Consonance/Dissonance and the Critical Band

Why Some Sounds are More Pleasant than Others

There is something satisfying about musical sounds that blend and harmonize. However, some combinations of sounds are unpleasant.

This section fo the course beirfly examines some of the characteristics of our ear/brain hearing system in order to explain why some basic sounds sound pleasant, and some sound raucous and unpleasant.

Music involves such highly complex sounds that trying to analyze just what is affecting what on is very difficult.
So, in order to simplify the issues, we use pure tones to probe into the question of why some tonal combinations sound good and some do not. We shall base this exercise on a tone of 500 Hertz at a comfortable listening level: AUDIO

Now listen to a second tone, an identical 500 Hertz of the same amplitude: (make sure your playback sysem is loud enough to hear the differences) AUDIO

Notice that there is an increase in loudness. Thi is because the two sine waves have a time relationship described as being "in phase." (see diagram).

Because the two tones are in phase, they add constructively (2 +'s make a +) and the resulting combination has twice the amplitude of either single tone hear alone.

Adding two waves of the same frequency, amplitude and phase produces a 6 decibel increase in signal level. Refer back to the loudness section of the course if you're unsure why.
Now, listen to what happens if the same two 500 Hertz sine waves are combined "out of phase" or in "phase opposition", that is, when one waveform goes positive, the other goes negative and vice versa.

First, one signal alone: AUDIO

And now the second tone will be added momentarily and then taken away: AUDIO

That dead spot in the middle was caused by adding the second, equal 500 Hertz tone out of phase. When the two signals are in "phase opposition", one cancels the other and the resultant output is zero.

The previous examples used signals of the same frequency. When two tones of differing frequency are combined, some very interesting things happen that have a direct bearing on our sense of musical sounds. A tone of 500 Hertz added to a tone of 501 Hertz sounds like this: AUDIO

The two tones, only 1 Hz apart, alternately combine in phase and phase opposition to produce a 1 Hz beat.

By holding the 500 Hertz tone constant and changing the frequency of the second tone, the beat frequency can be varied in a regular way: AUDIO

The frequency of the beating is determined by the difference between the frequencies of the two tones which are heard together. Thus, if a tone of either 490 Hertz or 500 Hertz is combined with the 500 Hertz tone, a beat of 10 Hertz is produced.

As the difference between the two tones is increased so that the beat frequency increases to about 20 Hertz, the ear becomes unable to discern the individual beats: AUDIO

Beyond 20 Hertz, a harsh, rattling sound is heard: AUDIO

Note the roughness! It is the basis of what we consider to be unpleasant musical effects, as we shall see later.

The critical band seems to be involved in what we hear wehn two tones which are sounded together. If the two tones are a critical bandwidth apart, they are heard, not as beats or roughness, but as two separate tones.

In the following example, notice the transition from beats, through roughness, to a more pleasant or settled sound as the two combined tones are increasingly separated in frequency: AUDIO

To avoid the region of roughness, and for the ear to separate the two tones, they must be at least a critical bandwidth apart.

When tones are sounded simultaneously, the result may be considered as either pleasant or unpleasant. Another way of describing these sensations is with the terms consonant or dissonant. In a psychoacoustical context, the term "consonance" means tonal, or sensory consonance. This is distinguished from the way musician's use of the word, which is dependent on Helmholtz frequency ratios, music theory and is in fact ultimately culturally defined. In this contecxt we are referring to a human perception. Of course, in an ultimate sense, the two definitions are related.

NB. The audibility of these roughness effects does NOT depend upon musical training.

Now consider the same beating effect between two tones in terms of their separation in fractions of a critical bandwidth. As we have seen, at 500 Hertz the critical band is somewhere around 100 Hertz wide. Let us define 100 Hertz as "unity" and consider fractions of that band.

When two tones have zero separation, they sound as a single tone which has maximum consonance and minimum dissonance. AUDIO

That is point number #1 on our curve.

And now, here are the two tones separated by about 1/4 of a critical bandwidth:

This is the least consonant, or the most dissonant, sound.

When the two tones are separated by about one-half a critical bandwidth, the roughness has partially receded to give us about 40 percent of full consonance: AUDIO

At a separation of about 3/4s of a critical bandwidth, a further improvement in consonance, to about 80 percent, is noted: AUDIO

When two tones separated by a full critical bandwidth are combined, 100 percent consonance results: AUDIO AUDIO(sgi)

This puts the effects of combining two tones into perspective:
If their frequencies are separated by a critical bandwidth, or more, the effect is consonant.
 If their frequencies are separated by less than the critical band, varying degrees of dissonance is heard.
The most dissonant/least consonant spacing of two tones is about 1/4 of a critical bandwidth.

When two areas on the basilar membrane which are close to each other are stimulated simultaneously, a interference or roughness is head and we call that roughness tonal, or sensory disssonance.