Digital Signal Processing Reference
In-Depth Information
(a)
(b)
(c)
(d)
Fig. 6.5
Pattern for the basic feature types. The vertical axis label “validation” was taken over for
all types from Krumhansl's Probe Tone Ratings, where human listeners rated how well a heard note
fits a previously heard chord-progression and thus reflects the 'weight' of a semitone within a scale
[
44
].
a
Scale based pattern
b
chord based pattern
c
PTR-major pattern
d
PTR-minor pattern
to the CHROMA vector by correlation. In doing so, one obtains the pattern shown
in Fig.
6.5
a by labelling the notes appearing in the scale beginning with the root as
semitone 1. In this 'hard' template the seven notes associated to the key are set to 1
and the remaining five notes outside the key are set to 0. Based on this pattern, one can
construct an according template for each root note. For the feature type scale
s
and
the root note C one obtains the following template
t
s
(
(the index of the templates
abbreviates the respective feature in the ongoing, and the root note is underlined in
the vectors that always start with A as in (
6.67
)):
C
)
)
=
1
0
T
t
s
(
C
,
0
,
1
,
1
,
0
,
1
,
0
,
1
,
1
,
0
,
1
,
.
(6.69)
To create corresponding templates for other keys, the same pattern is simply shifted
(i.e., 'transposed') by multiplication with the shifting matrix
M
(
6.70
). The shifting
matrix rotates the template vector and keeps the pattern but starts on base of the target
root.
⎡
⎣
⎤
⎦
000
...
00 1
100
00 0
M
=
(6.70)
.
.
.
.
.
000
...
01 0
For the creation of the particular templates
t
s
(
k
)
with
k
={
A
,
A
#
,...,
G
#
}
,the
basic template of A major
t
s
(
A
)
is used which is then shifted by the matrix
M
to the
respective root:
M
3
t
s
(
t
s
(
C
)
=
A
).
(6.71)
