Scale

A scale is a collection of pitches, ascending or descending in fundamental frequency, which adheres to a system of organization allowing it to define a mode, key area, or some other form of pitch collection. While there is a wide variety of scales cross-culturally, most cultures allow for octave equivalence in their scale systems, with scales frequently consisting of between five to seven pitch classes per octave.

However, the defining characteristic of a scale is not the specific pitches used, but rather the intervallic content of the collection resulting from the pitch categories used. Most scales are asymmetrical in nature (unequal distances between adjacent scale notes), which allows tones to have different functions within a scale and thus for there to be some hierarchical structure or tonal center created by the scale.

From a psychological perspective, the intervallic content of a scale allows a listener to create a mental representation of that scale. Both musicians and nonmusicians can quickly determine the scale used in a piece of music and are able to tell if pitch classes are members of that scale. The statistical learning framework theory posits that listeners develop a mental representation of the frequency with which pitches occur in an established system, both tonal and nontonal, and that this mental representation helps with key determination in tonal contexts and with recognizing and learning nontonal contexts. The source of this musical knowledge is not clear: it may be the result of constraints in the auditory system as well as enculturation. Moreover, syntactic processes shared with language may underlie our ability to recognize when a note is not in the ongoing scale.

Chromatic Scale

The chromatic scale represents the Western practice of division of the octave into 12 equally spaced tones, creating intervals of a half step, or semitone, and arranged in ascending and descending order. The chromatic scale is a symmetrical division of the octave and thus does not provide any context for a tonal center, so the beginning and ending pitch of the notated scale is arbitrary (see Example 1).

Example 1The chromatic scale