The material of a musical composition is usually taken from a collection of pitches known as a scale. Because most people cannot adequately determine absolute frequencies, the identity of a scale lies in the ratios of frequencies between its tones (known as intervals). In music, a scale is any set of musical notes ordered by fundamental frequency or pitch. Ascending scales are ordered by increasing pitch, while descending scales are ordered by decreasing pitch. Sometimes, scales contain both an ascending and a descending portion (for instance, see Chromatic scale and Melodic minor scale). Often, especially in the context of the common practice period, part or all of a musical work including melody and/or harmony, is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature. A measure of the distances (or intervals) between pairs of adjacent notes provides a method to classify scales. For instance, a major scale is defined by the interval pattern T-T-S-T-T-T-S, where T stands for whole tone, and S stands for semitone. Based on their interval patterns, scales are divided into categories including diatonic, chromatic, major, minor, and others. A specific group of notes can be described, for instance, as a C-major scale, D-minor scale, etc.. This takes into account the selection of a special note, also known as the first degree (or tonic) of the scale. For example, C-major indicates a major scale in which C is the tonic. Scales are typically listed from low to high. 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. The notes of a scale are numbered by their steps from the root of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to each other: C and E create an interval of a third (in this case a major third); D and F also create a third (in this case a minor third). In music theory, an interval is the difference between two pitches. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, the most commonly used intervals are those formed between the notes of the chromatic scale. Intervals smaller than a semitone, the smallest interval found in the chromatic scale, are called microtones. These are most commonly found in non-Western music using scales of more than 12 notes. Some of the very smallest named intervals stem from considerations of intonation. For example, the syntonic comma. However, intervals can theoretically be arbitrarily small, even if imperceptible to the human ear.