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TTC Video - How Music and Mathematics Relate
TTC Video - How Music and Mathematics Relate | 3.5 GB
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Great minds have long sought to understand the relationship between music and mathematics. On the surface, they seem very different. Music delights the senses and can express the most profound emotions, while mathematics appeals to the intellect and is the model of pure reasoning.

Yet music and mathematics are connected in fundamental ways. Both involve patterns, structures, and relationships. Both generate ideas of great beauty and elegance. Music is a fertile testing ground for mathematical principles, while mathematics explains the sounds instruments make and how composers put those sounds together. Moreover, the practitioners of both share many qualities, including abstract thinking, creativity, and intense focus.

Description of the lectures
Lecture #3 - Pitch and Auditory Illusions
Lecture #4 - How Scales Are Constructed
Professor Kung contrasts a passage from Vivaldi with a Chinese folk tune. Why is one so easily distinguishable from the other? Probe the diverse mathematics of musical scales, which explains the characteristic sound of different musical traditions. Learn how a five-note scale is constructed versus a more complex seven-note scale. What are the relative advantages of each? As a bonus, discover why no piano is ever in tune.

Lecture #5 - How Scale Tunings and Composition Coevolved
Lecture #6 - Dissonance and Piano Tuning
All compositions depend on rhythm and the way beats are grouped under what are called time signatures. Begin with a duo for clapping hands. Next, probe the effect produced by a distinctive change in the grouping of beats called a hemiola. Also investigate polyrhythms, the simultaneous juxtaposition of different rhythms. Listen to examples from composers including Handel, Tchaikovsky, and Chopin. Close with an unusual exercise in which you use musical notation to prove a conjecture about infinite sums.

Lecture #8 - Transformations and Symmetry
Bach and other composers played with the structure of music in ways similar to what would later be called mathematical group theory. Explore techniques for transforming a melody by inversion, reversal, transposition, augmentation, and diminution. End with a table canon credited to Mozart, in which the sheet music is read by one musician right-side up and by the other upside down. Professor Kung is joined by a special guest for this duet.

Lecture #9 - Self-Reference from Bach to Godel
Lecture #11 - The Digital Delivery of Music
Lecture #12 - Math, Music, and the Mind
Conclude with an eight-part finale, in which you range widely through the territory that connects mathematics, music, and the mind. Among the questions you address: What happens in the brain of an infant exposed to music? Why do child prodigies often excel in the areas of math, music, or chess? And how do creativity, abstraction, and beauty unite music and mathematics, despite being on opposite ends of the arts and sciences?
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