Math in Music makes sense
Mathematical thinking is embedded in most of the music study activities. During singing games, students count how many children are added to the game with each song and soon predict where the song will stop in the circle. A child will observe that the participants have been chosen in a pattern, i.e., girl, girl, boy, girl. Another child will calculate how many more turns are needed until everyone has been chosen to join the game. Through their observations the students naturally connect the temporal length of the song with the movement through time and space. The games are alive with the multi-faceted thinking that is taking place.
Pattern Detection in Music
When working with notation, students eagerly point out where they see patterns in the various combinations of notes and rests. The habit of scanning the score for patterns establishes a musical habit that is essential for “sight-reading” in music. The students’ zeal for pattern detection keeps everyone alert with an incredible focus of attention. Pattern detection stimulates a greater depth of musical investigation and understanding when studying musical form. Students discover the common forms of folk songs. When the beats of the songs are written in the form, the phrases can be represented as a math problem. For example, “London Bridge” has phrases of 4, 2, 2, and 8 beats, a total of 16 beats. Students enjoy checking the form of every song they know to see if it fits an existing form or creates a new one.
Fractions in Notation
For countless years the study of music notation has created webs of confusion for students. Young learners often think, “Shouldn’t a half note get half a beat?” In the intermediate grades, “music math” offers a more understandable way to begin. After examining the relationship of notes, i.e., two half notes equal a whole note; the notes are represented as fractions. When a measure of notation written as fractions is added, it equals the meter, such as ¾. Students say that the exercise of writing and adding notation “equations” helps them understand music and is “easy” math.
The Science of Sound
Study of the science of sound is a common feature in music classes as students learn about the instruments of the orchestra, sing, and play classroom instruments. They identify the source of vibrations and the resonance chamber of each instrument. Students study how the vocal folds change when producing faster and slower vibrations. They observe the relationship between instrument size and its pitch range. For example, students can see the changing size of xylophone bars in relation to the scale of pitches they hear. They also discover how pitch and dynamic differences are produced. We explore how the tone quality of various instruments changes when it is played in different ways. When students sing and play recorders they study the effect of breath flow and energy. Playing an instrument successfully requires that all systems are working in a coordinated way.