Music theory describes how sounds, which travel in waves, are notated, and how what is sounded, or played, is perceived by listeners. The study of how humans interpret sound is called psychoacoustics, while the cognitive aspects of how perceived sounds are interpreted into musical structures is studied in music cognition. In music, sound waves are usually measured not by length (or wavelength) or period, but by frequency.
Every object has a resonant frequency which is determined by the object's composition. The different frequencies at which the sound producers of many instruments vibrate are given by the harmonic series. The resonators of musical instruments are designed to exploit these frequencies. Different instruments have different timbres due to variation in the size and shape of the instrument as well as the choice of materials from which the parts of the instrument are constructed.
A note is generally perceived as a sound on a single pitch. Notes have a regular wave beat on the eardrum that humans (and perhaps other animals as well) find pleasing. This may be in part due to the fact that from the moment the hearing function becomes available to an unborn child, there is the regular rhythm of the mother's heartbeat.
Often the fundamental aspects of sound and music are described as pitch, duration, intensity, and timbre
Pitch
Sounds can be classified into pitches, according to their frequencies or their relative distance from a reference pitch. Tuning is the process of assigning pitches to notes. The difference in pitch between two notes is called an interval. Notes, in turn, can be arranged into different scales and modes. The most common scales are major, harmonic minor, melodic minor, and pentatonic.
The Key of a piece of music determines what frequency each note is played at. A piece in the key of D major will put all the notes two semitones higher than a piece in the key of C major. Changing the key can change the feel of the piece of music dramatically, as it changes the relation of the pitches of the composition to the pitch range of the instruments on which the piece is being performed, often effecting timbre as well as having other more technical implications for the performers. However, key changes may also go unrecognized to the audience, as changing the key does not (by definition) change the relation of the pitches of the composition to each other, and so different keys can in many cases be considered equivalent and a matter of choice on the part of performers (this is especially true for popular and folk musics).
Rhythm
Rhythm is the arrangement of sounds in time. Meter animates time in regular pulse groupings, called measures (or bars in British English). The time signature specifies how many beats are in a measure, and which kind of written note is counted and felt as a single beat. Through increased stress and attack (and subtle variations in duration), particular tones may be accented. There are conventions in most musical traditions for a regular and hierarchical accentuation of beats to reinforce the meter. Syncopated rhythms are rhythms that accent parts of the beat not already stressed by counting. Playing simultaneous rhythms in more than one time signature is called polyrhythm.
In recent years, rhythm and meter have become hot topics among music scholars. Recent work in these areas includes books by Fred Lerdahl and Ray Jackendoff, Jonathan Kramer, Christopher Hasty, William Rothstein, and Joel Lester.
Melody
Melody is the unfolding in musical time of a principle single line. This line can be sounded alone, unaccompanied; or it can be the top (or sometimes an inner) note of a sequence of chords, or sounded against chords as a background by accompanying instruments or voices. Melodic rhythm is usually rooted in the accent patterns of language, and/or the animating rhythms of dance steps and forms.
In much of Western music, melody is often the most identifiable theme. Melodies will often imply certain scales or modes. Counterpoint is the study of combining and layering more or less independent melodies.
Harmony, consonance, & dissonance
Harmony can generally be thought of as occurring when two or more pitches are sounded simultaneously, although harmony can be implied when pitches are sounded successively rather than simultaneously (as in arpeggiation). Harmonies involving three or more pitches sounded simultaneously are referred to as chords, though the term is generally used to indicate an organized selection of pitches rather than just any three or more pitches.
Consonance can be roughly defined as harmonies whose tones complement and augment each others' resonance, dissonance as those which create more complex acoustical interactions (called 'beats'). Another manner of thinking about the relationship regards stability; dissonant harmonies are sometimes considered to be unstable and to "want to move" or "resolve" toward consonance. However, this is not to say that dissonance is undesirable. A composition made entirely of consonant harmonies may be pleasing to the ear and yet boring because there are no instabilities to be resolved.
Brief audio (MIDI) musical examples of the interaction and effect of consonance and dissonance upon each other can be found here: "The effect of context on dissonance'" and here: "The role of harmony in music"
Melody is often organized so as to interact with changing harmonies (sometimes called a chord progression) that accompany it, setting up consonance and dissonance.
"Harmony" as used by music theorists can refer to any kind of simultaneity without a value judgment, in contrast with a more common usage of "in harmony" or "harmonious", which in technical language might be described as consonance.
Texture
Musical texture is the overall sound of a piece of music commonly described according to the number and relationship between parts or lines of music: monophony, heterophony, polyphony, homophony, or monody. The perceived texture of a piece may also be affected by the timbre of the instruments playing these parts and the harmony and rhythms used, among other things.
Notation
Music notation is the graphical representation of music. In standard notation, pitches (notes) are represented on the vertical axis and time (rhythm) is represented as symbols on the horizontal axis. Together, these two components make up the musical staff, along with directions indicating the key, tempo, dynamics, etc.
