Extracting Melodic Contour Using Wavelet-based Multi-resolution Analysis

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