Before starting Problem Set 1, read this excerpt from Dmitri Tymoczko:
Reading for Problem Set 1
Dmitri Tymoczko, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford: Oxford University Press, 2011), Chapter 2, pp. 28–38 (though just the first two lines of p. 38).
Problem Set 1: Pitch Representation and Manipulation
Tymoczko’s Pitch Representation
Tymoczko is mostly thinking in a Pitch Space or a Pitch Class representation, where, for instance, C# and Db are the exact same note. Don’t try this in 21M.302 or other tonal harmony classes: In these cases, the notes “A”, “Db”, “E” are not an A-major triad. There are some places where it makes sense to think this way, but, as you surely saw in the discussions (or in theory class), there are worlds where spelling matters.
Pay close attention to when problems in PSets assume pitch spelling matters and when it does not. Obviously, if we are writing “flip_enharmonic” then spelling matters!
A Note on the Universality of Octave Equivalence
On p. 30, Tymoczko writes, “Octave equivalence seems nearly universal in human cultures.” Since the book came out, this has been shown not to be true. For those interested the article about it is in Current Biology 29(19), 2019, and written by a team including two people at MIT.
