Changes

Two tones played together form an [[interval (music)|''interval'']]. The simplest of all intervals is the ''[[octave]]'', formed by two tones, one of whose frequencies is the exact double of the other. The full collection of tones that one can play between the two notes of an octave is called a ''[[musical scale|scale]].'' In Western music, most scales are ''semi-tonal'', with twelve tones between the octave notes. (The high end of the octave is considered a repetition of the low end, but at twice the frequency.) [[Oriental]] music commonly has ''quarter-tonal'' scales, with twenty-four separate tones within an octave. Quarter tones are often difficult to distinguish for a Western listener, and such music, as a result, tends to suggest the sinuous movement of a snake.

Two tones played together form an [[interval (music)|''interval'']]. The simplest of all intervals is the ''[[octave]]'', formed by two tones, one of whose frequencies is the exact double of the other. The full collection of tones that one can play between the two notes of an octave is called a ''[[musical scale|scale]].'' In Western music, most scales are ''semi-tonal'', with twelve tones between the octave notes. (The high end of the octave is considered a repetition of the low end, but at twice the frequency.) [[Oriental]] music commonly has ''quarter-tonal'' scales, with twenty-four separate tones within an octave. Quarter tones are often difficult to distinguish for a Western listener, and such music, as a result, tends to suggest the sinuous movement of a snake.

The [[Greece|Greeks]] recognized early that fundamental tones in music have a simple and strict [[mathematics|mathematical]] relationship. As mentioned, the octave consists of two notes, one at double the frequency of the other. At ''triple'' the frequency, one hears a low fundamental tone, and a higher tone that is past the octave but roughly midway toward the second octave. If one then divides the high-tone frequency by two, one creates the interval called the ''perfect fifth'' or ''dominant'' interval, one of the most common intervals used in Western music. One can test this relationship by striking a note on a [[piano]] while holding down another key that is one octave higher than the perfect fifth. The second note will sound in sympathy with the first—because it is resonating with the overtone from the first note.

The [[Greece|Greeks]] recognized early that fundamental tones in music have a simple and strict [[mathematics|mathematical]] relationship. As mentioned, the octave consists of two notes, one at double the frequency of the other. At ''triple'' the frequency, one hears a low fundamental tone, and a higher tone that is past the octave but roughly midway toward the second octave. If one then divides the high-tone frequency by two, one creates the interval called the ''perfect fifth'' or ''dominant'' interval, one of the most common intervals used in Western music. One can test this relationship by striking a note on a [[piano]] while holding down another key that is one octave higher than the perfect fifth. The second note will sound in sympathy with the first because it is resonating with the overtone from the first note.

=== Melody and counterpoint ===

=== Melody and counterpoint ===