Scale (music)

In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency.

The word "scale" originates from the Latin scala, which literally means "ladder". Therefore, any scale is distinguishable by its "step-pattern", or how its intervals interact with each other.

Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature.

Due to the principle of octave equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or interval) between two successive notes of the scale. However, there is no need for scale steps to be equal within any scale and, particularly as demonstrated by microtonal music, there is no limit to how many notes can be injected within any given musical interval.

A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern W–W–H–W–W–W–H, where W stands for whole step (an interval spanning two semitones, e.g. from C to D), and H stands for half-step (e.g. from C to D♭). Based on their interval patterns, scales are put into categories including pentatonic, diatonic, chromatic, major, minor, and others.

A specific scale is defined by its characteristic interval pattern and by a special note, known as its first degree (or tonic). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern. For example, C major indicates a major scale with a C tonic.

Scales are typically listed from low to high pitch. Most scales are octave-repeating, meaning their pattern of notes is the same in every octave (the Bohlen–Pierce scale is one exception). An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B–[C], with the bracket indicating that the last note is an octave higher than the first note, and the decreasing C major scale is C–B–A–G–F–E–D–[C], with the bracket indicating an octave lower than the first note in the scale.

The distance between two successive notes in a scale is called a scale step.