Pitch class space

In this space, there is no distinction between tones separated by an integral number of octaves.

Deutsch and Feroe (1981), and Lerdahl and Jackendoff (1983) use a "reductional format" to represent the perception of pitch-class relations in tonal contexts.

These two-dimensional models resemble bar graphs, using height to represent a pitch class's degree of importance or centricity.

One could therefore display Lerdahl's graph as a series of five concentric circles representing the five melodic "alphabets."

According to David Kopp (2002, 1), "Harmonic space, or tonal space as defined by Fred Lerdahl, is the abstract nexus of possible normative harmonic connections in a system, as opposed to the actual series of temporal connections in a realized work, linear or otherwise."