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Education » Video Tutorials
TTC.Video How Music and Mathematics Relate TUTORiAL screenshot
TUTORiAL | 3.53 GB
Gain new perspective on two of the greatest achievements of human culture-music and math-and the fascinating connections that will help you more fully appreciate the intricacies of both.

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.

Understanding the connections between music and mathematics helps you appreciate both, even if you have no special ability in either field-from knowing the mathematics behind tuning an instrument to understanding the features that define your favorite pieces. By exploring the mathematics of music, you also 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.

Among the insights offered by the study of music and mathematics together are these:
Harmonic series: The very concept of musical harmony comes from mathematics, dating to antiquity and the discovery that notes sounded together on a stringed instrument are most pleasing when the string lengths are simple ratios of each other. Harmonic series show up in many areas of applied mathematics.

"Air on the G String": One of Bach's most-loved pieces was transposed to a single string of the violin-the G string-to give it a more pensive quality. The mathematics of overtones explains why this simple change makes a big difference, even though the intervals between notes remain unchanged.

Auditory illusions: All voices on cell phones should sound female because of the frequency limits of the tiny speakers. But the human brain analyzes the overtone patterns to reconstruct missing information, enabling us to hear frequencies that aren't there. Such auditory illusions are exploited by composers and instrument makers.

Atonal music: Modern concert music is often atonal, deliberately written without a tonal center or key. The composer Arnold Schoenberg used the mathematics of group theory to set up what he called a "pan-tonal" system. Understanding his compositional rules adds a new dimension to the appreciation of this revolutionary music.

In 12 dazzling lectures, How Music and Mathematics Relate gives you a new perspective on two of the greatest achievements of human culture: music and mathematics. At 45 minutes each, these lectures are packed with information and musical examples from Bach, Mozart, and Tchaikovsky to haunting melodies from China, India, and Indonesia. There are lively and surprising insights for everyone, from music lovers to anyone who has ever been intrigued by mathematics. No expertise in either music or higher-level mathematics is required to appreciate this astonishing alliance between art and science.

A Unique Teacher
It is a rare person who has the background to teach both of these subjects. But How Music and Mathematics Relate presents just such an educator: David Kung, Professor of Mathematics at St. Mary's College of Maryland, one of the nation's most prestigious public liberal arts colleges. An award-winning teacher, mathematician, and musician, Professor Kung has studied the violin since age four, and he followed the rigorous track toward a concert career until he had to choose which love-music or mathematics-would become his profession and which his avocation. At St. Mary's College, he combines both, using his violin as a lecture tool to teach a popular course on the mathematical foundations of music. He even has students invent new musical instruments based on mathematical principles.

In How Music and Mathematics Relate, you see and hear some of these ingenious creations, which shed light on the nature of all sound-producing devices. Across all 12 lectures Professor Kung plays the violin with delightful verve to bring many of his points vividly to life.

Uncover Musical Structure Using Math
You will discover how mathematics informs every step of the process of making music, from the frequencies produced by plucking a string or blowing through a tube, to the scales, harmonies, and melodies that are the building blocks of musical compositions. You even learn what goes on in your brain as it interprets the sounds you hear. Among the fascinating connections you'll make between music and mathematics are these:
Woodwind mystery: Why can a clarinet produce sounds much lower than a flute? Both are vibrating tubes of similar length. A student-designed instrument called the Wonder Pipe 4000 demonstrates how mathematics predicts this phenomenon.

Why is a piano never in tune? Elementary number theory explains the impossibility of having all the intervals on a piano in tune. Study the clever solutions that mathematicians, composers, and piano tuners have devised for getting as close as possible to perfect tuning.

Timbre: Nothing is more distinctive than the "twang" of a plucked banjo string. But take off the initial phase of the sound-the "attack"-and a banjo sounds like a piano. Analyze different sound spectra to learn what gives instruments their characteristic sound or timbre.

Using fractions to show off: Professor Kung plays a passage from Mendelssohn's Violin Concerto to demonstrate a common trick of showmanship for string players. The technique involves knowing how to get the same note with different fractional lengths of the same string.

And you'll hear how one of the greatest philosophers and mathematicians of all time described the connection between music and mathematics. "Music is a secret exercise in arithmetic of the soul, unaware of its act of counting," wrote Gottfried Wilhelm Leibniz, co-inventor of calculus with Isaac Newton. What Leibniz means, says Professor Kung, is that music uses many different mathematical structures, but those structures are hidden. With How Music and Mathematics Relate, you'll see these hidden connections come to light.


1 Overtones-Symphony in a Single Note
2 Timbre-Why Each Instrument Sounds Different
3 Pitch and Auditory Illusions
4 How Scales Are Constructed
5 How Scale Tunings and Composition Coevolved
6 Dissonance and Piano Tuning
7 Rhythm-From Numbers to Patterns
8 Transformations and Symmetry
9 Self-Reference from Bach to G?del
10 Composing with Math-Classical to Avant-Garde
11 The Digital Delivery of Music
12 Math, Music, and the Mind

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  Resident 10.09.2012 8 1318
headbang SUNNY headbang

Sunny = the president
  Resident 14.02.2013 220
u tryin to teach me math eh?
the only way to deal with an unfree world is to become so absolutely free that your very existence is an act of rebellion - camus
  Resident 16.08.2010 19 613

Ahah my thoughts exactly rofl

But when it comes to music i'll take anything. Thanx Sunny wink
  Resident 11.12.2011 4 954
WOW wow

Thank you, thank you, thank you Sunny!!!

Always wanted to know the relation between music and mathematics, and despite i have some books about it, a video tutorial is a lot much better yes

Thanks again! mates
The future of mankind depends on love and not on new technologies
  Member 15.02.2013 32
Thanks!!!! I always wanted to know this relation too!!! I'm a math teacher, but I don't know about this kind of stuff!!!

Thanks Sunny!!!
  guest -- 0
  guest -- 0
thank God i graduate music university
  Resident 10.04.2012 189
great upload. any chance for extabit links??
Trust, but verify.
  Resident 1.11.2010 2 342
Maths and Music, Maths and Architecture, Medicine, Human Measurements, Chimiques, how much floor and sugar or salt to cook, the number of eggs in the cake. TTC.Videos are wonderful.

Sometimes they invent so much fantasy about the math, and say they are gold secrets. Who studied music until the last consequences, learn that the mathematics of music and absurdly simple and without any secrets, is it because we can't say "Music Theory", that is no theory and that simplicity is what makes the music more fascinating, simple mixing flour with eggs and sugar and decorate the cake at the end with the desired colors. But, the quantity of floor and eggs, makes one composer different from the other.

This is the biggest secret of the mathematics of music, quantity and decoration, what can be done to excess such as in the Baroque Era or less as in Romanticism. The sound of the instrumentation, equilibrium or what you call personnel art, you decide. But, the maths on the ground are the same.

But, studying the simple math of the Russian composer "Igor Stravinsky" and his Russian music phase time is something fascinating. He simply numbered the sound from top to bottom (notes: E = 0, D = 2, C # = 3, B = 5, A = 7, G = 9) and uses only six notes in music making transpositions. He called this 0,2,3,5,7,9 a sonority and when the ear gets tired, he decides to use the Russian Octatonic Scales that is: (0,2,3,5, 6,8,10,11), you must have noticed that the commom sound 0,2,3,5 best known among jazz musicians, is the dorian scale. So, all Stravinsky's long scores of his wonderful Atonal Russian period is the simple maths that we learn on the first degree of school: theory of sets of numbers.
  guest -- 0
You must be clever to analyse that weste, or you took it from some book, if yes, tell us about such stuff. Whatever, a must for higher studies.
  Member 13.10.2012 56
thx....when we transpose music say from C to G, we alrady using math
  Resident 1.11.2010 2 342
guling, Sure, but don't forget the instruments 'tessitura', they will scape 7 semitones of their own register. So, the Trumpet must loose 5 essential notes from the bottom 'E2 note' and the upper note after transposition from C to G will have now the B5-C-D-E and F5s notes, than you have to change that 'Tp' part to trombone for the bottom and Piccolo Trumpet to the Higher notes, or re-write the melody, if, just if, it belongs to you. That's a good Math challenge.

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