Play Clip 1, Musical Ratios. Then ask students these questions and discuss the answers below.
- According to the video, why do different objects produce different sounds? How does that lead to the creation of music?
Different objects vibrate at different speeds (frequencies); those frequencies determine pitch. By combining and controlling pitches and their relationships, we create musical tones, harmonies and melodies.
- According to the video, what do ratios describe?
Ratios describe the relationship between two things — here, how one value compares to another.
- What does a musical ratio describe?
It describes the relationship between two frequencies (how many times one vibrates compared to the other).
- What is a 2:1 ratio called in music?
A 2:1 ratio is called an octave (the higher pitch vibrates twice as fast as the lower pitch).
- Who was one of the early mathematicians interested in ratios and musical ratios? What tool did he use?
Pythagoras studied musical ratios and used a monochord to measure and calculate relationships between string lengths and pitches.
- How would you describe the monochord?
A monochord is a simple single-string instrument mounted over a sound box with a movable bridge. By changing the string length above the bridge, you change the vibrating length and therefore the pitch. It lets you measure and compare exact ratios of lengths and hear the resulting pitch relationships.
Teacher's closing remarks (75 words, Ally McBeal cadence):
Lovely job — you listened, you thought, you answered. When you explain the sounds, say: different objects vibrate at different speeds, so they make different pitches. When you explain ratios, say: ratios describe relationships between two things. Musical ratios compare two frequencies. A 2:1 ratio is an octave. Pythagoras studied this using a monochord, a single-string instrument with moveable bridge to measure lengths and calculate pitch. Keep exploring — curious, precise, musical. Bravo. Stay tuned, class. Always.