Digital Signal Processing Reference
In-Depth Information
To build the scale based feature vector
s
element-wise, the CHROMA vector
x
is
next correlated with the particular key pattern
t
s
(
)
k
:
⎡
⎤
⎡
⎤
x
T
t
s
(
x
T
t
s
(
A
)
A
)
⎣
⎦
=
⎣
⎦
.
x
T
t
s
(
x
T
M t
s
(
A
#
)
A
)
s
=
(6.72)
.
x
T
t
s
(
.
x
T
M
11
t
s
(
G
#
)
A
)
This operation is repeated for every root and the derived pattern by multiplying the
template with the shifting matrix
M
. This provides a 'confidence' for each of the 12
possible keys, which reflects the intensity and at the same time the probability of the
respective key.
6.2.2.5 Chord-based
For the next type of CHROMA-based features, only a key's main four chords' notes
are considered. These chords are: tonic, sub-dominant, dominant, and the relative
minor chord of the tonic. Again, only notes in the respective key are allowed. Now,
however, these are weighted differently: according to their number of appearance
in the key's main four chords. Obviously, other definitions can be thought of, such
as including the relative minor chords of the sub-dominant and dominant. Again, a
12 dimensional 'chord vector'
c
is created by repeated correlation of the CHROMA
vector
x
with accordingly shifted chord templates
t
c
(
)
k
for each root
k
(exemplified
is the root C):
)
=
2
0
T
t
c
(
C
,
0
,
1
,
3
,
0
,
1
,
0
,
2
,
1
,
0
,
2
,
.
(6.73)
In [
52
] a similar method is suggested. Their approach bases on templates related
to the chord by use of the histogram of semi-tones and additional overlay of all
triads belonging to a scale. These templates also tend to have values close to zero at
semi-tones outside the scale.
6.2.2.6 PTR Major/Minor-Based
Alternatively to these music theory motivated templates, one can consider templates
based on human perception, such as the Probe Tone Ratings (PTR) [
53
]. PTR were
collected in listening experiments as follows: A chord-progression within a given
key was played, then a note was presented to the participating subjects. These had
to rate how well the note fits the progression. The observed validations show good
correlation with hard templates consisting exclusively of semi-tones belonging to the
scale and thus can be considered as histogram of the intensities of semi-tones within
a key. As an advantage, PTR templates allow scale external semi-tones such as 'blue
notes'. Fig.
6.5
c, d depict the PTR templates for major and minor keys starting from
