HomeNotes

Waveform, spectrum, spectrogram. Each plot shows one thing.

The chain is straightforward: we produce sound, the air vibrates, a microphone records those changes, and plots reveal different parts of the signal. The examples here use teaching synthesis so you can change one variable at a time and hear what it does.

The chain

A source, a filter, and finally a stream of numbers.

Lungs supply airflow. Voiced sounds come from nearly periodic vocal-fold vibration. Sounds like s squeeze the air into turbulence. Tongue, lips, and cavities then reshape which frequencies come out strong.

  1. 1How a person produces sound
  2. 2How air vibrates
  3. 3What the recording keeps
  4. 4What the graph displays
  5. 5Why we hear pitch, stress, and tone

A practical model: a source, then a vocal-tract filter, then pressure in the air.

SourceVocal-fold pulse or airflow noise
→
FilterTongue, lips, oral and nasal cavities
→
OutputAir pressure changing over time

Hold roughly the same pitch and say ah — ee — oo. As your mouth changes shape, the timbre changes too. Pitch and vowel quality are separate dimensions.

01 · Waveform

How fast it repeats, and how far it swings.

A microphone first sees air pressure over time. The recording turns that into numbers. The plot’s x-axis is time; the y-axis is pressure, or a proportional amplitude. Up and down is sign, not “the sound is going higher.”

  • Waveform: the x-axis is time.
  • Up and down is relative amplitude, not pitch.

Repeats every 6.67 ms (bracket above).

frequency = 1 / time for one repeat

If it repeats every 5 ms, it repeats 200 times a second: 200 Hz.

A real vowel is messier, but you can still see a shape repeating. That overall repeat is F0. Do not count every little spike as another glottal pulse.

Sampling rate is not F0. 48,000 Hz means 48,000 numbers a second. 150 Hz F0 means 150 cycles a second — about 320 samples per cycle at that rate.

02 · Spectrum

Harmonic spacing and vocal-tract resonances.

A complex sound is a sum of sinusoids. Ask “how much energy at each frequency” and you get a spectrum.

  • Waveform: x is time.
  • Spectrum: x is frequency.

On a nearly periodic vowel, the spectrum shows evenly spaced lines — harmonics. If F0 is 150 Hz, they sit near 150, 300, 450, 600 Hz…

The vocal tract boosts some regions. Those peaks are F1, F2, F3… formants. They follow tract shape, and they are a main cue for vowels.

The key distinction: F0 is not “formant zero”, and F1 is not the first harmonic. Both are measured in hertz, but they describe different mechanisms.

Try this model · F1 730 · F2 1090 · F3 2440 Hz

A working body map: F1 often tracks tongue height and opening; F2 often tracks front vs back. Lip rounding and tract length also matter — one number never tells you the whole mouth.

03 · Spectrogram

One sound: waveform → spectrogram → F0.

Speech keeps changing. Cut the wave into overlapping windows, take a spectrum of each, and line those spectra up in time. That collage is a spectrogram.

  • x-axis: time.
  • y-axis: frequency.
  • Darker or stronger colour: more energy near that time and frequency.

Waveform, spectrogram, and playback are the same samples: vowels are sawtooth through formant filters; s is high-passed noise. The spectrogram is a short-time Fourier transform of that clip. F0 is the value we set, not a tracker output.

  1. Look at the vowels. a, i, and u light up different frequency regions, but F0 stays 150 Hz. Vowel change is not pitch change.
  2. Look at s. High frequencies are busy; F0 is empty. There is sound, but no stable voiced pulse train.
  3. Look at silence. Waveform and spectrogram both go quiet. That is different from “no F0, but friction.”
  4. Switch the window. 30 ms separates harmonics; 5 ms shows fast changes in time.

Longer windows separate nearby frequencies; shorter windows locate the moment something changed. The same recording can make spectrograms that look different and are useful for different jobs.

A lot of energy high on the spectrogram does not mean the speaker’s pitch is high. s is the counterexample. Vowel harmonics can sit at several kHz while F0 is only 100–200 Hz.

F0 on the plot is an estimate. Shift a voiced bit of wave and look for a repeat. If 5 ms later looks similar, 200 Hz is a candidate. The tracker can also grab a harmonic and print 200 as 100.

04 · Pitch trace

The same 啊, three F0 paths.

How fast the waveform repeats becomes how high the line sits. Shorter period → higher F0 → usually heard as higher pitch.

The same one-second vowel model at the same overall level. The line shows the F0 set by the synthesiser.

In the raw wave, cycles get shorter; on the F0 plot, the number goes up; in the ear, pitch usually rises.

Strictly, F0 is an acoustic quantity and pitch is a percept. They track each other for ordinary voiced speech, but they are not the same word.

A rising 啊 may sound like a question; a falling 啊 may sound like confirmation. That contrast is useful, but a pitch curve alone does not reveal a speaker’s state of mind.

People hear intonation with several cues at once:

  • Pitch path: rise, fall, level, and where it turns
  • Range: higher, lower, or more moved than this speaker’s usual
  • Duration and pauses: which syllable stretches, where it stops
  • Loudness and voice quality: stronger, breathier, tighter, creakier
  • Wording and context: answering, correcting, pushing back, or continuing

Xiao Wang bought black tea. — who

Xiao Wang bought black tea. — did what

Xiao Wang bought black tea. — bought what

In Mandarin, lexical tone and sentence intonation share the same F0 line. A final light tone, or where the focus sits, will change the curve you see. “Questions must rise, statements must fall” does not hold.

Read the recording

Notice the change without over-interpreting it.

When you inspect a recording, separate what the plot shows, the most likely explanation, and the conclusion the data cannot support on its own.

What you seeConsider firstDon’t conclude
Waveform looks biggerThe recorded signal is strongerThe speaker is trying harder or more excited
F0 is higher overallThis stretch repeats fasterThe speaker is more nervous
F0 breaks in the middleVoiceless, silence, irregular voice, or a tracker missThere is definitely no sound
F0 suddenly doubles or halvesCheck period tracking firstA real jump definitely happened
More high-frequency energyFriction, harmonics, or timbre changePitch went up

The recording chain moves these plots too: distance, gain, automatic level control, noise reduction, room. Keep the setup still when you compare.

Especially loudness: a file’s digital amplitude is not dB SPL unless the chain was calibrated.

A two-second phone test. Keep distance the same:

If you can explain the first four, you can read a plot. The fifth is where those cues meet real intent.

Check

Think, then tap.

Two vowels can share the same F0, and high-frequency energy on a spectrogram does not automatically mean high pitch.

1. You keep F0 at 150 Hz and switch 啊 to 衣. What should change most?

2. A waveform repeats every 5 ms. What is the frequency?

3. The spectrogram is dark up at 4 kHz. Does that mean pitch is high?

4. Is F0 the same thing as F1?

5. The waveform looks bigger this time. Safe conclusion?

Once you can read the signal, compare your pitch in Jyutone

You now know how F0 differs from vowel quality—and why a curve alone cannot reveal intent. Record a phrase in the app and compare your pitch contour with the reference.