Big Chord Data Extraction and Mining

Harmonic progression is one of the cornerstones of tonal music composition and is thereby essential to many musical styles and traditions. Previous studies have shown that musical genres and composers could be discriminated based on chord progressions modeled as chord n-grams. These studies were however conducted on small-scale datasets and using symbolic music transcriptions. In this work, we apply pattern mining techniques to over 200,000 chord progression sequences out of 1,000,000 extracted from the I Like Music (ILM) commercial music audio collection. The ILM collection spans 37 musical genres and includes pieces released between 1907 and 2013. We developed a single program multiple data parallel computing approach whereby audio feature extraction tasks are split up and run simultaneously on multiple cores. An audio-based chord recognition model (Vamp plugin Chordino) was used to extract the chord progressions from the ILM set. To keep low-weight feature sets, the chord data were stored using a compact binary format. We used the CM-SPADE algorithm, which performs a vertical mining of sequential patterns using co-occurence information, and which is fast and efficient enough to be applied to big data collections like the ILM set. In orderto derive key-independent frequent patterns, the transition between chords are modeled by changes of qualities (e.g. major, minor, etc.) and root keys (e.g. fourth, fifth, etc.). The resulting key-independent chord progression patterns vary in length (from 2 to 16) and frequency (from 2 to 19,820) across genres. As illustrated by graphs generated to represent frequent 4-chord progressions, some patterns like circle-of-fifths movements are well represented in most genres but in varying degrees. These large-scale results offer the opportunity to uncover similarities and discrepancies between sets of musical pieces and therefore to build classifiers for search and recommendation. They also support the empirical testing of music theory. It is however more difficult to derive new hypotheses from such dataset due to its size. This can be addressed by using pattern detection algorithms or suitable visualisation which we present in a companion study

Visualising Chord Progressions in Music Collections: A Big Data Approach

In the Digital Music Lab project we work on the automatic analysis of large audio databases that results in rich annotations for large corpora of music. The musicological interpretation of this data from thousands of pieces is a challenging task that can benefit greatly from specifically designed interactive visualisation. Most existing big music data visualisation focuses on cultural attributes, mood, or listener behaviour. In this ongoing work we explore chord sequence patterns extracted by sequential pattern mining of more than one million tracks from the I Like Music commercial music collection. We present here several new visual representations that summarise chord patterns according to chord types, chroma, pattern structure and support, enabling musicologists to develop and answer questions about chord patterns in music collections. Our visualisations represent root movement and chord qualities mostly in a geometrical way and use colour to represent pattern support. We use two individually configurable views in parallel to encourage comparisons, either between different representations of one corpus, highlighting complimentary musical aspects, or between different datasets,here representing different genres. We adapt several visualisation techniques to chord pattern sets using some novel layouts to support musicologists with their exploration and interpretation of the corpora. We found that differences between chord patterns of different genres, e.g. Rock & Roll vs. Jazz, are visible and can be used to generate hypotheses for the study of individual pieces, further statistical investigations or new data processing and visualisation. Our designs will be adapted as user needs are established through ongoing work. Means of aggregating, focusing and filtering by selected characteristics (such as key,melodic patterns etc.) will be added as we develop our design for the visualisation of chord patterns in close collaboration with musicologists

Detailed equilibrium and dynamical tides: impact on circularization and synchronization in open clusters

Binary stars evolve into chemically-peculiar objects and are a major driver of the Galactic enrichment of heavy elements. During their evolution they undergo interactions, including tides, that circularize orbits and synchronize stellar spins, impacting both individual systems and stellar populations. Using Zahn's tidal theory and MESA main-sequence model grids, we derive the governing parameters $\lambda_{lm}$ and $E_2$, and implement them in the new MINT library of the stellar population code BINARY_C. Our MINT equilibrium tides are 2 to 5 times more efficient than the ubiquitous BSE prescriptions while the radiative-tide efficiency drops sharply with increasing age. We also implement precise initial distributions based on bias-corrected observations. We assess the impact of tides and initial orbital-parameter distributions on circularization and synchronization in eight open clusters, comparing synthetic populations and observations through a bootstrapping method. We find that changing the tidal prescription yields no statistically-significant improvement as both calculations typically lie within 0.5$\sigma$. The initial distribution, especially the primordial concentration of systems at $\log_{10}(P/{\rm d}) \approx 0.8, e\approx 0.05$ dominates the statistics even when artificially increasing tidal strength. This confirms the inefficiency of tides on the main sequence and shows that constraining tidal-efficiency parameters using the $e-\log_{10}(P/{\rm d})$ distribution alone is difficult or impossible. Orbital synchronization carries a more striking age-dependent signature of tidal interactions. In M35 we find twice as many synchronized rotators in our MINT calculation as with BSE. This measure of tidal efficiency is verifiable with combined measurements of orbital parameters and stellar spins.Comment: 24 pages, 29 figures includings appendices. Accepted for publication in MNRA

Visualisation of Origins, Destinations and Flows with OD Maps

We present a new technique for the visual exploration of origins (O) and destinations (D) arranged in geographic space. Previous attempts to map the flows between origins and destinations have suffered from problems of occlusion usually requiring some form of generalisation, such as aggregation or flow density estimation before they can be visualized. This can lead to loss of detail or the introduction of arbitrary artefacts in the visual representation. Here, we propose mapping OD vectors as cells rather than lines, comparable with the process of constructing OD matrices, but unlike the OD matrix, we preserve the spatial layout of all origin and destination locations by constructing a gridded two‐level spatial treemap. The result is a set of spatially ordered small multiples upon which any arbitrary geographic data may be projected. Using a hash grid spatial data structure, we explore the characteristics of the technique through a software prototype that allows interactive query and visualisation of 105‐106 simulated and recorded OD vectors. The technique is illustrated using US county to county migration and commuting statistics