Counting Melodies revision 2: from rhythms to Young diagrams
Counting Melodies, revision 2 is now available in my mathematical publication archive.
The question is concrete: how many monophonic melodies fit into a fixed duration when notes have pitch, rests have no pitch, and consecutive rests are merged? The manuscript develops the counting model through compositions, regular languages, and generating functions.
This revision adds engraved musical examples, ribbon and Young/Ferrers diagrams, the full catalogue of 32 rhythms of a 3/8 bar, and a reference to my earlier work from 2005. It remains an author-published draft, with its attribution and novelty qualifications intact.
The rhythm and shape laboratory lets you cut a time span into events, navigate the rhythms sharing a partition, change pitches and rests, and hear the result. Shape puzzles and an inversion-polynomial experiment provide additional ways to explore the mathematics. These are companion experiments; they do not alter the manuscript.
I have also added two earlier works to the archive:
Both are preserved as original revision 1 editions. The original files remain downloadable, and the archive records their checksums. Later revisions and work on subproblems will be published separately.