Alma Harris The ?eld of school leadership is currently preoccupied with the idea of distributed leadership. Few ideas, it seems, have provoked as much attention, debate and c- troversy. Whatever your position on distributed leadership, and you cannot fail to have one, it is irrefutable that distributed leadership has become the leadership idea of the moment. Yet, it is an idea that can be traced back as far as the mid 20s and possibly earlier. So why the interest? Part of the answer can be found in a move away from theorizing and empirical enquiry focused on the single leader. This shift has undoubtedly been fuelled by structural changes, within schools and across school systems that have resulted in - ternative models or forms of leadership practice. Evidence highlights how those - cupying formal leadership positions are increasingly recognizing the limitations of existing structural arrangements to secure organizational growth and transformation (Fullan et al. , 2007; Harris et al. , 2008; Chapman et al. , 2008). As a consequence, many heads and principals are actively restructuring, realigning and redesigning leadership practice in their school (Harris, 2008). While the terminology to describe such changes varies, the core principle is one of extending or sharing leadership practice. While scholars have long argued for the need to move beyond those at the top of organizations in order to examine leadership (Barnard, 1968; Katz and Kahn, 1966) until relatively recently, much of the school leadership literature has tended tofocusupontheheadortheprincipal.

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This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style. This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.