3.1. Fundamental Frequency Estimation
The estimation of the fundamental frequency from a monophonic signal is a widely studied area; see [8] for a review. As
proposed by Rabiner [9], we take advantage of the autocorrelation function to efficiently estimate the f0.
3.2. Amplitude estimation
Since we are interested in the evolution of the amplitude
over time, we integrate the signal power over small intervals:
iA+I
a(i) = s n (n)2
n=iA
(2)
where A is the hop size in samples. This parameter is estimated at the same frame rate as f 0(i).
3.3. Perceptive Scaling
The evolution of the sound parameters reflects the performance of a musician while following constraints expressed
perceptively. The Fechner law applies to every sensory organ
and states that the sensation is proportional to the logarithm
of the excitation. For example, we can consider a crescendo
/ decrescendo tone (one of the exercises; see Section 4). In
Figure 3, we can see that the curve of the amplitude of an expert performance follows a linear evolution in the dB scale.
It is therefore convenient to express the parameters using perceptive scales, such as in Figure 2. The amplitude is then
expressed in deciBels. Similarly, the fundamental frequency
is expressed using the Equivalent Regular Bandwith (ERB).
4. EXERCISES
We consider the metrics proposed in [1] to extract some
evaluation criteria from the performance of the saxophonist.
Specifically, we evaluate the ability of the saxophonist to control his air pressure during the performance by considering
the evolution of the pitch and the amplitude while playing
simple notes such as in Figure 1.
viorato
S -" tT|__ tT| ___ tT _ tII
Figure 2. Pitch and amplitude vectors of a long tone
crescendo / decrescendo played by two performers. In double solid line, the performer is an expert and in solid line, the
performer is a mid-level student.
of the frequency parameter will not be perceptible. To cope
with this issue, we consider a standard deviation of the observation vector weighted by the amplitude. This computation is
performed in a sliding fashion, using fixed-size blocks to be
able to compare several performances, see Figure 2.
4.2. Long Tones crescendo / decrescendo
When the instrumentalist performs a long tone crescendo
/decrescendo, the amplitude should start from an amplitude
close to 0, linearly increases to reach a maximum value M at
index m, and linearly decreases to reach an amplitude close
to 0. From the evolution of the amplitude of a partial A, we
compute the piecewise linear evolution L and compare the
analysed evolution against this ideal evolution. Two examples
of the difference between A and its piecewise linear version
L are shown in Figure 3.
80 -: ý-- -1
p
mf f pp-<ff -pp mf
Figure 1. Sample saxophone exercise.
40
- 3
4.1. Straight Tones
When performing a straight tone, the instrumentalist is
requested to produce a sound with constant frequency and
amplitude. To evaluate the quality of its performance, it is
natural to consider the standard deviation of the observations.
However, if the amplitude is very high, a slight deviation
of the fundamental frequency will be perceptively important.
On contrary, if the amplitude is very low, a major deviation
Time s5
Time (s)
Figure 3. Amplitude vector A and piecewise linear vector L
of a partial for two long tones crescendo / decrescendo. The
difference between the two vectors is plotted on the bottom.
382
0
