How Music and Mathematics Relate

Rated 5 out of 5 by from Fascinating! On a per lesson basis, the best Great Courses offering I've seen. A major steppingstone on my road to understanding Music Theory.
Date published: 2021-03-07
Rated 5 out of 5 by from Enlightening! Despite being aware of the intrinsic link between math and music, this is the first time I've seen it articulated. Dr Kung clearly loves the subject matter and does an excellent job of explaining the relationship.
Date published: 2020-12-30
Rated 5 out of 5 by from Happy Student Dr Kong did an excellent job with this material. I have a Masters Degree in Electrical Engineering so I have a solid background in Fourier transforms but Dr Kung brought the subject to life by applying the topic to musical instruments and why they sound different. The topic of scale construction was very helpful. Dr Kung is such an accomplished musician too! He expanded my little knowledge of classical music which makes me want to hear more. Thank you for a great course. Thank you for this offering.
Date published: 2020-11-21
Rated 4 out of 5 by from Insightful and heartfelt I found this course a little challenging, having to listen to some sections more than once, and even complementing a bit with online videos. IT WAS WORTH THE EFFORT. As a result, I have a deeper understanding of the physical phenomena that underlie what I hear. Experienced several aha moments, like understanding what happens when I play harmonics in my guitar, or why our musical tradition uses certain notes instead of others, among others. I especially appreciate professor Kung´s passion for both math and music. I play guitar since I am 10 years old, but never learned to read music, nor have I taken musical theory classes in the past. Feel that is about to change after taking this course.
Date published: 2020-10-22
Rated 5 out of 5 by from Exceptional The relationship of music and math is elegantly presented by Prof. Kung who is something of a virtuoso in both. The course is systematically presented, first in its component parts and then in a thrilling conclusion that puts all these minute considerations into a composite whole. I can't tell you how listenable these lectures are. Prof. Kung is an exceptional speaker and teacher. The presentations were rich in graphics, visual cues, musical examples and video devices all calculated to clarify and enliven the material. Really well done. While I'm coming at this from the musical composition side, I did come to appreciate the role of math even while the formulas pretty much escaped me. I would recommend this course whole-heartedly to anyone interested in music or math. It is a stimulating and inspiring journey.
Date published: 2020-08-25
Rated 2 out of 5 by from Over my head but the concept is interesting. I had several math classes in college but this guy is way beyond anything I ever studied. Never realized music was so complicated!
Date published: 2020-07-28
Rated 5 out of 5 by from Music and Math Course 1373 This is the best course I have ever watched, and I've watched many of them. As a lifetime music lover I didn't fully appreciate the connection between music and math.In just 12 lectures Prof. Kung has given an amazingly comprehensive introduction to a complex subject. His explanations are very clear and his style is extremely friendly. Playing his violin to clarify topics is very helpful and lends a nice touch. His visuals are outstanding and very necessary!
Date published: 2020-07-20
Rated 4 out of 5 by from More Music than Math I wasn’t able to grasp much coherency from the math end of this course from lecture to lecture. But in nine hours Professor Kung slaps together a lot of mind-boggling correlations between the two. This is a wow course, entertainment. The Teaching Company takes you deep behind the scenes into its production. At one point Professor Kung steps out of a screen onto the lecture floor. I was looking for harmony, and the math behind it, and did not find it here. (I also could not find it in a satisfactory manner in Professor Greenberg’s course from a thrift store missing discs and looking like a bomb hit it. It did have the three 45-minute lectures on harmony, but Professor Greenberg doesn’t name all of the chords he is striking and why, which is crushing; plus, the recorded music in that course was a half step sharp, though Professor Greenberg plays the most beautiful piano.) Professor Kung does explain how we derive our scales from the ideas of Pythagoras. If you would like to be highly entertained, this course will deliver, and it will sprinkle a few correlations between math and music. The course was a great idea; in my opinion, it could have gone a little further. It is very pleasant to see a diversity of professors. And Professor Kung gets the most beautiful tone off of his violin.
Date published: 2020-07-01
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How Music and Mathematics Relate
Course Trailer
Overtones-Symphony in a Single Note
1: Overtones-Symphony in a Single Note

Start the course with a short violin passage from Bach, played by Professor Kung. Then analyze the harmonic series behind a single note, which involves a mixture of different frequencies, called overtones or harmonics. Learn about the physics of stringed and wind instruments, and study the sounds produced by a range of instruments, including the violin, flute, clarinet, timpani, and a fascinating ...

50 min
Timbre-Why Each Instrument Sounds Different
2: Timbre-Why Each Instrument Sounds Different

After hearing the opening measures of Bach's "Air on the G String," investigate why this piece is conventionally played on a single string of the violin. The reason has to do with timbre, which determines why a flute sounds different from a violin and why a melody played on the G string sounds not just lower, but altered. The study of timbre introduces you to a mathematical idea called the Fourier...

46 min
Pitch and Auditory Illusions
3: Pitch and Auditory Illusions

The fundamental frequency of a male voice is too low to be reproduced by the speaker of a cell phone. So why don't all callers sound like women? Learn that the answer involves the way your brain fills in missing information, convincing you that you hear sounds that aren't really there. Explore examples of auditory illusions that will leave you wondering if you can ever believe your ears again....

48 min
How Scales Are Constructed
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 n...

48 min
How Scale Tunings and Composition Coevolved
5: How Scale Tunings and Composition Coevolved

Compare passages from Bach's "Chaconne" and a very modern piece, noting how the compositional styles of Western music have evolved alongside small differences in scale tunings. Then explore the mathematics of tuning, focusing on how the exact pitches in a scale are calculated and why there are 12 notes per octave in Western music. Investigate the alternatives, including a scale with 41 notes per o...

46 min
Dissonance and Piano Tuning
6: Dissonance and Piano Tuning

Dissonance is a discordant sound produced by two or more notes sounding displeasing or rough. The "roughness" is quantifiable as a series of beats-a "wawawa" noise caused by interfering sound waves. Learn how to predict this phenomenon using basic trigonometry. Consider several examples, then discover how to use beats to tune a piano. End with a mathematical coda, proving the beat equation using b...

50 min
Rhythm-From Numbers to Patterns
7: Rhythm-From Numbers to Patterns

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. C...

45 min
Transformations and Symmetry
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...

50 min
Self-Reference from Bach to Godel
9: Self-Reference from Bach to Godel

Music and mathematics are filled with self-reference, from Bach's habit of embedding his own name in musical phrases, to Kurt Gödel's demonstration that mathematics cannot prove its own consistency. Embark on a journey through increasingly complex levels of self-reference, discovering that music and mathematics are like a house of mirrors, reflecting ideas between them. For example, the table...

43 min
Composing with Math-Classical to Avant-Garde
10: Composing with Math-Classical to Avant-Garde

Sometimes composers create their works using mathematics. Mozart did this with a waltz, whose sequence of measures was determined by the roll of dice-with 759 trillion resulting combinations. Learn how Arnold Schoenberg used mathematics in the 20th century to design an alternative to tonal music-atonal music-and how a Schoenberg-like system of encoding notes has more recently made melodies searcha...

45 min
The Digital Delivery of Music
11: The Digital Delivery of Music

What is the technology behind today's recorded music? Delve into the mathematics of digital sampling, audio compression, and error correction-techniques that allow thousands of hours of music to fit onto a portable media player at a sound quality that is astonishingly good. Investigate the difference between analog and digital sound, and explore the technology that allows Professor Kung's untraine...

46 min
Math, Music, and the Mind
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 en...

48 min
David Kung

I've loved both math and music since I was a kid. I was thrilled to discover the many connections between these two passions of mine. Sharing that excitement with Great Courses customers has been incredibly gratifying.


University of Wisconsin


St. Mary’s College of Maryland

About David Kung

Dr. David Kung is Professor of Mathematics at St. Mary's College of Maryland. He earned his B.A. in Mathematics and Physics and his Ph.D. in Mathematics from the University of Wisconsin, Madison. Professor Kung's musical education began at an early age with violin lessons. As he progressed, he studied with one of the pioneers of the Suzuki method and attended the prestigious Interlochen music camp. While completing his undergraduate and graduate degrees in mathematics, he performed with the Madison Symphony Orchestra. Professor Kung's academic work focuses on mathematics education. Deeply concerned with providing equal opportunities for all math students, he has led efforts to establish Emerging Scholars Programs at institutions across the country. His numerous teaching awards include the Homer L. Dodge Award for Excellence in Teaching by Junior Faculty, given by St. Mary's College, and the John M. Smith Teaching Award, given by the Maryland-District of Columbia-Virginia Section of the Mathematical Association of America. Professor Kung's innovative classes, including Mathematics for Social Justice and Math, Music, and the Mind, have helped establish St. Mary's as one of the preeminent liberal arts programs in mathematics. In addition to his academic pursuits, Professor Kung continues to be an active musician, playing chamber music with students and serving as the concertmaster of his community orchestra.

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