David Meredith

Gissel Velarde, Tillman Weyde, David Meredith

We present a novel method of classification and segmentation of melodies in symbolic representation. The method is based on filtering pitch as a signal over time with the Haar-wavelet, and we evaluate it on two tasks. The filtered signal corresponds to a single-scale signal ws from the continuous Haar wavelet transform. The melodies are first segmented using local maxima or zero-crossings of w_s. The segments of w_s are then classified using the k-nearest neighbour algorithm with Euclidian and city-block distances. The method proves more effective than using unfiltered pitch signals and Gestalt-based segmentation when used to recognize the parent works of segments from Bach's Two-Part Inventions (BWV 772-786). When used to classify 360 Dutch folk tunes into 26 tune families, the performance of the method is comparable to the use of pitch signals, but not as good as that of string-matching methods based on multiple features.

Gissel Velarde, Tillman Weyde, David Meredith

The aim of this study is to evaluate a machine-learning method in which symbolic representations of folk songs are segmented and classified into tune families with Haar-wavelet filtering. The method is compared with previously proposed Gestalt-based method. Melodies are represented as discrete symbolic pitch-time signals. We apply the continuous wavelet transform (CWT) with the Haar wavelet at specific scales, obtaining filtered versions of melodies emphasizing their information at particular time-scales. We use the filtered signal for representation and segmentation, using the wavelet coefficients' local maxima to indicate local boundaries and classify segments by means of k-nearest neighbours based on standard vector-metrics (Euclidean, cityblock), and compare the results to a Gestalt-based segmentation method and metrics applied directly to the pitch signal. We found that the wavelet based segmentation and wavelet-filtering of the pitch signal lead to better classification accuracy in cross-validated evaluation when the time-scale and other parameters are optimized.

Emmanuel Deruty, David Meredith, Maarten Grachten et al.

Aims. This study suggests that the use of multiple perceived pitches arising from a single harmonic complex tone is an active and intentional feature of contemporary popular music. The phenomenon is illustrated through examples drawn from the work of electronic artist Vitalic and others. Methods. Two listening tests were conducted: (1) evaluation of the number of simultaneous pitches perceived from single harmonic tones, and (2) manual pitch transcription of sequences of harmonic tones. Relationships between signal characteristics and pitch perception were then analyzed. Results. The synthetic harmonic tones found in the musical sequences under study were observed to transmit more perceived pitches than their acoustic counterparts, with significant variation across listeners. Multiple ambiguous pitches were associated with tone properties such as prominent upper partials and particular autocorrelation profiles. Conclusions. Harmonic tones in a context of contemporary popular music can, in general, convey several ambiguous pitches. The set of perceived pitches depends on both the listener and the listening conditions.

David Meredith

We present a polynomial-time algorithm that discovers all maximal patterns in a point set, $D\subset\mathbb{R}^k$, that are related by transformations in a user-specified class, $F$, of bijections over $\mathbb{R}^k$. We also present a second algorithm that discovers the set of occurrences for each of these maximal patterns and then uses compact encodings of these occurrence sets to compute a losslessly compressed encoding of the input point set. This encoding takes the form of a set of pairs, $E=\left\lbrace\left\langle P_1, T_1\right\rangle,\left\langle P_2, T_2\right\rangle,\ldots\left\langle P_{\ell}, T_{\ell}\right\rangle\right\rbrace$, where each $\langle P_i,T_i\rangle$ consists of a maximal pattern, $P_i\subseteq D$, and a set, $T_i\subset F$, of transformations that map $P_i$ onto other subsets of $D$. Each transformation is encoded by a vector of real values that uniquely identifies it within $F$ and the length of this vector is used as a measure of the complexity of $F$. We evaluate the new compression algorithm with three transformation classes of differing complexity, on the task of classifying folk-song melodies into tune families. The most complex of the classes tested includes all combinations of the musical transformations of transposition, inversion, retrograde, augmentation and diminution. We found that broadening the transformation class improved performance on this task. However, it did not, on average, improve compression factor, which may be due to the datasets (in this case, folk-song melodies) being too short and simple to benefit from the potentially greater number of pattern relationships that are discoverable with larger transformation classes.

David Meredith

We introduce two algorithms, RECURSIA and RRT, designed to increase the compression factor achievable using point-set cover algorithms based on the SIA and SIATEC pattern discovery algorithms. SIA computes the maximal translatable patterns (MTPs) in a point set, while SIATEC computes the translational equivalence class (TEC) of every MTP in a point set, where the TEC of an MTP is the set of translationally invariant occurrences of that MTP in the point set. In its output, SIATEC encodes each MTP TEC as a pair, <P,V>, where P is the first occurrence of the MTP and V is the set of non-zero vectors that map P onto its other occurrences. RECURSIA recursively applies a TEC cover algorithm to the pattern P, in each TEC, <P,V>, that it discovers. RRT attempts to remove translators from V in each TEC without reducing the total set of points covered by the TEC. When evaluated with COSIATEC, SIATECCompress and Forth's algorithm on the JKU Patterns Development Database, using RECURSIA with or without RRT increased compression factor and recall but reduced precision. Using RRT alone increased compression factor and reduced recall and precision, but had a smaller effect than RECURSIA.