How to describe the shape of a melodic phrase? Scholars have often relied on typologies with a small set of contour types. We question their adequacy: we find no evidence that phrase contours cluster into discrete types, neither in German or Chinese folksongs, nor in Gregorian chant. The test for clustering we propose applies the dist-dip test of multimodality after a UMAP dimensionality reduction. The test correctly identifies clustering in a synthetic dataset, but not in actual phrase contours. These results raise problems for discrete typologies. In particular, type frequencies may be unreliable, as we see with Huron's typology. We also show how a recent finding of four contour shapes may be an artefact of the analysis. Our findings suggest that melodic contour is best seen as a continuous phenomenon.
Figures & tables
Figure 1: Three contour typologies. (A) [ 10 ] divided Lakota songs into five contour classes, each identified by one representative song. (B) [ 1 ] considers all possible orderings of the four boundary pitches: the type 3412 means that the initial note (i.e., 3) is above the final (2). In between, the melody first reaches a higher (4) and then a lower (1) pitch. (C) [ 21 ] considers the ordering of the average pitch on the first, middle, and final parts of a melody.
Figure 2: Tempo distributions of songs of the Maidu and Nuu-chah-nulth. Shown are histograms and kernel density estimates ( kde ). The tempos in Maidu music (A) cluster in multiple groups, suggesting a typology with a slow , medium and possibly fast type—which would not be appropriate for music of the Nuu-chah-nulth (B) .
Figure 3: Preprocessing. All contours are represented as sequences of 50 pitches, sampled from a step curve interpolating the melody (A–B) . Pitch is then standardized in five ways (C) : not at all ( pitch ), by centering to mean 0, by tonicizing or finalizing so that the tonic or final note is 0, or by normalizing so that the range is [0,1] . We add two relative representations (E) : the intervals between consecutive notes and a smooth version thereof. Finally, we compute the cosine contour , here illustrated in 2d (D) . Pairwise distances are computed using Euclidean distance, dtw dissimilarity, or distance in a 10-dimensional umap projection.
Figure 4: The dip-dist test discriminates clustered and unclustered synthetic datasets. (A) Synthetic contours are samples from a Markov process whose parameters are estimated from actual phrase contours. We create a clustered dataset by subsampling contours close to five suitably chosen cluster centers. (B) A two-dimensional umap visualization of the uniform dataset (gray) in which the clustered dataset (colored) is projected. The grid of black contours illustrates that umap organizes the space almost exactly like two-dimensional cosine contours ( “ascendingness” horizontally, “archedness” vertically). The cluster centers (encircled) correspond to distinct shapes. (C) The dip-dist test applies the Hartigans’ dip test on pairwise distances: a multimodal dataset should have a multimodal distribution of pairwise distances. (D) The dist-dip test correctly identifies the clustered dataset as multimodal but only using distances in a ten-dimensional umap embedding. This lower dimensional manifold appears more informative in that it more clearly separates the clusters (E) .
Figure 5: Melodic phrase contours do not cluster. Shown are the distributions of pairwise distances between contours in various conditions. If contours cluster, we expect multimodal distance distributions. We test this using the Hartigans’ dip test and let colors indicate p -values, such that grey distributions are not significantly multimodal ( α=0.05) . Eight different representations (vertically) and two metrics (horizontally) are analyzed: Euclidean distance and the distance in a lower-dimensional umap embedding. The latter successfully discriminates unclustered from clustered synthetic data ( C vs. D ; see also Figure 4 ). However, neither in phrases (A) nor in random segments (B) does the test find clear evidence for clustering.
Figure 6: A tolerance parameter ϵ distorts type frequencies in Huron’s typology. This typology compares the average pitch on a contour’s start, middle, and end, considering two pitches equivalent if their absolute difference is below a tolerance ϵ . The value of ϵ strongly influences the type distribution (A) . We propose to choose the ϵ that divides contours over types as evenly as possible (B) . While a small value ( ϵ=0.2 ) obscures partly horizontal types, a large one ( ϵ=3.0 ) exaggerates it (C) . Shown is a umap projection of aggregate phrase contours for only 5 out of the 9 types. Frequencies of all types are shown as histograms (D-F) .
Figure 7: k-Means centroids reflect cosines. A 2d principal component projection of unclustered synthetic contours is shown, colored according to a (k=4) -means clustering A . A grid of black contours in (A) illustrates how the space is organized, with the first two components essentially measuring ascendingness and concavity. More precisely, the principal components of such data approximate cosines of increasing frequency (B) . The clustering is stable across bootstrapped runs, as shown by the close centroids (crosses in A), and by their similar shapes (C) . The centroids consistently fall close to the principal axes, resulting in ascending, descending, convex and concave shapes—for primarily mathematical, not musical reasons.
Figure 8: Average phrase contours differ across three traditions. The average phrase contours of German folksongs, Gregorian chant, and Chinese folksongs compared to baselines of random melodic segments from the respective corpus (gray). They support the overall tendency for arch- or descending average contours but show interesting differences: the Chinese average is not arch-shaped and, strictly speaking, a counter-example to the melodic arch hypothesis. This illustrates how a continuous approach to contour typology can directly reveal cultural differences.
The vocal music of each language carries a distinctive sonic identity, even without instrumental accompaniment. We ask whether these differences are measurable and traceable to specific phonemes. To tackle this question, we introduce phoneme-conditional analysis, which isolates the acoustic effect of typologically distinctive phonemes by comparing marker syllables against matched non-marker controls within the same song, holding singer, melody, and genre constant. Across nine typologically diverse languages and thousands of songs, we measure effects along five acoustic dimensions. Song-level profiles built from these effects identify the language of an unaccompanied vocal at 85.5% balanced accuracy in a nine-way classification with folds grouped by artist; whether the separability arises by accumulation of the phoneme-local effects themselves is left open. Our findings suggest that phonological structure leaves systematic and measurable traces in how each language is sung.
Hayoon Kim, Kyogu Lee
Music and Audio Research Group, Seoul National University · Department of Intelligence and Information, Seoul National University · AIIS, Seoul National University +1
Computational analysis of music often relies on discrete representations, yet many musical traditions are organized around continuous pitch movement that resists segmentation into note-like units. For such traditions, the discrete units that analysis would build on are not given in advance. We address this gap by learning a vocabulary of local pitch-contour patterns directly from unlabeled audio, using a VQ-VAE that quantizes fixed-length contour segments into a finite codebook. To make the learned tokens stable across segmentation positions and small variations in timing and pitch range, we train the model with a reconstruction objective evaluated under the best alignment among a set of candidate temporal and pitch-domain transformations. Applied to Korean traditional music, the learned tokens recover information about expert-defined sigimsae categories without supervision, and in pansori individual tokens align with the two principal modes, Gyemyeonjo and Ujo, supporting their use as units for corpus-level analysis of contour-centric traditions.
Seonguk Ju, Seola Cho, Sooin Chung +2
Music & Arts Learning (MALer) Lab, Sogang University, South Korea · Graduate School of Culture Technology, KAIST, South Korea
This paper addresses the general problem of extracting music-theoretic and psychological features from symbolically encoded melodies. We review existing melodic feature extraction toolboxes, enumerate their features, and organise them into a common taxonomy. We then describe a new software library that provides implementations of all of these features in a straightforward Python package. We then demonstrate the combined feature set on the Essen Folksong Collection, using the dataset to produce a series of style classification models. These models help us answer key questions about the interpretability and dimensionality of the feature set. Our results show excellent classification accuracy using the full feature set, and promising performance for an eight-dimensional factor-analytic solution that improves the interpretability of the classifier. We distribute our new toolbox as an open-source Python package, melody−features, which can easily be used in various applications within music analysis, music psychology, and music information retrieval.
David M. Whyatt, Peter M. C. Harrison
Centre for Music and Science, Faculty of Music, University of Cambridge, United Kingdom