Moving to the music
Jul 24, 2008 6 comments
If your idea of enjoying a concert is sitting in a nice comfortable seat and listening to a group of musicians playing a meticulously rehearsed piece of music then you may have to think again.
Kaća Bradonjić, a physicist at Boston University in the US, has used the Doppler effect (the change in the pitch of a sound that occurs when its source and the listener are moving relative to each other) to show how the perceived emotional character of a chord changes as the listener moves.
She has calculated exactly what velocities a listener would need to travel at to create specific variations of mood, in order that they can tailor their “listening experience” (arXiv:0807.2493).
The perceived mood of a chord can be relative to a listener’s frame of reference Kaća Bradonjić, Boston University
Bradonjić’s day job is to carry out research on general relativity, but she also takes an interest in all things musical and artistic and realized that, as she puts it, “the perceived mood of a chord can be relative to a listener’s frame of reference”.
In her paper, she considers the conventional Western “chromatic” musical scale, in which the frequencies of neighbouring notes differ by a factor of 21/12 (an interval known as a semitone). Using the Doppler transformation for a stationary emitter and moving observer she shows that a listener must travel (1-2-1/12) times the speed of sound away from the source of a note in order to reduce the perceived pitch of that note by a semitone.
Bradonjić then considered the velocities that a listener must travel at to transform specific three-note chords when the notes are emitted by three separate sources positioned away from the listener along orthogonal axes.
Major to minor
For example, to hear the happy-sounding C major (which consists of the notes C, E and G) as the sad-sounding C minor (C, E flat and G) the listener would have to move with a speed of 19.25 ms-1 (about 70 km/h or 43 mph) away from the E emitter. Making the opposite transformation would instead require travelling in the opposite direction with a speed of 20.40 ms-1.
She then goes on to show how a listener can make more complex changes by moving in three dimensions. However, she points out that the upper limit of the speed of sound and the power-law nature of the chromatic scale result in an upper limit on how much a perceived frequency can increase — which is one octave. There is no limit when decreasing pitch, says Bradonjić.
Bradonjić says the motivation behind her research is “to put the listener into the ‘driver's seat’, letting him navigate through the song as he pleases.” She concedes that putting a room full of concert goers literally into the driver’s seat could present certain logistical difficulties, especially since they would not be moving any slower than they would on the roads.
She suggests that individuals of an adventurous persuasion could perhaps “use a jet pack to zig-zag around a set of giant speakers”, but she thinks that people interested in her idea should instead simulate such an experience in a virtual computer environment. She adds that the information on the listener's path could then be used to create visual effects similar to those created by computer music players.
About the author
Edwin Cartlidge is a science journalist based in Italy