The Duochord

This OER was designed by the OU Academy of the Lynx (oulynx.org) in conjunction with the "Galileo's World" (galileo.ou.edu) exhibition at the University of Oklahoma.

This activity is designed to be completed in 5 minutes by a typical visitor to the exhibition. For adaptations to other age levels and pedagogical settings, visit the "Duochord Educational Cluster" below.

Introductory Duochord Activity

The duochord is an instrument designed to teach the interrelationship between mathematics and music.

** The only supply necessary to complete this activity is a duochord. We suggest this one if you do not already have one, http://www.drmass.com/set-of-3-monochord-strings.html?gclid=CLj09-KhrsgCFZSCaQode8IKRg.

Before beginning, first make sure that the strings of the duochord are in tune with one another.

Pythagorean Octave - 2:1 

1. Locate the marker on the duochord that divides the string into equal halves.
2. Place a moveable bridge under the halfway marker of one string and pluck half of the string. The resulting note will be one octave higher than the unaltered string. 

Pythagorean Perfect Fifth - 3:2 

1. Locate the markers on the duochord that divide the string into three equal segments. 
2. Place a moveable bridge over one marker dividing the string into segments of 1/3 and 2/3 of its entire length. Pluck the long side, or 2/3 of the divided string, to produce an interval of a perfect fifth higher than the unaltered string. 

Pythagorean Perfect Fourth - 4:3 

1. Locate the markers on the duochord that divide the string into four equal segments. 
2. Place a moveable bridge over one marker dividing the string into segments of 1/4 and 3/4 of its entire length. Pluck the long side, or 3/4 of the divided string, to produce an interval of a perfect fourth higher than the unaltered string.

Enjoy a downloadable pdf of this activity:

Historical Background for the Duochord

The duochord is an instrument designed to teach the underlying mathematical foundation to music. Since at least the time of Pythagoras, who lived in the 6th century BCE, nature was believed to have an underlying ratio, or harmony. These geometric ratios brought together the natural world and the musical world in such a way that they were interconnected. Thus in the liberal arts tradition the four arts, known as the "quadrivium", were arithmetic, geometry, astronomy, and music.

In the time of the Renaissance, in the fifteenth and sixteenth centuries, the significance of music was being reconsidered as a result of previously unknown ancient Greek texts being rediscovered. All of this contributed to various Renaissance debates about the relationship between mathematics and music. Galileo's father, Vincenzo Galilei, was involved in such debates. Read more about this here, https://galileo.ou.edu/exhibits/dialogue-ancient-and-modern-music.

With mathematics serving as the foundation of both music and astronomy, many individuals during the Renaissance explored the interrelationship between music and astronomy. This was most famously done by Johnnes Kepler in his Harmony of the Universe. Read more about this here, https://galileo.ou.edu/exhibits/harmony-universe.

Robert Fludd also produced a work in which he presented the universe as a monochord. https://galileo.ou.edu/exhibits/two-worlds-namely-major-and-minor.

Further OER's on the Duochord

Use the following OER's to further explore the planisphere.

• "The Harmony of the Spheres" from Museo Galileo website, http://brunelleschi.imss.fi.it/galileopalazzostrozzi/multimedia/TheHarmonyOfTheSpheres.html.
• "Pythagoras" from MacTutor History of Mathematics, http://www-history.mcs.st-and.ac.uk/Biographies/Pythagoras.html.

Use the following OER's to further explore the Galileo's World exhibition.

• Galileo's World iPad Exhibit Guide, itunes.apple.com/us/book/galileos-world-exhibit-guide/id1032005948?mt=1.
• Galileo's World iTunes U Course, itunesu.itunes.apple.com/enroll/FDS-EYK-MRL.
• Galileo's World website, galileo.ou.edu.

Duochord Educational Cluster

We want to create variations on this activity that connect the Duochord to a variety of ages. Use the following chart and hyperlinks to find the one to best fit your group.