The LerDial
This is an invention for demonstrating how to compute intraregional (diatonic non-modulating) chord distances according to the theory proposed in Fred Lerdahl's Tonal Pitch Space (2001). (I invented this and presented it to Lerdahl in 2010. I then publicly presented it in 2018 at Music Theory and Music Cognition: A Conference in Honor of Fred Lerdahl)

The device is easily constructed using a printout on paper (affixed to cardboard or other stiff material), a printout on a transparency, and a 1-inch metal fastener (puncturing through the center).

To use the LerDial:
1. Align the two layers to the starting position, that is so their dots are perfectly aligned. (A colored tab can be affixed to the end of five-dot column on the transparency, to make it trivial to move this column to the upright position.)
2. Put your finger on the starting chord from which you are measuring.
3. Dial the shortest distance to the destination chord, counting the number of moves. Call this number j.
4. Count the number of new dots (circles) left exposed by the dialing maneuver. Call this number k.

The chord distance is j+k.

Click on the image below to see and hear a computer demonstration.
NOTE: You can manually move the slider of the playback control of the QuickTime movie.

Click here or on the picture to watch the movie

© Joshua Banks Mailman 2010. All rights reserved.
The documents and media here are the intellectual property of Joshua Banks Mailman.