Digital Signal Processing Reference
In-Depth Information
Fig. 6.3
The pitch helix as
presented in [
45
]. The height
axis is associated with a note's
frequency and the rotation
correspondsto the pitch class
of a note. Here, B
n
is one
octave below B
n
+
1
[
46
]
typically with 15
110 (corresponding to the notes C2-B9) and therefore
covering 96 semitones (8 octaves). In order to overcome 'tape speed variation' or
intentionally different tunings, pitch correction can be applied as was suggested
in [
47
]: a long term frequency analysis computes the prominent frequency
f
p
and
determines a factor
c
≤
i
≤
f
p
f
r
c
=
(6.63)
with
1
.
f
p
f
i
−
f
r
=
arg min
f
i
(6.64)
Next, all semitones
f
i
are multiplied with this correction factor
c
for pitch adjust-
ment. For mapping of frequencies to the semitones, band-filters with Gaussians
g
i
(
x
)
centred at
f
i
given by
x
−
f
i
f
i
−
2
1
f
i
−
1
e
−
g
i
(
x
)
=
√
2
·
σ
=
0
.
125
(6.65)
2
2
σ
σ
π
can be used. The resulting sub-bands
s
i
are normalised by dividing each one belonging
to the same octave
O
by the sum of these sub-bands according to
s
i
,
O
s
i
,
O
s
i
=
ˆ
s
i
,
O
=
s
i
∈
O
.
(6.66)
