Jerry, I promised that I would stop.
JLRC: The emotions that different compositions raise in me are not expressed in first order logic. JFS: I certainly agree with that point... I'll quit on this point of agreement.
But this morning I woke up with the realization that music notation is based on the Peirce-Aristotle ontology of time. Zeno's paradox about Apollo and the tortoise is based on the assumption that points are the ultimate parts of a line or time interval. But Aristotle resolved that paradox by claiming that the parts of a line or time interval are smaller parts and points are just markers on a line. Cantor followed Zeno. Peirce admired Cantor's hierarchies of infinity, but he followed Aristotle. Peirce claimed that no discrete set of points could ever form a true continuum. For discussion, see the intro to RLT by Ketner and Putnam. With the Peirce-Aristotle ontology of time, there is only one temporal system in music: a continuous line subdivided in intervals. The beats per measure are markers on that interval. And by the way, Euclid also followed Aristotle. He used letters to mark significant points on his figures, but those points are are markers, not parts. Ketner and Putnam discuss this "point". John
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