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Two tones played together form an ''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''. 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 ===

''Counterpoint'' is a specific technique for creating secondary melodies that intertwine with and compliment the main melody. When two or more notes sound at the same time, it is called a ''chord,'' and the distance between the notes is the ''interval.''  In the western 12-note scale common usage, an interval is often  expressed in relative terms, using the eight notes that make up an octave and prefixing 'major' or 'minor' to account for the interstitial notes.  For instance, the interval between 'C' and 'E' is a ''3rd'' because 'E' is the 3rd note in the major scale of C.  One-half step below that is a ''minor 3rd,'' although this exact same note could also be called a ''major 2nd''.   

''Counterpoint'' is a specific technique for creating secondary melodies that intertwine with and compliment the main melody. When two or more notes sound at the same time, it is called a ''chord,'' and the distance between the notes is the ''interval.''  In the western 12-note scale common usage, an interval is often  expressed in relative terms, using the eight notes that make up an octave and prefixing 'major' or 'minor' to account for the interstitial notes.  For instance, the interval between 'C' and 'E' is a ''3rd'' because 'E' is the 3rd note in the major scale of C.  One-half step below that is a ''minor 3rd,'' although this exact same note could also be called a ''major 2nd''.   

Many of the feelings and emotions that music can evoke are a result of the tension between the ''harmonic'' sound of some intervals, and the ''dissonant'' sound of others.  During the development of western music, certain rules were established for proper melodic counterpoint, and these rules specified how intervals (chords) could change over time in the music.  For example, in the chants of Gregorian Monks, chords containing certain intervals, like 7ths, were required to 'resolve' to their harmonious natural key, while other intervals, like minor 5ths, were deemed ugly and even considered evil, and banned from use in liturgic music.  Johann Sebastian Bach (1685-1750) represents the pinnacle of this style of strict rule-based composition, as many of his keyboard compositions and all of his sacred work adhere to the rules of counterpoint.  From the height of the Baroque era (1700's) to the present, the history of western music has unfolded as each generation of composers has pushed the boundaries of these these rules right up to, and then in the 20th century, way beyond, all limits.

Many of the feelings and emotions that music can evoke are a result of the tension between the ''harmonic'' sound of some intervals, and the ''dissonant'' sound of others.  During the development of western music, certain rules were established for proper melodic counterpoint, and these rules specified how intervals (chords) could change over time in the music.  For example, in the chants of Gregorian Monks, chords containing certain intervals, like 7ths, were required to 'resolve' to their harmonious natural key, while other intervals, like minor 5ths, were deemed ugly and even considered evil, and banned from use in liturgic music.  Johann Sebastian Bach (1685-1750) represents the pinnacle of this style of strict rule-based composition, as many of his keyboard compositions and all of his sacred work adhere to the rules of counterpoint.  From the height of the Baroque era (1700s) to the present, the history of western music has unfolded as each generation of composers has pushed the boundaries of these these rules right up to, and then in the 20th century, way beyond, all limits.

In modern popular music, the bass line is often seen as an example of counterpoint.  Another, more accurate example would be dueling guitar leads.

In modern popular music, the bass line is often seen as an example of counterpoint.  Another, more accurate example would be dueling guitar leads.

Any one of these notes may carry a beat, and a measure may have any number of beats. Thus every piece of music commonly carries at least one ''time signature'' describing how many beats a measure has, and which type of note carries one beat. The most common time is "four-quarter time" (four beats per measure, with the beat given to the quarter note), which is therefore called "common time." Other commonly used time signature include three-quarter, six-eighth, nine-eighth, or rarely, two-half (called ''Alla breve'' or "cut time"). Even rarer are the time signatures with prime numbers of beats (other than three-quarter), including five-quarter or even eleven-eighth.

Any one of these notes may carry a beat, and a measure may have any number of beats. Thus every piece of music commonly carries at least one ''time signature'' describing how many beats a measure has, and which type of note carries one beat. The most common time is "four-quarter time" (four beats per measure, with the beat given to the quarter note), which is therefore called "common time." Other commonly used time signature include three-quarter, six-eighth, nine-eighth, or rarely, two-half (called ''Alla breve'' or "cut time"). Even rarer are the time signatures with prime numbers of beats (other than three-quarter), including five-quarter or even eleven-eighth.

''Tempo'' (Italian for "time") describes how frequently the beats occur. The typical tempo signature is a drawing of the note that has the beat, followed by the number of beats per minute.

''Tempo'' ([[Italian]] for "time") describes how frequently the beats occur. The typical tempo signature is a drawing of the note that has the beat, followed by the number of beats per minute.

Notes may be ''accented'' at any time. In fact, often the accent will fall on the weak beat and make the beats seem to sound out-of-sequence. The result is ''syncopated'' rhythm.

Notes may be ''accented'' at any time. In fact, often the accent will fall on the weak beat and make the beats seem to sound out-of-sequence. The result is ''syncopated'' rhythm.