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We ran an experiment in which subjects heard a succession of high and
low tones, like beep..boop... beep..boop... played over
headphones. Subjects were asked to repeat a phrase like Beg for a
duck along with the beep patterns such that beg was aligned
with the high tone (the beep) and duck with the
target phase, low tone
(or boop). The first example here is an easy one to do
since the boop occurs exactly halfway between the beeps.
The second example has the boop at 0.4.
Because we
could control exactly where the low tone fell in the
beep-to-beep cycle, we were effectively asking them to
place a beat at an arbitrary phase of the phase repetitions cycle.
You can try this task yourself by clicking on one of the buttons to the
right. You will hear a sample stimulus. Try and align beg and
duck with the high and low tones, respectively.
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Metronome Pattern, Easy
Metronome Pattern, Hard
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| In the panel below you can see the result from one
typical subject. This subject took part in 90 trials (where each
trial is a whole series of productions of the phrase produced on a
single exhaling breath). On each trial a target phase was randomly
selected from the range 0.3 to 0.7, so that any number in that range
was equally likely to occur. For each trial we measured the average
phase produced, and the distribution of these 90 values is shown. Now
the targets were selected so that any number between 0.3 and 0.7 was
equally likely to occur. If the subjects could do just what we told them,
then all the columns in the figure should be about the same height.
Instead, you can see that certain phases are much
more likely to be produced than others. The three peaks in the
histogram correspond to three distinct patterns which are regularly
produced. Any other pattern is unstable and dispreferred. These
three patterns are illustrated below using musical notation (the
sample phrase here is Beg for a dime).
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Sample
histogram of observed phases
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Although the target phases were distributed evenly across
the X axis (the phase axis), subjects produced beats only in three
regions along the phase axis, near 1/2, 1/2 and 2/3. This is
remarkable and implies a very severe constraint either on their
ability to perceive these phase lags, or to produce them.
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This result, which we have replicated several times,
suggests that the laws of harmonic timing -- the same laws that make
strings oscillate at a fundamental frequency and only at integral
multiples of that frequency. Thus, there may be three preferred
(apparently GREATLY preferred) phase angles for the second stress
syllable of these phrases. Those three are easily expressed with
musical notation as shown at right. Yes, you might have expected that
our subjects, several of whom were highly skilled musicians (from the
IU School of Music), but no matter what target phase we gave them
(between 0.3 and 0.7), they gave us only these 3 phases as apparent targets.
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The Three Preferred Patterns
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So the beats that correspond to syllable onsets
cannot fall anywhere (at least if people repeat a phrase over and
over), but at temporal locations suggested by a simple harmonic model
with preferences for simple fractions. We have demonstrated
objectively that, given a few typical constraints, there is almost
unavoidable rhythm in speech.
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