Off-by-one errors also explain a struggle I always had with music theory. Moving along piano keys is measured in terms of the number of notes encompassed: hitting C on a piano, skipping D, and then hitting E is an interval called a third, because E is the third note on the scale. But what really matters is not how many notes are used but the difference between them. This is the reverse-fence-post problem: music intervals count the posts when they should count the fence!*
