Harmony is a relation that holds both between simultaneously sounded notes of a musical chord, and between successive notes or chords. It is this relation (which is distinct from consonance) that defines "meaningful" musical sequences or progressions, such as "cadences", in which chords (whether consonant or dissonant) establish expectations and ambiguities which other succeeding chords resolve.
The paper builds on work by Longuet-Higgins, who has shown that the harmonic relation between a pair of notes can be expressed as a vector in a three-dimensional discrete space whose generators are respectively related to prime integer frequency ratios of two, three, and five. It shows that this space can be considered as the denotation of chords and chord-sequences, and that musical chord sequences constitute a language "about" that domain. This language can be parsed using grammars which have surprisingly close affinities to natural language grammar, and suggest similar possibilities for integrating probabilistic techniques with rule based parsing
If I have time I will discuss the question of why this particular space or group should play such a central role in the music of our culture. I will argue that harmonic systems founded on any different relation, with more dimensions or different prime generators have quite different properties from the tonal harmonic system, for a combination of cognitive and computational reasons.
This talk sets out a programme of work in the area of dependability. The research is to be pursued under the aegis of a six-year "Inter-Disciplinary Research Collaboration". The aim is to consider computer-based systems which comprise humans as well as hardware and software. The overall programme will be described in addition to a more detailed discussion of how formal methods ideas, coupled with structuring proposals, can help handle faults (mechanical and human) by viewing them as interference.
History seems to show that there is one right way to do many of the decisions of uniprocessor computer architecture. After a wide divergence, there has been a surprising convergence. Many alternatives have been explored over 50 years. To a surprising degree, we have come back home - Today's architecture has a stunning resemblance to the original proposal by Burks, Goldstine, and von Neumann.
There have been generations, mostly defined by technology, and revolutions, driven by new market concepts. In each of the minicomputer and the microcomputer revolutions, the designers have started all over, often apparently ignorant of most previous design experience.
We survey this conceptual evolution over the first half-century of computer design. It is especially instructive to see what has not been conserved, both the changes and the additions. It is irresistible to speculate about the future.