Connections: Math and Music

 

Pitches, Scales, Geometry: An old page from Drexel University, but it’s a good one.

http://mathforum.org/library/drmath/view/52312.html


More detailed than a beginner needs, but this has good graphics showing the relationships (fractions) of music notes and rests.

http://www.dolmetsch.com/musictheory2.htm


A good article about temperament (tuning). A short paragraph about Pythagoras, and some very detailed information.

http://www.yuvalnov.org/temperament/


A really good page (with sound files) about Pythagorean tuning:

http://www.music.sc.edu/fs/bain/atmi02/pst/index.html


A very technical page with short movies which show how strings vibrate.

http://www.kettering.edu/~drussell/Demos/string/Fixed.html


This starts with a good table showing ratios of intervals, and then it becomes a very technical page about different drums and their acoustical properties.

http://www.kobushi.com/acoustics/index.html


One of the best pages I’ve seen yet of math/music basics.

http://members.cox.net/mathmistakes/music.htm


Simple music patterns and how you can use them to create your own music.

http://www.creativemusicworks.com/impl3ost.htm


A good page on the harmonic series

http://cnx.org/content/m11118/latest/


Information about tuning

http://www.kirnberger.fsnet.co.uk/TempsII.htm


To learn more about drums and rhythms try this page:

http://blog.drumcrazy.co.uk/blog/_archives/2007/2/20/2751927.html


If you want to learn 1200 (really!) rhythmic patterns, this is the place to start:

http://www.rhythm-patterns.narod.ru/1216-01.html


Flute acoustics: there is a whole series of pages here, with lots of interesting animations and links. Everything you ever wanted to know about how flutes (and other wind instruments) work!

http://www.phys.unsw.edu.au/jw/fluteacoustics.html#overview


The same website above (phys.unsw.edu) has a good FAQ page for lots of other musical questions:

http://www.phys.unsw.edu.au/jw/musFAQ.html


Pythagoras: a class at Dartmouth put up these pages with interesting illustrations and text that make sense of Pythagoras’ ideas about music and numbers.

http://www.dartmouth.edu/~matc/math5.geometry/unit3/unit3.html


Steve Reich’s “clapping music”; an old, small-screen video of two people performing the work

http://www.stevereich.com/multimedia/clappingMedProg.html


The score for “clapping music” can be found at:

http://www.lichtensteiger.de/clapping_music.html


There are several YouTube videos of “clapping music”. One of my favorites shows 6 jugglers---I have no idea how they do it!

http://www.youtube.com/watch?v=dXhBti625_s


A fun interactive game using music.

http://balldroppings.com/js/


Make music using the digits of pi

http://avoision.com/experiments/pi10k





I’ve presented Math and Music to audiences of all ages, from elementary school students to knowledgeable adults at the Smithsonian. The main topics covered include simple arithmetic (counting, fractions); graphs; ratios; patterns; frequencies; harmonics (also called overtones); and tuning. Other topics get thrown in tangentially. 



A few related websites: