Extracting Melodic Countour Using Wavelet-based Multi-resolution Analysis
Tetsuro Kitahara (Nihon Univ., Japan) and Masaki Matsubara (Univ. of Tsukuba, Japan)
Introduction
To establish a theory of non-experts’ melody cognition
Non-experts don’t listen to individual notes separately
Our hypothesis
They grasp a whole melody as a single stream
We explore a melody representation that is:
Non-notewise Hierarchical
Our final goal
GTTM vs our approachGTTM Our approach
Pitch trajectory
...
Melody reduction means:Reducing less important notes
Reducing the resolution of the melody representation
2.5
-2.5
0.25 -0.125
7.5 2.5 7.5
DWT
IDWT
Pitch trajectory
Distance between contour trees
0.0
-2.5
0.20 -0.175
0.0 0.0 0.00.0
-2.5
0.25 -0.125
0.0 0.0 0.0
Root mean square of each element’s difference
But normalized by the num. of elements for each depth
Application 1: Repetetion detection1) Caclulate distances between subtrees
2) Detect low-distance subtree pairs
Sq. dist.=4.27
Sq. dist.=326.63
Sq. dist.=68.41
Sq. dist.=0.78 Sq. dist.=9.13
and
Method
Target melody
Result
Squared distances of repeated phrases are small
How similar phrases are regarded as repetition can becontrolled by the fineness of the contour.
Application 2: Cognitive(?) melodic similarity
Piano sonata K.331 (first 8 measures)
Method Compare ours with GTTM-based method
Target melodies 12 Vars. on “Ah, vous dirai-je, maman”
Dist. between Theme and each Var.
Obtained contours
Apply rules
Thresholding
Time-spantree
0.0
-2.5
0.25 -0.125
0.0 0.0 0.0
Thresholding
Melodic contour
Contour tree
T1 T2
(Continued from buttom left)
(Dis)similarities
Distances (dissimilarities)
Similarities (-2.0 to 2.0)Higher but weak
MatsubaraICMC 2014
Hirata CMMR 2013
Mismatch. Sound like two streams
In the future...
Real-time analysis
Stream segregation
Integration with schema-based one
Use of RNN-based melody prediction
...and a lot