6. Beats and Just Noticeable Difference

Main Ideas

Just Noticeable Difference

When two tones begin at the same frequency, they sound like one note. A small increase in one tone’s frequency may initially be too slight to detect. The smallest change a listener can perceive is called the just noticeable difference (JND); the subtitles also call it a “subtle difference.”

The JND varies with register. It is roughly a tenth of a semitone in the middle register, increasing to about half a semitone in the low bass. Until the difference is large enough to distinguish, listeners may hear one pitch rather than two.

Beats

Even when two nearby tones are perceived as one pitch, their combined sound can fluctuate in loudness. These repeated rises and falls are called beats, producing a “wah-wah” effect.

For example:

• Combining 500 Hz and 501 Hz still sounds like a single pitch, but with a slow beat.
• With 500 Hz and 510 Hz, the perceived pitch is around 505 Hz, while the sound’s amplitude rises and falls 10 times per second.

The beat rate equals the difference between the two frequencies.

Why Beats Occur

The waves of two tones repeatedly move in and out of phase. The presenter compares this to two people walking at the same overall speed but taking steps at different rates: they fall out of step, then periodically line up again. Similarly, the sound waves alternately reinforce and cancel each other, changing the combined amplitude.

From Beats to Roughness and Separate Pitches

As the frequency difference grows, the beats become faster. Eventually, the fluctuations are too rapid to be heard as distinct beats, and the sound instead seems rough or buzzy. Beyond the frequency-discrimination limit, listeners hear two separate notes.

The stated limit depends on the sound:

• For pure sine waves, it may be one or two semitones at low frequencies and up to three semitones at high frequencies.
• More complex sounds can be distinguished at smaller intervals, which helps explain why piano notes a semitone apart are heard as separate pitches.

The presenter notes that roughness occurs over larger intervals in the bass, contributing to the unpleasant quality of some close intervals in the low register.

Beating in Music

Strong or excessive beating can make notes sound unpleasant or out of tune. Subtle beating, however, can add richness. For example, orchestral violins playing nominally the same note may have small differences in frequency and phase, creating a fuller sound.

This effect is called the chorus effect. It can also be produced electronically, such as with a guitar effects pedal.

Second-Order Beating

A related effect occurs when two tones—such as an octave—are slightly out of tune. Rather than mainly producing changes in loudness, this type of beating produces changes in the waveform that are heard as variations in timbre.

Speakers and Sources Featured

• One unnamed narrator/presenter, explaining the acoustics concepts.
• Illustrative examples mentioned:
  • Tones at 500 Hz, 501 Hz, and 510 Hz
  • Finger-touch analogy
  • Walking-step analogy
  • Bass and regular guitars
  • Piano
  • Orchestral violins
  • Guitar effects pedal