| What is "pitch"? What are the origins of pitch? How do we derive pitch? What are the physical properties of pitch? What is the nature of the interaction between the physics of sound and culture? How did ancient civilizations derive pitch? What is a "scale"? What is equal temperament? What is just intonation? What is the
difference between scale and mode? What is the relationship between pitch and scale? What are consonance and dissonance? What is the origin of the twelve semitones? What is a Pythagorean comma? How is the study of pitch the study of proportion? How much of pitch is physics and how much culture? What is equal temperament? |
Purposes
To understand the nature of pitch and pitch relationships.
To consider the physical and cultural bases of pitch systems. |
Team Tasks
Work together in a group to build a monochord. (Note: The purpose of a monochord
is to measure pitch and not to be a musical instrument.)
Calculate and produce a set of just intonation and equal temperament intervals
giving the string lengths of these intervals for your monochord.
Calculate and produce a set of intervals that is neither just intonation
nor equal temperament. Give the string lengths and calculate
the cents value of your intervals.
The study group will demonstrate for the class their tuning systems (just
intonation, equal temperament, and original system) and explain
how you arrived at your measurements.
Each individual will submit separately a hard copy of your tables showing
string lengths, proportions, and cents for each of the interval
systems.
|
Essay
Suggestions
Describe the logic underlying any of the pitch systems and the advantages and
disadvantages of this approach to deriving pitch.
Why were Pythagoras and his associates so concerned with measuring pitch?
Why did we develop equal temperament?
How did the musical thinking of the Enlightenment reflect cultural milieu?
How does your cultural milieu influence your musical thinking about pitch?
Why did Prince Chu Tsai-Yu study the problem pitch?
|
| Teams 2011 |
|
| Internet Sources |
| Calculating cents from string ratios using the Calculator in Microsoft Windows |
| Finding the intervals on the Monochord |
| A Brief History of the Monochord |
| About Just Intonation |
| The Monochord Thread |
| Bibliography for the Monochord Thread |
| Wikipedia: Pythagorean Tuning |
| Authentic Tuning |
| Pythagoras of Samos |
|
| Print Sources |
| Kuttner,
Fritz A. 1975. Prince Chu Tsai-Yu's Life and Work: A Re-Evaluation
of His Contribution to Equal Temperament Theory. In Ethnomusicology 19 (2): 163-206. [Available through the JSTOR link on the
Scribner Library site.] |
| Randel,
Don Michael. Interval. In The New Harvard Dictionary of
Music (Don Randel, editor). Cambridge, Mass.: The Belknap
Press of Harvard University Press, 1986. |
|
|
12 April, 2011
|