Superlesson
Project 6-1
Foundations of Algebra and Geometry
Chapter 6, Using Ratios to Compare
Ratios and proportions have wide applications in music and in the science of sound.
Part B, Understanding Ratios
1. In the Baltimore Symphony Orchestra, what is the ratio of:
a. second violinists to first violinists?
b. female bassoonists to bassoonists?
c. brass players ("Horns" through "Tuba") to percussionists ("Timpani" through "Organ")?
d. violinists ("First" and "Second") to string players ("First Violin" through "Basses")?
e. Which symphony orchestra, Baltimore or Cleveland, has the greater ratio of bass players to cello players?
f. One-sixth of the string players in the Cleveland Orchestra play a single instrument. Which one?
g. In the Baltimore Symphony, what percent of the woodwind players ("Flutes" through "Contrabassoon") are women?
h. How many timpani players must the Cleveland Orchestra add to its ranks for timpanists to make up 1/3 of the percussion section ("Timpani" through "Keyboard Instruments")?
Part C, Rates
2. As sound travels, it alternately compresses and expands the molecules
of air. The distance between two compressions is the "wavelength"
of the sound. The number of wavelengths that go by in 1 second is a unit
rate called the "frequency" of the sound.
A trumpet played the note "G" at room temperature (about 16° Celsius). Answer these questions to find the wavelength of the sound.
a. What was the Frequency of the note? (Frequencies appear immediately after the note.)
b. The velocity of sound depends upon the temperature. What is the Speed of sound at 16° Celsius? (The formula gives velocities in the unit rate ft/sec). Round to the nearest tenth.
c. Wavelength (w), velocity (v), and frequency (f) are related by the formula w = v/f. Find the wavelength of the trumpet note from a. Round to the nearest tenth.
Part E, Making Connections
3. Answer the following questions.
a. "Tempo" indicates the speed of a piece of music. How many beats would there be in 40 seconds of the above piece? How many measures would be played in 40 seconds?
b. Most pianists take more than a minute to play Polish composer Frederic Chopin's "Minute Waltz." Write the "normal" length of the piece in seconds.
c. The "Minute Waltz" is 140 measures long. The time signature is 3/4. To complete the piece in the normal length of time, what number should be written after "A= " at the beginning of the music?