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How Music and Mathematics Relate

Gain new perspective on two of the greatest achievements of human culture-music and math-and the unexpected and fascinating connections that bind the two together.
How Music and Mathematics Relate is rated 4.6 out of 5 by 167.
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Rated 5 out of 5 by from Best presentation I've seen in the Great Courses Professor Kung's presentations are exceedingly well organized, clear, and well illustrated. I found the content fascinating and now have a much deeper understanding of what music is and how our ears and brains process sound.
Date published: 2021-09-15
Rated 5 out of 5 by from How Music and Mathematics Relate I thoroughly enjoyed the breadth of ideas relating mathematics and music that this course provided. The instructor is knowledgeable in both areas and his demonstrations were perfect. His use of the violin clearly demonstrate basic principles discussed and his use of computer generated examples helped to clarify more technical ideas. Students with a little background in either or both music or mathematics may be able to more easily relate to the discussions.
Date published: 2021-09-13
Rated 5 out of 5 by from Absolute genius and mast see This course was so great , I can't stop watching or listening even with my eyes closed after long workdays.. All you need to truly understand the universe of music. The rest will be your own creativity.
Date published: 2021-09-11
Rated 5 out of 5 by from Two favorite subjects together at last This course really exceeded my expectations. As a mathematician who has loved music since childhood, I didn't expect to learn much new here, but I figured I'd give it a try. I was so wrong! I learned a great deal, particularly about the way scales are constructed as they are, and how not everyone does it the same way. I've known about fundamentals and harmonics for a long time, but had no idea how crucial the harmonic series was in deciding how to divide up the octave. I've always assumed that dissonance was just cultural, but now I realize the physical basis. Right off the bat, Professor Kung tells us of his difficulty with the Bach Chaconne, so when, in a later lecture, he started off playing an excerpt from that very piece, I thought, "Bravo! You learned it after all!". Which he finally comes back to in the final lecture with a joke about tenure. I admired Kung's bravery in talking Wave Equation, Fourier expansions, even Fourier Transforms from the get-go. I just hope this isn't too intimidating to folks who have never heard of such things. But looking at sound "in the frequency domain" is clearly crucial to much of what is taught here. I was fascinated to learn, for example, how we can think we are hearing a low fundamental that isn't there, just because we are hearing its higher harmonics. On rhythm, I wish he had said more about the asymmetric meters found in music of the Balkans, since he came so close. When he revealed that an Indonesian scale is almost alone in lacking a 5th, I questioned his use of the word "Gamelan" as the name of an instrument. I have always understood this as referring to the entire ensemble of (mostly percussion) instruments. Clearly, these are very minor quibbles. Kung ends by playing final passages from the Chaconne which, in light of the "back story", is just thrilling.
Date published: 2021-07-24
Rated 5 out of 5 by from Excellent and clear teaching I commend Prof. Kung on such a good job presenting the material in just 12 lectures. I am a computer scientist and electrical engineer but also play classical guitar. I am 70 now but like him I always had a strong sense of the relation between mathematics and music. needless to say, I enjoyed this course. His students got lucky to have him as a teacher. On behalf of so many people that can benefit for the course, I appreciate Prof Kung's effort and taking the time to put together the material.
Date published: 2021-07-03
Rated 5 out of 5 by from Tour de force I’ve taken dozens of great courses from Great Courses over the years, but this one gave me the most pleasure and satisfaction. I taught physics and mathematics at a community college before retiring, and I’ve played the piano since I was 5 years old, so the topics and level of instruction were perfect for me. Dr. Kung has a wonderful manner of teaching: he is sharing things he loves and finds delightful with an intelligent but perhaps not so knowledgeable audience. His violin playing is superb and brings the topics to life: music, mathematics, biology, engineering, and psychology. It’s all here and beautifully organized. A tour de force.
Date published: 2021-05-24
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
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Overview

Get a new perspective on two of the greatest achievements of human culture in the 12 dazzling lectures of How Music and Mathematics Relate, taught by award-winning mathematician and musician David Kung of St. Mary's College of Maryland. Understanding the connections between music and mathematics helps you appreciate both, even if you have no special ability in either field. By exploring the mathematics of music, you learn why non-Western music sounds so different, gain insight into the technology of modern sound reproduction, and start to hear the world around you in exciting new ways. No expertise in either music or higher-level mathematics is required to appreciate this astonishing alliance between art and science.

About

David Kung
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.

INSTITUTION

St. Mary’s College of Maryland

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.

By This Professor

How Music and Mathematics Relate
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How Music and Mathematics Relate

Trailer

Overtones-Symphony in a Single Note

01: 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

02: 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

03: 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

04: 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

05: 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

06: 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

07: 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

08: 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

09: 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