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A.Diederich– International University Bremen – USC – MMM – Spring 5

The Perception of Frequency cont'd

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Combination tones

What happens with our tone sensation when the frequency of the variable tone f2 increases beyond the critical band, while f1 is kept constant?

Combination tones are additional pitch sensations that appear when two pure tones of frequencies f1 and f2 are sounded together; they are most easily perceived if the latter are of high intensity level.

The additional pitch sensations are not present in the original sound stimulus.

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A.Diederich– International University Bremen – USC – MMM – Spring 5

The most easily identifiable combination tone at high intensity level is one whose frequency is given by the difference of the component frequencies

fC1= f2 – f1

This is called difference tone. When f2 is an octave above f1, fC1 = 2f1 – f1 = f1 . The

difference tone coincides with the lower component f1.

When f2 is halfway between f1 and 2f1, i.e., f2 = 3/2 f1 (a musical interval called the fifth), the difference tone has a frequency fC1 = 3/2 f1 – f1 = ½ f1 (one octave below that of f1)

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Other combination tones that are most easily identified: fC2 = 2 f1 – f2

fC3 = 3 f1 – 2f2

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Frequencies of combination tones fC1, fC2, fC3, evoked by two-tone superposition (f1, f2)

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A.Diederich– International University Bremen – USC – MMM – Spring 5

How are these extra tone sensations generated?

(They are not present in the original sound vibration) There are indeed activated regions on the basilar

membrane at the positions corresponding to the frequencies of the combination tones.

They are thought to be caused by a "nonlinear" distortion of the primary wave form stimulus in the cochlea (see Prof. Oliver's lecture a couple of weeks ago)

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A.Diederich– International University Bremen – USC – MMM – Spring 5

"Fake" combination tones can be generated in electronic organs and low quality hi-fi- amplifiers and speakers.

Apparently this sensation can be created by an electronic organ

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Beats of mistuned consonances

f2 = 2f1 + Beat frequency is equal to Called second order beats of subjective beats It is a result of neural processing

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A.Diederich– International University Bremen – USC – MMM – Spring 5

As long as the octave is perfectly in tune, the phase difference remains constant – our ear does not distinguish one form from the another

When f2 = 2f1 + the mutual phase relationship will change continuously with time

The ear is sensitive to a slow changing phase difference between two tones.

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A.Diederich– International University Bremen – USC – MMM – Spring 5

(A) Mistuned unison, (B) Mistuned octave

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Fundament tracking and missing fundamental

f2 = 3/2f1

pattern repeats after 0

1 period of the lower pitch tone

repetition rate f0 =1/0 =1/2 f1

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Two pure tones

Repetition rate

f2 = 3/2 f1 f0=1/2 f1

f2 = 4/3 f1 f0 = 1/3 f1

f2 = 5/4 f1 f0 = 1/4 f1

f2 = 6/5 f1 f0 = 1/5 f1

Our auditory system is sensitive to these repetition rates.

The perception of the repetition rate is called fundamental tracking.

The tone of frequency f0 is not present as an original component.

This tone is called the missing fundamental.

The corresponding pitch sensation is called periodicity pitch, subjective pitch, residue tone, or virtual pitch

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A.Diederich– International University Bremen – USC – MMM – Spring 5

The frequency f0 is not present in the cochlear fluid oscillation (whereas the combination tones are).

The missing fundamental is perceived even if the two component tones are fed in dichotically, one into each ear.

This indicates that the missing fundamental, or periodicity pitch, must be the result of neural processing at a higher level.

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Subjective pitch detection only works in the lower (but musically most important) frequency range, below about 1500 Hz.

The smaller the interval between the component tones, the more difficult for the auditory system to identify the missing fundamental.

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A.Diederich– International University Bremen – USC – MMM – Spring 5

The individual components of frequency 2f0, 3f0, 4f0, 5f0, …, etc. are called upper harmonics of the fundamental frequency f0.

Any two successive tones of the upper harmonic series form a pair with the same repetition rate of fundamental frequency f0.

All upper harmonics , if sounded together, will produce one single subjective pitch sensation corresponding to f_0 – even if that latter frequency is totally absent in the multitone stimulus!

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Implications for music

Because real musical tones happen to be made up of a superposition of harmonics, fundamental tracking is the auditory mechanism that enables us to assign a unique pitch sensation to a complex tone of a musical instrument.

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A.Diederich– International University Bremen – USC – MMM – Spring 5

The perception of consonance and dissonance

Consonance and dissonance are subjective feelings.

Tonal music of all cultures seems to indicate that the human auditory system posses a sense for certain special frequency intervals – the octave, fifth, fourth, etc.

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A.Diederich– International University Bremen – USC – MMM – Spring 5

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A.Diederich– International University Bremen – USC – MMM – Spring 5

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A.Diederich– International University Bremen – USC – MMM – Spring 5

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A.Diederich– International University Bremen – USC – MMM – Spring 5

Tone chroma

Notes with the same letters have the same tone chroma.

1 octave