Counting possible tunes in a tiny musical world
A tiny musical universe with three notes and four positions already contains 81 possible note sequences. More notes, rhythms, or longer phrases make the count grow quickly. Yet a new sequence of symbols is not necessarily a new musical idea.
Questions you could explore
- What should count as the same song: its notes, rhythm, or the way listeners recognize it?
- How does allowing repeated notes change the number of four-note sequences?
Start reading
- Eric Lehman, F. Thomson Leighton and Albert R. Meyer; MIT OpenCourseWare, 2015Mathematics for Computer Science
The product rule explains why three available notes in four ordered positions give 81 sequences. Counting sequences does not tell us which ones make good songs.
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