The following projects and abstracts represent some of the work currently in progress, and publication information will be added as soon as it is known.
I: Identification and evolution of musical style I - Hierarchical transition networks and their modular structure
In this paper we propose a methodology to assist with the problem of identifying musical styles using mathematical tools that is related to the transition network approach developed by David Cope in his Experiments on Musical Intelligence. This extension allows for the possibility of defining stylistic cells at different scales as motifs and moduli of networks at the corresponding scale. We also outline how this methodology can be used to systematically study stylistic changes in different contexts by incorporating probabilistic and statistical tools and connections with other approaches.
In Agustín-Aquino, O A, Lluis-Puebla, E and Montiel, M (eds.), Mathematics and Computation in Music (2017), 258-79, http://www.springer.com/us/book/9783319718262
II: Identification and evolution of musical style II -
a statistical approach
With large amounts of data, the success of mathematical tools in helping to solve the problem of identifying musical styles is greatly enhanced. In this paper we propose a statistical methodology related to the transition network approach developed by David Cope. We outline how this methodology can be used to systematically study stylistic changes, with particular reference to the disputed attributions (Wilson, 2013) of the fine corpus of harpsichord music by 'Monsieur Couperin' (attributable to Charles or Louis Couperin) in the Bauyn manuscript. [Paper ready for submission]
III: Louis Couperin's viol fantasies - a question of
As well as the several hundred harpsichord and organ works attributed to Louis Couperin in modern editions, there are a number of chamber works, including two viol fantaisies and three 'symphonies'. These comprise his surviving non-keyboard works; and all are found in the late-17th century Bauyn manuscript from which the harpsichord works come. Couperin was both organist and treble viol player, so one might expect such repertoire to exist. The question of the secure attribution of the viol works can now be discussed by stylistic comparison with the 'Monsieur Couperin' harpsichord (possibly by Charles or Louis) and organ (definitely by Louis) works, using new computational and mathematical models developed for a whole-corpus study of this important repertoire. [Paper currently in final draft]
IV: Chambonnières versus Louis Couperin: attributing
the F major Chaconne
Chambonnières left four extant chaconnes in the Bauyn manuscript. Of these, the fine Chaconne in F has been assigned to Louis Couperin by a number of editors and writers on grounds of style (see for example, Curtis  vol.ii, pp.ix and 117). The aim of this study is to use computational and mathematical models developed for a whole-corpus study of the organ works of Louis Couperin and the harpsichord works now proposed to be by his brother Charles Couperin (Wilson, 2013), in order to compare analytically the style of this Chaconne with other works by Louis, by 'Charles' and Chambonnières himself, and arrive at a more secure attribution. In addition, the two extra couplets that appear in the Parville but not the Bauyn source, which have sometimes been regarded as a later addition, are compared in order to judge their stylistic similarities.
Harpsichord & fortepiano, xx/i (Nov 2017), 28-32
V: The attribution of Taverner and Tye's O Splendor gloriae
The five-part motet O splendor gloriae is attributed to Taverner in two important sources, but to both Taverner and Tye in the other two sixteenth-century sources. Joint works of this kind are extremely rare and common authorship difficult to assess. Scoring and many other musical features here are consistent, but the style of each half seems different. Davison (1987, xvii-xviii) attributes the second part as likely by Tye on grounds of stylistic characteristics. It certainly seems more modern in its imitative treatment, which may be consistent with the fact that Tye was a little younger than Taverner. In this paper we employ a new mathematical modelling methodology in order to provide an objective criterion for analysis, as additional evidence to standard musicological methods. The results support the claim attributing each half to a different composer. [Paper ready for submission]
VII: 'Analytical methods
for the attribution of early Bach keyboard works'
A surprising number of early Bach keyboard works have historical attributions that are contested by modern scholars on grounds of style, and therefore remain on the margins of the canon. Using a variety of mathematical modelling tools developed for a whole-corpus analysis of the keyboard works attributed to members of the Couperin couperin, we compare the stylistic components of one such work, the Suite in Bb BWV821. The dance movements are compared with equivalent works from later in Bach's career, using Principal Component Analysis and Clustering technqiues, to search for patterns that can help identify if there are convincing Bachian fingerprints in this and other early works. [Paper ready for submission]
X: 'The mathematical
modelling of aspects of stylistic development in Haydn's string quartets'
Haydn's string quartets contain some of his finest music, and were written over half a century of his compositional career. The standard forms he employed mean that there is sufficient consistency of content to use mathematical modelling tools and pattern recognition processes, including a graph-theoretical approach, to study stylistic change during Haydn's career, observing both consistencies and differences in, for example, melodic and harmonic patterns, during a period which transitioned all the way from the late Baroque to the early Romantic. [Paper ready for submission]
XXIII: Mathematical methods for musical composition: a practical approach
Contemporary composers face an interesting challenge: to generate new musical structures that depart from traditional forms. The use of mathematical procedures and algorithms in music (which date back to at least Guido d'Arezzo in the 11th century) can provide one interesting starting point as a source of ideas. We present a series of examples using mathematical ideas accessible to anyone familiar with basic arithmetic. They should be taken not as instructions on their own, but as material to be modified and further elaborated. In other words, we do not intend to automatically generate music by a given procedure, but rather to give composers additional tools and materials. For a practical outcome see http://www.fitz.cam.ac.uk/news/music-and-maths [Paper ready for submission]