly an octave above a 110 Hz target, even though both are called A. Looking only at the letter can conceal a large register mistake. Looking only at tiny cent changes can distract from choosing the right target first.
How the note table is calculated
The equal-tempered frequency for a MIDI note number n is A4 × 2^((n − 69) ÷ 12). Standard E2 is note 40, so at A4 = 440 Hz it is about 82.41 Hz. Each capo fret adds one semitone to the sounding target. The published tables use 440 Hz and round for readability; changing the live A4 setting changes the actual targets. A printed table and an adjusted live tuner can therefore disagree without either calculation being wrong.
Calibration is not an alternate tuning
Choosing A4 = 442 Hz raises every target slightly, by about 7.85 cents relative to 440. Selecting half-step-down tuning lowers each string by 100 cents. These are very different operations. Use calibration to agree with a deliberately chosen reference, and use the tuning preset to choose the actual string layout. If every note disagrees with a recording, investigate the exact version and reference before assuming one particular A4 value is historically correct.
Precision on a display is not measurement accuracy
A screen can show two decimal places even when microphone placement, background sound or pitch instability dominates the result. More digits describe formatting; they do not certify the input. TuneGuitar smooths accepted pitch readings and uses a five-cent window for its stable-note confirmation. That is an interaction rule, not a universal accuracy specification for every guitar and phone. Read the known-reference results alongside their conditions and distinguish numerical tests from physical device tests.
Why equal-tempered chords can still sound complex
A tuner centres the selected equal-tempered notes. It does not remove beating from every interval, correct all fret positions or compensate for excessive hand pressure. Before adjusting an apparently correct guitar by ear, decide what you are trying to optimise: open-note targets, one particular chord, or agreement with other instruments. Tuning one chord especially sweetly can move its strings away from the agreed reference elsewhere on the fretboard. Keep the baseline explicit so your experiment is reversible.
An experiment without recording audio
Use an independent steady A at 220 Hz and run the known-reference check. Record the median cents offset and spread, then repeat at a different input level without changing the reference. If the result changes, you have learned about that measurement condition rather than a new definition of A. The export contains numbers and notes, not microphone audio. Do not call the result certified calibration unless the entire reference and measurement chain has actually been certified.