{"content":[{"text":"PHYSICAL SOUNDS COLIMITS TOPOS \n AS IN THE \n MONAD CONTROL \n UNDER","bbox":{"left":0.166667,"top":0.109342,"width":0.670852,"height":0.05376600000000001}},{"text":"NICK ROSSITER, MICHAEL HEATHER \n Computer and Information Sciences, Pandon Building \n Northumbria University, Newcastle NE2 1XE, UK \n Corresponding Author’s email: nick.rossiter1@btinternet.com","bbox":{"left":0.190461,"top":0.215877,"width":0.619157,"height":0.07302899999999998}},{"text":"ABSTRACT \n Music is a testing challenge for formal information systems. To pro- \n vide an insight into the processes involved, the intension/extension \n relationship is explored over ﬁve levels from the Universe through \n the discourse of music, scores and their variants to actual musical \n performances. We apply the full power of category theory to the \n challenge, involving the topos for data structuring and the monad \n for process. The topos handles many aspects of the data for a per- \n formance including the score and its variants as musical notation, \n the orchestral players and the conductor. The monad as process \n controls the adjointness between the functors representing articu- \n lation and intonation, based on perceived activity in the brain in \n professional musicians. We present a musical performance as a cat- \n egorical composition over time signatures that proceed in succes- \n sive adjoint steps with the monad looking back and its associated \n comonad looking forward. The physical complexity of each musical \n sound operates in its respective time-frame, represented by a limit, \n as a colimit. The formalism can be implemented in a functional \n programming language such as Haskell.","bbox":{"left":0.166667,"top":0.350211,"width":0.6668019999999999,"height":0.347462}},{"text":"1","bbox":{"left":0.166667,"top":0.727914,"width":0.018662999999999985,"height":0.022160999999999986}},{"text":"Introduction","bbox":{"left":0.222723,"top":0.727914,"width":0.20569499999999996,"height":0.022160999999999986}},{"text":"Much work has been done on computer representations of music \n at the physical level. Developments by Klumpenhouwer such as K- \n nets [15] provide a way for representing transformations from one \n pitch-class to another. A pitch class is all notes an octave apart, \n for example all C available on a piano. In a classical system there \n are 12 pitch classes, one for each note on the 12-note scale. K-nets \n represented a fundamental change from a set-theoretical approach","bbox":{"left":0.166667,"top":0.766662,"width":0.6667559999999999,"height":0.12607000000000002}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}