Music, Math, and Patterns - Math Central
Music theory has no axiomatic foundation in modern mathematics, yet the basis of musical . Because we are often interested in the relations or ratios between the You may need to play the samples several times before you can pick the. Also there are books about music which use a lot of mathematics in order to express music. An extreme example is the book by Guerino Mazzola, The Topos of. Math and music are usually organized into two separate categories, without obvious overlap. For example, a quarter note with a dot after it would be held for 3/8 It is important for musicians to understand the relationships and values of.
Geometry and angles My masters thesis is devoted in part to a method for teaching math concepts using a drum machine organized on a radial grid. Placing rhythms on a circle gives a good multisensory window into ratios and angles. Wave mechanics The brain turns out to be adept at decomposing sinusoids into their component frequencies. If two pitches share a lot of overtones, we tend to hear them as consonant, at least here in the western world.
The relationship between absolute pitches and pitch classes is an excellent doorway into logarithms generally. You also need logarithms to understand decibels and loudness perception. Symmetry Music is really just a way of applying symmetry to events in time.
See this delightful paper by Vi Hart about symmetry and transformations in the musical plane. Combinatorics and graph theory Generating diatonic chords from a scale is an exercise in combinatorics.
Seventeenth-century European bellringing introduced one of the earliest nontrivial results in graph theory, change or method ringing. Discrete mathematics The pitch continuum is, well, continuous, but tuning systems and scales are discrete. Mozart is well-known to have written music that is both beautiful and structurally impeccable.
Displace one phrase and the structure would fall. The theme is introduced immediately, and then developed into countless polyphonic variations.
Computer music With these connections between mathematics and music, it was perhaps inevitable that both mathematicians and musicians would turn to computers.
Music and mathematics
Thus the field of computer music was born. Numerous tools have been developed to assist in this task; indeed, many modern-day musicians, covering a wide range of specialties, now utilize computers in their work.
Some of the more interesting work in this area is to program computers to actually compose music.
David Copefor instance, has written computer programs that can analyze a corpus of music, say by a particular composer, and then create new works in a similar style. He was most successful in replicating and producing variations of the music of Bach and Mozart, which is perhaps not surprising given the highly mathematical structures used by these composers.
The Connection Between Music and Mathematics | Kent State Online Master of Music in Music Education
So to return to one of our original questions, is there a link between mathematical talent and musical talent? Furthermore, it is not as easy as one might think to scientifically test such a proposition.
Summary In short, while it is problematic to claim any kind of innate link between mathematical ability and musical ability, it is clear that the two disciplines have a deep commonality.
One of us Borwein has taught many students who were vacillating between musical, medical, and academic careers. And at many mathematical conferences, entertainment is provided by international-level pianists or violinists whose day job is mathematics. May your mathematical future also be a musical one! April 30th, Category: