1. A.Diederich– International University Bremen – USC – MMM – Spring 5 1 The Perception of Frequency cont'd

2. A.Diederich– International University Bremen – USC – MMM – Spring 5 2 Combination tones  What happens with our tone sensation when the frequency of the variable tone f 2 increases beyond the critical band, while f 1 is kept constant?  Combination tones are additional pitch sensations that appear when two pure tones of frequencies f 1 and f 2 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.

3. A.Diederich– International University Bremen – USC – MMM – Spring 5 3  The most easily identifiable combination tone at high intensity level is one whose frequency is given by the difference of the component frequencies f C1 = f 2 – f 1  This is called difference tone.  When f 2 is an octave above f 1, f C1 = 2f 1 – f 1 = f 1. The difference tone coincides with the lower component f 1.  When f 2 is halfway between f 1 and 2f 1, i.e., f 2 = 3/2 f 1 (a musical interval called the fifth), the difference tone has a frequency f C1 = 3/2 f 1 – f 1 = ½ f 1 (one octave below that of f 1 )

4. A.Diederich– International University Bremen – USC – MMM – Spring 5 4  Other combination tones that are most easily identified:  f C2 = 2 f 1 – f 2  f C3 = 3 f 1 – 2f 2

5. A.Diederich– International University Bremen – USC – MMM – Spring 5 5 Frequencies of combination tones f C1, f C2, f C3, evoked by two-tone superposition (f 1, f 2 )

6. A.Diederich– International University Bremen – USC – MMM – Spring 5 6 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)

7. A.Diederich– International University Bremen – USC – MMM – Spring 5 7  "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

8. A.Diederich– International University Bremen – USC – MMM – Spring 5 8 Beats of mistuned consonances  f 2 = 2f 1 +   Beat frequency is equal to   Called second order beats of subjective beats  It is a result of neural processing

9. A.Diederich– International University Bremen – USC – MMM – Spring 5 9  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 f 2 = 2f 1 +  the mutual phase relationship will change continuously with time  The ear is sensitive to a slow changing phase difference between two tones.

10. A.Diederich– International University Bremen – USC – MMM – Spring 5 10 (A) Mistuned unison, (B) Mistuned octave

11. A.Diederich– International University Bremen – USC – MMM – Spring 5 11 Fundament tracking and missing fundamental f 2 = 3/2f 1 pattern repeats after  0  1 period of the lower pitch tone repetition rate f 0 =1/  0 =1/2 f 1

12. A.Diederich– International University Bremen – USC – MMM – Spring 5 12 Two pure tones Repetition rate f 2 = 3/2 f 1 f 0 =1/2 f 1 f 2 = 4/3 f 1 f 0 = 1/3 f 1 f 2 = 5/4 f 1 f 0 = 1/4 f 1 f 2 = 6/5 f 1 f 0 = 1/5 f 1  Our auditory system is sensitive to these repetition rates.  The perception of the repetition rate is called fundamental tracking.  The tone of frequency f 0 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

13. A.Diederich– International University Bremen – USC – MMM – Spring 5 13  The frequency f 0 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.

14. A.Diederich– International University Bremen – USC – MMM – Spring 5 14  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.

15. A.Diederich– International University Bremen – USC – MMM – Spring 5 15  The individual components of frequency 2f 0, 3f 0, 4f 0, 5f 0, …, etc. are called upper harmonics of the fundamental frequency f 0.  Any two successive tones of the upper harmonic series form a pair with the same repetition rate of fundamental frequency f 0.  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!

16. A.Diederich– International University Bremen – USC – MMM – Spring 5 16 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.

17. A.Diederich– International University Bremen – USC – MMM – Spring 5 17 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.

18. A.Diederich– International University Bremen – USC – MMM – Spring 5 18

19. A.Diederich– International University Bremen – USC – MMM – Spring 5 19

20. A.Diederich– International University Bremen – USC – MMM – Spring 5 20

21. A.Diederich– International University Bremen – USC – MMM – Spring 5 21 Tone chroma Notes with the same letters have the same tone chroma. 1 octave