Digital Signal Processing Reference
In-Depth Information
(b)
(c)
(a)
Fig. 11.14
Exemplary results for correlation, basic, and derived features in the circle of fifths [
28
].
a
Correlation results for scale attribute,
b
Correlation results for scale dom attribute,
c
Correlation
results for scale and attribute
shows the correlation results for scale features with a minimum for F# major and
a maximum for G major. Thus, the key a fifth above the correct key C would be
assumed. This can be avoided by addition of the dominant to enlarge the search
mask to the two highest neighbouring values. In Fig.
11.14
b the maximum value for
the feature
'scale dominant'
is likewise shifted from G major to C major leading
to the correct key assumption. Finally, in Fig.
11.14
c the feature
'scale cadence'
is
visualised: In the example the addition of the fifth above and below help to cope with
the light variations of notes interfering in the feature
'scale'
.
In the case of distinction between 24 keys those feature types able to distinguish
musical modes are concatenated to a 24-dimensional vector
for correlation. These
are PTR major and minor features and dominant and cadence features. The key is
determined accordingly by retrieving the semitone
k
that maximises correlation in
analogy to Eq. (
11.29
), yet. However, the 24-dimensional feature vector
κ
κ
with
p
T
T
T
p
T
maj
T
p
T
maj
p
T
min
p
T
min
p
T
min
κ
∈
maj
,
,
dom
,
,
cad
,
(11.31)
,
,
dom
,
,
cad
is used with an according 24-dimensional correlation template vector
t
cor
(
k
)
created
using the previous
t
cor
(
)
by appending 12 zero-entries at the end or beginning for
major or minor keys, respectively. Thus, in the example in Eq. (
11.30
), 12 zero-entries
would be appended at the end.
k
11.4.4 Data-Driven Analysis
Besides the knowledge-based method, a data-driven one based on SVMs with poly-
nomial Kernel, SMO, and a one-versus-one multi-class discrimination strategy [
122
]
is now described. This approach allows to combine all feature types in a super-vector
v
. Given the 13 feature types with 12 features, each, its dimension resembles 156.
The vector is shown in Eq. (
11.32
):
