Pitch Perception

From Auditory Demonstrations CD (see discussion here):

• Circularity in PItch Judgement

• Stretched and Compressed Scales;

• Strike Note of a Chime

• Cancelled Harmonics

• Linear and Logarithmic Tone Scales (or Logarithmic and Linear Frequency Scales)

• Pitch of Complex Tones

• Difference Limenof JND

• Virtual Pitch

• Analytic vs. Synthetic Pitch (here, the pitch may seem to go up, or it may seem to go down, depending on whether you are listening analytically or synthetically)

• Scales with Repetition Pitch (2)

• Strike note of a chime

• Pitch paradox

 

Links

• Chris Darwin's lectures including discussions of some non-autocorrelation theories of pitch perception:http://www.lifesci.sussex.ac.uk/home/Chris_Darwin/PerMuSo/

• A contribution based on non-autocorrelatipn ideas by Terhardt and Seewan.

• Sensitivity to frequency: Just Noticeable Differences of three notes * dead link* - a test of your hearing. Test your sensitivity to frequency differences!

• PHYSCLIPS Intro to Pitch

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Helholtz's Blunder

Yes, Helmholtz. The almost Aristotelian authority on sound. On many auditory topics, his authority has far too much incluence over historic and many modern practioners. His most greivous error, astonishingly central to much of his book, "On the Sensations of Tone", is to blur the distinction between a pure sinusoidal partial, and a "tone", which can be a complex tone like humming, with many partials.or a tone with a definite pitch but missing any partial at that pitch. This sloppiness helped Helmholtz maintain his delusion that "missing fundmentals" or what we now call residue pitch are due to nonlinear vibrations of the ear, causing it to actually vibrate at the frequency of the missing pitch. But, pardon the all caps PITCH IS NOT PARTIAL. A siusoidal vibration, i.e. a partial, produced nonlinearly in the ear or arriving from the outside, would sound just like a partial should sound. Again, pardon the all caps: BUT WHEN WE HEAR A RESIDUE PITCH, WE DO NOT HEAR THE SOUND OF A PARTIAL AT THE FREQUENCY OF THE PITCH, BUT SOMETHING QUITE DIFFERENT: WE HEAR THE SENSATION WE CALL PITCH. Therefore no nonlinear mechanism is needed producing a partial that is not there in the first place: it isn't there if it is missing in the sound arriving at the ear, and the ear does not manufacture it either, for if it did we'd hear the sound of a partial. Pich is a synthetic sensation, an executive summary of sound. Unless only on partial is present in a sound, the sensation of pitch and the sound of a partial are different.

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Helmholtz's translator was so frustrated with Helmholtz's sloppiness regarding what should have been the most carfully used word in his book, namely "tone," that he put in a footnote:

"Even Prof. Helmholtz himself has not succeeded in using his word 'Ton' [tone] consistently for a simple tone only..." (i.e. a simple partial) ... (John Ellis, Helmholtz's translator).

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Now to illustrate the point, live and in your ears, with this sound file, which first plays a pure partial at the frequency of what will be the missing fundamental or residue pitch of the following complex tone. Listen carefully: the pitch you hear is that of the preceding pure partial, BUT YOU DO NOT HEAR THE SOUND OF THE PURE PARTIAL AT ALL.

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Project: Analytic vs. Synthetic hearing

People with training can listen holistically to tones, and they can also parse the same tone analytically, perhaps discerning more than one pitch if present (this is itself a judgement call, however), and going down to the level of hearing individual partials ringing out of a complex tone.

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Fortunately no training is required if a simple trick is employed: play the tone, then deliberately oscillate the strength of the group of partials corresponding to a unique pitch, or oscillate an individual partial. It will jump out at you, and even when you restore it to its original strength most people are not able to shut the "analytic" parsing off for a while: you hear the partial or pitch ringing out and you might complain that it has not been restored yet to its original strength!

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This is easy to try in Paul Falstad's Fourier. Set up a sawtooth wave in playback, say around 200 Hz, and listen to it. Then grab the e.g. 600 Hz partial "stalk" and raise it in strength. It will stand out. Now lower it back to where it was - you will easily be able to pick it out as an individual partial in the midst of the complex tone. You can most accurately judge when the partial is back to where it began by monitoring the shape of the sawtooth. You are listening analytically!

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Residue pitch in a duet

A plausible note from a reed instrument is repeated a fifth above (a factor 3/2 higher in frequency); then the two are combined in a duet. The series f, 2f, 3f, ... of the first, and 3/2 f, 3f, 9/2 f, 6 f, ... of the second note together make of course f, 3/2 f, 2f, 3f, 4f, 9/2 f,.. that formally is a subset of partials based on fundamental of 1/2 f. Of course, some upper partials are missing, and others are shared by both notes, but still the residue pitch is 1/2 f. Do you hear it when the duet is played (klick below)? Last, a note is played down a octave at 1/2 f for comparison.

Also below is Beethoven's "Ode to Joy" played on a synthesizer, but the first five partials of each note are missing. As weird as the timbre is, the tune and pitch is clearly still the same.