Sound demonstrations of the pitch perception phenomena reported in

Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

Physical Review Letters 82, 5389-5392, (1999)

Julyan H. E. Cartwright1, Diego L. González2 and Oreste Piro3

     1Instituto Andaluz de Ciencias de la Tierra, IACT (CSIC-UGR), E-18071 Granada, Spain
     2Istituto Lamel, CNR, I-40129 Bologna, Italy
     3Institut Mediterrani d'Estudis Avançats, IMEDEA (CSIC-UIB), E-07071 Palma de Mallorca, Spain


 
 


 
Note: The sounds of these demonstrations should be listened to at low volume to minimize distortion and production of combination tones that might interfere with, or even mask, the phenomena we are attempting to illustrate here.
 

Sound files demonstrating the phenomena described in Fig. 1

Most of these demonstrations are made for pitches corresponding to a pure sinusoidal tone of 200 Hz.
 
 
 

 
 
 
 
 

Sound of a triangular wave
(harmonic components decaying as 1/n)
 

Missing Fundamental:

Sound of the triangular wave with the first five harmonic components removed.

This sequence compares the pitches of the triangular wave and the signal with the first five harmonic components missing.

And this one compares the pitch of the complex with the pitch of a pure tone at the missing fundamental frequency.
 

Pitch Shift:

This sequence is to compare the pitch of the same complex with and without pitch shift.
 
 
 
 
 
 
 
 
 

 

 
 
 
 
 
 
 

 Sound files demonstrating the match between theory and experiment displayed in Fig. 2

 

 
 







The following is a set of sequences comparing the pitch of a complex sound composed of a central component at the frecuency f and two lateral ones separated by g, to the pitch of a pure tone of frequency equal to the pitch predicted by our theory.  The intercomponent spacing g is 200 Hz in all cases. The sequences are arranged such that the first sound is the complex and the second is the pure tone of pitch predicted by our theory.

Examples keeping k fixed (k = 6):

  1. f = 1112 Hz
  2. f = 1145 Hz
  3. f = 1185 Hz
  4. f = 1215 Hz
  5. f = 1225 Hz
  6. f = 1255 Hz
  7. f = 1350 Hz
The following example shows the ambiguity of the pitch of a complex implied in its k dependence. The same complex (f = 1487 Hz) is compared to the pitch predicted with two different values of k:
  1. f = 1487 Hz, k = 6
  2. f = 1487 Hz, k = 7
An example for k = 8:
  1. f = 1687 Hz, k = 8
Finally a melody (Beethoven's Ode to Joy theme) played using several combinations of the effects described above.
 
  1. Ode to Joy theme played with single pure tones.
  2. Ode to Joy theme played with a three-frequency complex with g corresponding to each of the notes, but with a central frequency f six times higher implying that the first four harmonics are suppressed (missing fundamental perception effect).
  3. Ode to Joy theme played with a complex with g shifted a constant amount (20 Hz) from the actual notes, but the frequency taken so as to correct the pitch of each note according to the predictions of our theory.
  4. Ode to Joy theme played with g and k taken at random but f chosen to achieve the intended pitch of each note. Notice that even in this extreme case the melody is still recognizable.
  5. Ode to Joy theme played with arbitrary frequencies but chosen just to require g's in the neighborhood of 200 Hz to compensate the pitch of each note.