Fundamental Frequency, Pitch, and Cents: What Is the Algorithm Actually Tracking?

Fundamental Frequency Is a Repeating Period, Not the Sum of Timbre

When an approximately periodic sound repeats 220 times per second, its fundamental frequency (F0) is about 220 Hz. Human hearing usually perceives that period as pitch, but the signal is not only 220 Hz: it also contains harmonics at 440, 660, 880 Hz and so on, plus energy variations caused by noise and resonance.

Therefore, two people can both sing A3 with similar fundamental frequencies while one voice sounds bright and the other soft. F0 answers roughly “how fast does the pattern repeat?” Timbre also depends on harmonic balance, spectral shape, resonance, and changes over time.

Why the Algorithm Estimates Frame by Frame

Pitch changes continuously during speech, so the algorithm divides audio into overlapping short frames and searches each frame for the most likely period. YIN uses a difference function to find period candidates and refines them through interpolation; probabilistic pYIN considers multiple candidates and continuity over time. Short frames respond quickly but have limited frequency resolution, while longer frames are steadier but smooth over rapid changes.

CVoice tries YIN first and supplements it with pYIN when validity is insufficient. FrostNote prioritizes low latency, so it combines consecutive frames and hold time rather than treating a single-frame reading as the final answer.

Cents Make Ratio Differences Comparable

In twelve-tone equal temperament, an octave is divided into 1200 cents and a semitone into 100 cents. Cents compare frequency ratios rather than simple subtraction:

This means that 220→221 Hz and 880→881 Hz do not have the same perceptual meaning. FrostNote uses a success zone of about ±25 cents around the target so different registers share a consistent relative scale.

Why It Jumps to Double or Half

If the second harmonic is stronger than the fundamental, an algorithm may read 220 Hz as 440 Hz. If the periodic structure supports a longer interpretation, it may instead read 110 Hz. This is an octave error. Breathiness, nasal quality, humming, room resonance, phone noise reduction, and background music can all make it more likely.

The solution is not simply to sing louder. Sustaining a stable vowel, reducing reverberation, avoiding accompaniment, preventing microphone overload, and using medians and jump suppression across consecutive frames are usually more effective.

How to Use the Readings

• Look at the median and range over time rather than trusting a single-frame peak.
• Distinguish F0, note name, and timbre. They are related, but they are not the same concept.
• When comparing recordings, control the text, device, and environment; otherwise, changes will not come from vocal production alone.

Application examples:FrostNote use F0 for real-time pitch training;CVoice treats F0 as only one of eight voice dimensions.