Music theory is the field of study which analyses the various features of music in order to understand how music works. The components analysed include:
How high or low the notes sound, which is a result of the soundwave's frequency. The continuous spectrum of possible frequencies is divided into discrete, named units called notes. Every doubling in frequency (between, for example 100Hz and 200Hz, or between 200Hz and 400Hz), is known as an octave. Any two notes whose frequencies are in a 2:1 ratio share the same name. So, for example, the A above middle C has a frequency of 440 Hz. The notes with double or quadruple that frequency (880, 1760, ...) and the notes with a half or quater that frequency (220, 110, ...) are also named A.
In Western music, each octave is divided into twelve notes. Every scale contains eight, which are named after the first seven letters of the alphabet: A, B, C, D, E, F and G (the eighth note being, of course, the octave above the first note). On a piano, these correspond to the "white notes", while the "black notes" are written as modifications to them. Each black note is named after one of the white notes next to it; if it is immediately above A, it is referred to as A sharp. If it is immediately below A, it is known as A flat. There are, therefore, several different ways to write a note, all of which will produce the same sound. A G-sharp and an A-flat correspond to the same sound, and are known as enharmonic equivalents. Which spelling of a note one should use depends on the context in which it is written.
A group of notes played in sequence, also known as a tune, an air or a line. Melody is usually subdivided into phrases, and often come together to form periods. Having more than one melody played together (where none of the individual lines is felt to be of greater importance than the others) is known as counterpoint, and is most common in the works of Baroque composers such as Bach and Handel.
How the notes are organised temporally, and their relative durations. Most music contains a repeating pattern of stressed and unstressed beats. In written form, in what is known as Standard Notation, the start of each new unit of this pattern is marked by a vertical line known as a barline. Each such unit is referred to as a measure or a bar. The first beat of every bar is normally the most heavily emphasised, although the total number of beats in a measure differs between pieces and sometimes within a piece. A march typically has two or four beats per bar, while a waltz typically has three. The number of beats per bar is designated by a time signature.
Harmony is the study of notes which occur together or which are perceived as being together. This usually means notes which are played simultaneously, as in a chord, but can also apply to notes within a melody which outline a chord. The harmony that results from the combination of any two or more notes depends on the interval present between those notes. A system of Roman numerals is the most common means used to analyse harmony.
Form refers to the structural aspects of a piece of music. In formal analysis, a letter is assigned to each distinct section of a piece. Basic examples of form include binary form (A B), in which one section is followed by a contrasting section, or ternary form (A B A'), in which the first section returns, usually in slightly altered form (denoted by the addition of an apostrophe to the final A), to give a sense of formal closure. The typical form of a popular song might be written as ABABCAB, where A is the verse, B is the chorus, and C is the bridge. One commonly used form in the classical periods is Sonata form, which is a specialised, elaborate binary form. Sonata form, in classical music, is typically used as the first movement in most large-scale instrumental works such as symphonies and concertos. Another commonly used form is rondo form, in which a recurring section is contrasted with successive new sections, whose simplest version can be described as ABACA'. It is often used in the final movement of large works.
While these letters are used to describe contrasting sections, this contrast is sometimes created by a completely different melody or musical texture, and sometimes by changing the key (or modulating), often by both. A binary form, for example, usually contains very similar musical material in the A and B parts, but in different keys. In a sonata form, a succession of contrasting musical themes and a modulatory plan work together to define the structure of the movement.