Music can often be broken down into units called measures; a measure consists of a sequence of notes, each of which occupies a rational number fraction of the measure. Accordingly, our group wrote two music-making computer programs that express musical notes as fractions. One program, written in Scratch, lets the user make music from fractions, i.e., by inputting notes of different rational number fractions of unity. The other program, written in Processing, visualizes fractions that are present in rhythms tapped out by the user. Both programs are designed with the intention of making fractions more accessible to children via the culture-independent medium of music.
We had the pleasure to user-test both of our programs with 5th Grade students of School 2 in Troy. The following sections document this process and conclude with recommendations for the future development of this unique educational medium.
Previous teaching methods:
- Rhythm stick ratios (shown) and beat
notation using geometric shapes
- Fractions on a timeline denote when a beat is clapped
Ratios in Music
- Music representation involves ratios
- Underlying structure: a repeatable “measure” made of four “beats”
- A “note” is defined by initial creation of sound and the sustain that follows
- “Subdivision”- inserting a note between two other notes, effectively splitting it in half
- Notes are named by their relationship to the entire measure- quarter notes, eighth note, etc.
- Rhythms are formed by combinations of these differently sized notes