By the end of this lesson, students will be able to:
Hear the difference between equal temperament and other types of tuning.
Explain equal temperament and how it relates to other types of tuning systems used in early and contemporary classical music and non-Western music.
Sight-read rhythms that incorporate ties and dotted quarter notes in simple time.
"Tuning Systems," p. 197–207 (from Understanding Basic Music Theory)
Temperaments: What You Need to Know
(Early Music Sources, 20 mins)
Monochord: Discover how Pythagoras divided strings to create musical intervals using this interactive Monochord Generator.
Try it Out: Visit Ableton’s Tuning System page to explore 10 unique tuning systems. You can listen to and play melodies in each system—and if you continue, you’ll even have the chance to create your own custom tuning.
Compare Tuning Systems: Choose one tuning system featured in the videos below and analyze how it differs from the standard Western equal temperament system.
Just Intonation in the Renaissance
(Early Music Sources, 14 mins)
Tables from Gareth Roberts, "Comparing the Three Musical Tuning Systems Handout" from Music to Mathematics: Exploring Connections (2016)
Historical Perspectives: Discuss the evolution of tuning systems throughout history. Explore the development of different tuning systems, such as Pythagorean tuning, just intonation, mean-tone temperament, and equal temperament. Discuss the historical context and reasons behind the shift from one tuning system to another.
Equal Temperament: Explore the concept of equal temperament as the prevalent tuning system in Western music. Discuss the advantages and disadvantages of equal temperament, and how it affects the perception and interpretation of pitch. Explore the challenges of playing in tune within an equal temperament system.
Microtonal Tuning: Explore the concept of microtonal tuning and the use of intervals smaller than a semitone. Discuss different microtonal systems, such as quarter tones or non-Western tunings. Explore the expressive possibilities and challenges of microtonal music and the role of microtonal tunings in specific musical traditions.
Monochord: Check out the generator here. Compare the pitch differences between different tuning systems in this interactive pitch wheel on Chromatone. Discuss which intervals sound more in tune and why. Why might certain tuning systems be preferred in different types of music based on the scales and pitch practices used?
Tuning Practice: Split the class into two groups and try to sing a purely-tuned fifth. Then, compare your result with the same two pitches on an equal-tempered piano. Do the same for a major third. Are you able to hear the difference? What does this difference say about choices musicians make when tuning or following a particular system of intonation?
Pitch Matching Circle: Form a circle with the entire class. Start by having one student sing or play a single note or pitch. The next student in the circle then matches that pitch, and the process continues around the circle. Encourage students to actively listen and adjust their pitch to align with the preceding pitch. Discuss the challenges and strategies employed to maintain accurate tuning throughout the circle.
Rhythm Sight Reading: Ties and Dotted Quarters
Practice call & response and short dictation using the rhythm grid for the unit (see the activity in Unit 1-1 for an example).
Sight read and practice rhythm transcription with the rhythm examples from the repertoire.
Using Tuning Systems Expressively for String Instruments (ViolinMasterClass.com)
Equal Temperament
(BBC Documentary, 50 mins)
Pythagorean Comma
(The Exciting Universe of Music Theory)
Why It’s Impossible to Tune a Piano
(MinutePhysics, 4 mins)
G# and A♭ Are Not the Same Note
(Two-Minute Music Theory, 2 mins)
The Mathematical Problem with Music, and How to Solve It
(Yuval Nov, 32 minutes)