'[b]**THIS ARTICLE IS UNDER CONSTANT CONSTRUCTION AND EDITING!**'[/b]

A lot of the time, you'll hear people that claim music theory is not important, or maybe even that it stifles creativity. Often cited are case examples such as Paul McCartney's inability to read sheet music. While it is absolutely true that music theory is not required to write great music, for some people, it can help greatly, and introduce new ways to express oneself through music.

Music theory is a set of concepts and a language you can use to communicate ideas about music with other people. The main benefits of learning about music theory are that you will be able to express musical ideas in a concise and accurate manner and be able to think about music in a structured way.

Music theory is also dynamic. It looked much different 300, or even 50 years ago. What music theory really is, as all theory is, is documentation of things that happen, in this case, music! Different styles and techniques evolve over time, and they meld into theory along with everything else.

'[#[The Notes and Keeping Time]

A '[b]pitch'[/b] is a specific frequency of sound. This frequency may be expressed in '[b]Hertz'[/b] (Hz), a unit that measures cycles per second--in this case, oscillations per second of a pressure wave. Because of way the human ear and mind perceive sound, a pitch with a frequency that is an integer multiple of another pitch's frequency will sound very similar to it--for example, 440 Hz and 880 Hz. The pitches are clearly distinguishable, but seem to share a certain quality. Because of this effect, music has the concept of a '[b]pitch class'[/b]: a set of pitches with the same name that are considered more or less equivalent for the purposes of harmony (for example, "C"). In music, the most common way to refer to a pitch is by a combination of its pitch class and octave, such as "A4", a pitch of 440 Hz in modern tuning.

A sharp (not as in the note "A sharp" but as in the symbol ♯ commonly stylised as # in computer text) raises a pitch up by one semitone. For example the note C♯ is one semitone higher than the note C. A flat (not as in the note "A flat" but as in the symbol ♭ commonly stylised as b in computer text) lowers a pitch down by one semitone. For example the note B♭ is one semitone lower than the note B. Sharps and flats are called "accidentals". There is also another accidental called the natural ♮ which cancels any other accidental. For example if you have a key signature with B♭, E♭, and A♭ and you want to notate a B, you can put a natural sign to indicate B♮. 

The pitch classes are as follows:
A, A♯/B♭, B, C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭

Using sharps vs. flats depends on what key you are in and/or what direction the notes are going in (higher or lower). Typically if notes are descending an Trackers normally disregard this (and only use sharps in most trackers). Here is a '[l[http://upload.wikimedia.org/wikipedia/commons/thumb/3/33/Circle_of_fifths_deluxe_4.svg/600px-Circle_of_fifths_deluxe_4.svg.png[circle]] with all the different keys that use flats and that use sharps. 

'[t[2]Note Value'[/t]

The '[b]value'[/b] of a note is an expression of how much time it occupies.

A '[b]quarter note'[/b] is a quarter of a common time measure (see below). As an example, a 7/4 measure can hold seven quarter notes, while a 2/4 only two.
An '[b]eighth note'[/b] simply takes up half the time of a quarter note.
A '[b]half note'[/b] is twice the length of a quarter note.
A '[b]whole note'[/b] takes up an entire common time measure.

In sheet music, adding a single dot after a note increases its duration by half; thus, a '[b]dotted quarter note'[/b] means a note with a length or '[b]value'[/b] of a quarter note plus an eighth note.

'[t[2]Time Signatures'[/t]

A '[b]measure'[/b] is a unit in music which defines the length of an arbitrary phrase, sort of like a coherent musical statement. Measures are subdivided into equal time intervals called '[b]beats'[/b]. A '[b]time signature'[/b] is the way to express the number of beats in a measure. The time signature most often used in Western popular music is 4/4, also called '[b]common time'[/b].

The top number in a time signature tells how many beats are in a measure, and the bottom tells what note value makes up a single beat (ordinarily a quarter, eighth, or sixteenth note). A time signature is '[o]NOT'[/o] a fraction--3/4 are 6/8 denote two different meters (by convention, 3/4 denotes a measure split into 3 quarter-note pulses, and 6/8 denotes a measure split into 2 dotted-quarter-note pulses).

There are various different types or categories of time signature. The main types are:

'[b]Simple time'[/b]: Time signatures where the main beat is split into two equal parts are referred to as "simple time." The most common types are 2/4, 3/4, 4/4 and 3/8.

'[b]Compound time'[/b]: Time signatures where the main beat (top number) is split into 3, not 2, equal parts, so that one beat would be equal to a dotted note. 6/8, 9/8 and 12/8 are the most common compound time signatures.

'[b]Irregular/Complex time'[/b]: This is when there are a certain number of beats in a measure that cannot be divided into equal parts. For example, 5/4, 7/4, 11/8 etc. cannot be divided into equal groupings, and so are irregular. These sorts of time-signatures are very common in "progressive" rock, and can be an effective way of introducing "rhythmic dissonance" into a piece of music.

Those three are the only ones you'll really need to worry about. Some more advanced and obscure ones include:

'[b]Additive time'[/b]: An additive time signature is one where a measure is composed of several specific groupings. For example, a time signature of 2+3+2/8 would specify one group of 2, followed by a group of 3, followed by another group of 2 in a bar. This differs a from simply writing in 7/8, as the groupings are specified within the bar, and so "stress" on those particular beats are required. These sorts of time signatures are pretty advanced, complicated to use, and are only really effective when writing very rhythmic based music.

'[b]Irrational metres'[/b]: Okay, so maybe not a "main" type of time signature, or a particularly useful one. An "irrational metre" is one where the note value of a single beat within a bar (ie. the bottom number) is something other than 2, 4, 8, 16 etc. For example, a time signature of 4/3 would mean that one bar is composed of four dotted-crotchets. These sorts of time signatures are only really used when poly-rhythms are concerned, and they're not really worth worrying about (they are almost never used). I suppose this really just makes for a nice bit of music theory trivia, I guess.

'[t[2]Tempo'[/t]
'[b]Tempo'[/b] is the speed a piece is played at, and it is usually measured in '[b]beats per minute'[/b]. For an example, a piece at 100 beats per minute (BPM) means in one minute, there will be 100 evenly spaced beats played.

'[#[Intervals, Scales, and The Ionian (Major) and Aeolian (Minor) Modes] 
Now that we have our 12 notes, we have to figure out how they work relative to each other. A way of looking at relative pitch is examining '[b]consonance'[/b] and '[b]dissonance'[/b], which are respectively defined as when notes, when played simultaneously, either work 'well' together, or 'clash' with each other.
As a rule of thumb, the closer notes are together, the more they clash, until the difference becomes null to our brain. Notes that are one or two semitones apart are generally said to be dissonant. This has to do with frequency intervals and ratios (see Section VI).
The intervals relative to a base (or '[b]tonic'[/b]) are displayed below. Those '[o]italicized'[/o] are relatively important!

0 semitone difference = unison (the same note)
1 semitone difference = '[o]minor second'[/o]
2 semitone difference = '[o]major second'[/o]
3 semitone difference = '[o]minor third'[/o]
4 semitone difference = '[o]major third'[/o]
5 semitone difference = '[o]perfect fourth'[/o]
6 semitone difference = augmented fourth/diminished fifth/tritone
7 semitone difference = '[o]perfect fifth'[/o]
8 semitone difference = minor sixth
9 semitone difference = major sixth
10 semitone difference = minor seventh
11 semitone difference = major seventh
12 semitone difference = '[o]octave'[/o]

This is rather confusing at first glance. However, there seem to be recognizable patterns. For example, a minor  is always closer to the tonic than a major .
The perfect intervals are the most consonant intervals, other than the octave!

A '[b]scale'[/b] is a set of notes arranged in order by their pitch. A '[b]mode'[/b] is some manifestation of a scale.

The '[b]major scale'[/b] or '[b]Ionian mode'[/b] consists of a root note, that note's major second, its major third, its perfect fourth, its perfect fifth, its major sixth, its major seventh, and its octave.
So, we have a pattern of whole, whole, half, whole, whole, whole, half.
The C major scale is C, D, E, F, G, A, B, C.

The '[b]minor scale'[/b] or '[b]Aeolian mode'[/b] consists of a note, its major second, its minor third, its perfect fourth, its perfect fifth, its minor sixth, its minor seventh, and its octave.
We have a pattern of whole, half, whole, whole, half, whole, whole.
The C minor scale is C, D, E♭, F, G, A♭, B♭, C.

'[#[Chord Theory] 
Now that we've learned the two most widely-used scales, we can assign '[b]chords'[/b] to them. A chord is three or more notes played either simultaneously, or sequentially. A chord played sequentially is called a '[b]broken chord'[/b] or an '[b]arpeggio'[/b]. A chord consisting of a scale's note, that note's minor/major third, and its perfect fifth (usually, at least, the fifth can be flatted or sharpened) is known as a '[b]triad.'[/b]
In '[b]Roman relative chord notation'[/b], all chords are represented by a Roman numeral. The '[b]major chords'[/b] (which use a major third) are represented by capitalized numerals, while '[b]minor chords'[/b] (which use the minor third) and '[/b]diminished chords'[/b] (which uses a minor third and flats the fifth to an augmented fourth) are represented by a lowercase, with the diminished chords differentiated with a small circle next to the numeral.
In a major scale, the '[b]tonic chord'[/b] is represented by a Roman numeral I.

The chords are named as follows:

I = tonic
II = supertonic
III = mediant
IV = subdominant
V = dominant
VI = submediant
VII = leading

We will get into how each chord is used shortly.

The major scale has the following chords:

I ii iii IV V vi vii°

The minor scale has the following chords:

i ii° III iv v VI VII

As you can see, both of these (and all other modes of the diatonic scale) have three major chords, three minor chords, and a single diminished chord. The order is even the same! The only difference is which chords take prevalence in the mode. This leads us to one of my favorite revelations in all of music theory.
A '[b]relative key'[/b] is a key that has the same notes and chords as another key, but the parallel key is just shifted to become major or minor! Case example:
C major consists of C, D, E, F, G, A, and B. Therefore, its chords are:

I - C
ii - Dm
iii - Em
IV - F
V - G
vi - Am
vii° - B°

Now, shifted forward so that vi becomes i, we get A minor!

i = Am
ii° = B°
III = C
iv = Dm
v = Em
VI = F
VII = G

It's almost magic to me! And you can do this with any mode, even into modes that are not major or minor! (See Section V)

A '[b]parallel key'[/b] is a key that has the same root note as another key, but has different notes, and therefore, different chords! C major and C minor are parallel keys!

'[t[2]Chord Progressions and Cadences'[/t]
A '[b]chord progression'[/b] is a sequence of chords played one after another, usually looping several times.

A '[b]cadence'[/b] is a portion of a chord progression that 'leads' to another section in a piece, whether it be a new progression, or the same progression.

An '[b]authentic cadence'[/b] has only one form: V -> I. This just sounds right to our ears, and it's used in the majority of music, ever since the Baroque period.

A '[b]plagal cadence'[/b] is IV -> I. In contemporary pop and rock, this is used even more than the authentic cadence, by a significant amount.

An '[b]inauthentic cadence'[/b] is literally any other cadence which is not V -> I. These tend to fake us out, or give a feeling of dissonance. They can be well-applied, however.

Common chord progressions are:
I - V - vi - IV, the famous 'Four Chords' used in many pop and rock hits.
I - V - vi - iii - IV - I - IV - V, the progression made famous by Pachelbel's Canon in D.
i - VII - VI - V, the Andalusian cadence.
I - ii - V
I - V - IV
I - IV - V
I - V
I - IV

'[t[2]Modulation'[/t]
'[b]Modulation'[/b] is the act of changing keys in a single piece. It is usually achieved through a cadence involving a chord in the new progression, or through just using the next key or two up (colloquially known as a truck driver's gear change)

Examples:
C major -> C♯ major
C major -> G major (G is the V chord in C major)
C major -> C minor

'[t[2]Seventh and Extended Chords'[/t]
A '[b]seventh chord'[/b] is a triad that has had a seventh tacked on to it. There are three main types of seventh chords:

A '[b]dominant seventh chord'[/b] adds the minor seventh of the key to a major triad. For example a C dominant 7th chord (C7) is C E G B♭.
A '[b]minor seventh chord'[/b] adds the minor seventh to a minor triad. For example a C minor 7th chord (Cm7) is C E♭ G B♭
A '[b]major seventh chord'[/b] adds the major seventh to a major triad. For example a C major 7th chord (CM7 or Cmaj7) is C E G B.
A '[b]half diminished seventh chord'[/b] adds the minor seventh to a diminished triad. For example a C half diminished chord (C'[~s]ø7'[/~s] or Cm7♭5) is C E♭ G♭ B♭.
A '[b]full diminished seventh chord'[/b] adds the major sixth to a diminished triad. For example a C full diminished seventh chord (C°'[~s]7'[/~s] or Cdim7) is C E♭ G♭ A (B♭♭).

There are plenty of other seventh chords which are less common and you can explore those yourself.

An '[b]extended chord'[/b] is a chord with notes beyond the octave of a root note. To learn about these, we need to define more intervals.

13 semitone difference = minor ninth (octave+minor second)
14 semitone difference = major ninth (octave+major second)
15 semitone difference = minor tenth (octave+minor third)
16 semitone difference = major tenth (octave+major third)
17 semitone difference = minor eleventh (octave+perfect fourth)
18 semitone difference = major eleventh (octave+tritone)
19 semitone difference = major twelfth (octave+perfect fifth)
20 semitone difference = minor thirteenth (octave+minor sixth)
21 semitone difference = major thirteenth (octave+major sixth)
22 semitone difference = minor fourteenth (octave+minor seventh)
23 semitone difference = major fourteenth (octave+major seventh)
24 semitone difference = double octave (octave+octave)

A '[b]ninth chord'[/b] adds some sort of ninth to a seventh chord, usually a major ninth to a dominant seventh to for the '[b]dominant ninth chord'[/b]. For example, a C9 chord is C E G B♭ D. This pattern of tacking on notes can be repeated, especially with elevenths and thirteenths. Often adding ninths, elevenths, and thirteenths give the chord more color and more of a jazzy feel but they can be tricky to use at first.

'[t[2]Other Chords of Note'[/t]
An '[b]inverted chord'[/b], also known as a '[b]slash chord'[/b], is a chord with the same notes, but the root of the chord is not the '[b]bass note'[/b], in other words, it doesn't have the lowest pitch.
For every chord, there are at least two '[b]inversions'[/b].
For example: C Major is comprised, in order, of the notes C, E, and G.
Its '[b]first inversion'[/b] would therefore be E, G, C (because the C has to be moved up an octave)
Its '[b]second inversion'[/b] would be G, C, E.
A first inversion chord can be notated either as C/E (in the case of C Major) or as I'[~s]6'[/~s] in relativistic notation.
A second inversion would be notated as C/G or as I'[~s]6'[/~s]'[_s]4'[/_s].
As a note, seventh chords can have three inversions, due to the extra note.

A '[b]fifth chord'[/b] or '[b]power chord'[/b], often used in rock music or punk, consists of only a root note, its perfect fifth, and its octave. It is neither major nor minor, due to its lack of a third.
Another thirdless chord is the '[b]suspended chord'[/b], which suspends the third, and replaces it with either a major second (a '[b]suspended second chord'[/b]) or a perfect fourth (a '[b]suspended fourth chord'[/b]). In C, these can be notated as Csus2, and Csus4, respectively.

An '[b]augmented chord'[/b] is a major triad, with the fifth sharpened to a minor sixth. It can be represented with a subscripted plus sign, for example, a C augmented chord can be represented as C'[~s]+'[/~s].

'[t[2]Borrowed Chords and Harmonic Dissonance'[/t]
You don't just have to use the triads provided to you by a key! A '[b]borrowed chord'[/b] is a chord that is not in the key, but is instead borrowed from another, usually closely-related key. A '[b]related key'[/b] is a key that shares many similar chords to another key. For example, in A major, C and G are not chords in that key!
Borrowed chords are represented one of two ways:

With a flatted Roman numeral (such as ♭III, which means it is a semitone lower than the III chord)

Or you can notate it with a slash, representing which key the chord was taken from! (such as IV/V, which means you have taken the IV chord from the key in which the V chord is the I chord)
Dissonance can be used in a number of ways in harmony, such as creating emotions of suspense, dread, or horror, or simply as a transition to a more consonant chord.

'[#[Melody] 
Take a note. I will take C, and name it Do in '[b]solfege notation'[/b], which is a relative notation of the major (or minor) scale, any note can be Do. Let's also give it the number it corresponds with in its major mode. Therefore, we are working in C Major.

Do = 1 = C
Re = 2 = D
Mi = 3 = E
Fa = 4 = F
Sol = 5 = G
La = 6 = A
Ti = 7 = B

'[b]Melody'[/b] is the arrangement of notes in a piece to form a coherent, apparent statement. Melody and '[b]harmony'[/b], or the rhythm-, chord-oriented base of a song, have been intertwined ever since music was a thing. But a good rule of thumb for beginners is:
When a certain chord is playing, or is implied, it's a good idea for a note in the melody to be a note in the chord.
Of course, this does not apply in all circumstances, or even most of them.
An '[b]accidental'[/b] is a note in the melody that is somewhat like a borrowed chord, in that it is not in the key the rest of the piece is written in. If I had a melody that went C, G, D, D♯, C, if that piece was in C Major, the D♯ is an accidental. Accidentals are useful, but a lot of composers (usually novices) avoid them like the plague. My advice is to experiment a lot, and see what works, and what doesn't!

A '[b]motif'[/b] is a certain melodic phrase that is repeated in a song, or is very prominent of said song. An example of a motif is the dramatic introduction of Beethoven's 5th Symphony.
A '[b]hook'[/b] is a motif that is meant to be especially appreciated and remembered by the listener, used extensively in pop, rock, and hip-hop songs. Hooks often occur after pauses in the melody, often have wide interval jumps, and have more energy expressed through them than in the rest of the song.

'[b]Counterpoint'[/b] is the act of playing two different melodies at the same time. These melodies are often separated by wide intervals to avoid clashing notes. A common practice is to introduce one melody first, then the other, then both at once.

Counterpoint employs three types of '[b]motion'[/b], or several melodies' movement relative to each other.

'[b]Similar motion'[/b] is when two melodies move in the same general direction.
Example:
Part 1 moves from C -> G.
Part 2 moves from E -> A♯ (upwards).

'[b]Contrary motion'[/b] is when two melodies move in the opposite direction.
Example:
Part 1 moves from C -> G.
Part 2 moves from E -> D♯ (downwards).

'[b]Oblique motion'[/b] is when one melody moves in a direction, while another stays on the same note.

Example:
Part 1 moves from C -> G.
Part 2 stays on E.

In counterpoint, one should usually avoid '[b]parallel fifths'[/b], and '[b]parallel octaves'[/b], which occur when melodies stay consistently on the same intervals of each other, by way of a perfect fifth, or an octave. This violates the idea of independent melodies, and generally makes them sound more like chords.
Example:
Part 1 moves from C -> D.
Part 2 moves from G -> A, at the same time.
Contrary and oblique motions are usually employed to avoid this.

'[#[Unpitched Percussion] 
By definition, '[b]percussion'[/b] is defined as hitting or scraping an object to make music. By this definition, piano is soundly percussion, as hammers are used to strike strings when you press down keys. But this section is about '[b]unpitched percussion'[/b], percussion that doe not have a definite pitch, and in contemporary music, usually used to keep the beat. However, this was not always the case, as pitched instruments were usually used to keep time (such as cellos) in the classical periods.

'[#[Less Common Modes and Scales]
We know by now two scales! You may have been wondering that if we can shift the major scale a certain amount to become the minor scale, can't we shift it different amounts to become different scales? And indeed, we can!
These other modes are listed below, by the chord from the major scale that becomes I.

ii - Dorian
iii - Phrygian
IV - Lydian
V - Mixolydian
vii° - Locrian

These modes are not as commonly used as their major/minor counterparts, but are more common than one may think, and are often confused by novices for major/minor in various pieces. Each of these modes have their own unique feels different from minor and major.

Here are the scale modes we have looked at so far in C going from "most sharp" to "most flat":

C Lydian: C, D, E, F♯, G, A, B, C.
C Major: C, D, E, F, G, A, B, C.
C Mixolydian: C, D, E, F, A, G, A, B♭, C.
C Dorian: C, D, E♭, F, G, A, B♭, C.
C Minor: C, D, E♭, F, G, A♭, B♭, C.
C Phyrigian: C, D♭, E♭, F, G, A♭, B♭, C.
C Locrian: C, D♭, E♭, F, G♭, A♭, B♭, C.


'[t[2]More Scale Types'[/t]
A '[b]pentatonic scale'[/b] is essentially a stripped-down version of a regular scale, that is very useful for composition and improvisation. The '[b]major pentatonic scale'[/b] has only the root, major second, major third, perfect fifth, major sixth, and octave. The '[b]minor pentatonic scale'[/b] uses the root, minor third, perfect fourth, perfect fifth, minor seventh, and octave. Pentatonic scales can be shifted to other modes as well.
The C major pentatonic scale is C, D, E, G, A, C.
The C minor pentatonic scale is C, E♭, F, G, B♭, C.

Another scale we can derive from these pentatonic scales are the '[b]blues'[/b] scales. These scales are often used in jazz. 
The C '[b]minor blues scale'[/b] (usually simply known as "blues"): C, E♭, F, F♯, G, B♭, C.
The C '[/b]major blues scale'[/b] (less common): C, D, D♯, E, F, G, A, C.

In other styles of music such as jazz, modern classical, and traditional music from other cultures, other scales may be used in addition to or in place of the diatonic scale. One common example is the '[b]harmonic minor scale'[/b], equivalent to a minor scale with a major seventh instead of a minor seventh. By changing the root of this scale, we can create new modes such as '[b]Phrygian dominant'[/b] (equivalent to the diatonic Phrygian mode with a major third).
The C harmonic minor scale is C, D, E♭, F, G, A♭, B, C.

The '[b]melodic minor scale'[/b] is a special case, as it has different notes, depending on whether you are ascending or descending it. Ascending, it is the minor scale, or '[b]natural minor scale'[/b], with the minor sixth and minor seventh sharpened to their major counterparts. Descending, the scale is identical to the natural minor scale.
The C melodic minor scale ascending is C, D, E♭, F, G, A, B, C.
The C melodic minor scale descending is C, B♭, A♭, G, F, E♭, D, C.


The '[b]Egyptian scale'[/b] uses a root, a minor third, a major third, an augmented fourth, a perfect fifth, a minor seventh, a major seventh, and octave.
The C Egyptian scale is C, E♭, E, F♯, G, B♭, B, C.

'[t[2]Whole-Tone Scales'[/t]
As the name implies, '[b]whole-tone scale'[/b] is made up entirely of tones (or major seconds). Unlike a conventional scale like the major scale, the pattern goes "tone, tone, tone, tone, tone, tone." 
There are only two different transpositions of the whole-tone scale available: 
C, D, E, F♯, G♯, A♯, C
and
C♯, D♯, F, G, A, B, C♯

Whole-tone scales are a simple yet effective way of disguising tonality. As there are no semitones or leading notes in this scale, there's no sense of resolution. People often say that this scale gives a "mysterious" feel to a piece of music. 
Debussy's "Voiles" is a good example of a piece of music that is almost entirely composed of whole-tone scales.

'[t[2]Octatonic Scales'[/t]
In the same way that a pentatonic scale is a scale with 5 different tones, an '[b]octatonic scale'[/b] is one that uses 8 different tones. It is also sometimes referred to as a "diminished scale" in jazz theory, because it can be obtained through a combination of two diminished 7th chords. The intervals in this scale alternate between a semitone gap and a tone gap (so the pattern goes; semitone, tone, semitone, tone, semitone, tone, semitone, tone). 

An octatonic scale starting on C would go: C, C♯, D♯, E, F♯, G, A, A♯, C.
This version of the octatonic scale can be transposed twice. If we transpose up by a semitone each time, we can get:

C♯, D, E, F, G, G♯, A♯, B, C♯.
D, D♯, F, F♯, G♯, A, B, C, D.

If we transpose up by a semitone again, we get D♯ E F♯ G A A♯ C C♯, which if we compare it to our original octatonic scale on C, we notice that we end up with the same notes, but starting on D♯. 

There are two different versions of the octatonic scale. The first one we've just seen started off with a semitone interval. The other type starts off with a tone interval, and then alternates between tone and semitone. So, if we start on C, we get:

C, D, D♯, F, F♯, G♯, A, B, C.

Just like the other type of octatonic scale, this one can be transposed twice. Again, using this scale can be effective when combined with other scale types. Octatonic scales are more difficult to listen out for due to their highly chromatic nature.

'[t[2]Microtonality'[/t]
'[b]Microtonality'[/b] is the use of pitches in intervals that are smaller than a semitone. Microtonality is relatively uncommon, due to its jarring nature to those introduced to it, and it difficulty to perform on most instruments due to their being designed for music in standard semitone intervals.

'[t[2]Atonality and Chromaticism'[/t]
The '[b]chromatic scale'[/b] uses all twelve notes, and is usually associated with '[b]chromaticism'[/b], which is the synthesis of different scales, or '[b]atonality'[/b], which is the lack of a musical center (aka, a root note).
Atonality is usually coupled with an artistic statement which is similar to visual art styles such as abstract-expressionism or cubism: that music (or art) does not have to sound (or be) a certain way, and therefore does not need a tonal center, in other words, no key. Atonality also frequently relies on the equal treatment of all 12 notes of the chromatic scale. This doesn't mean it has to sound bad, or even strange, many pieces such as Schoenberg's 2nd String Quartet (4th movement) pioneered modern atonality, and are still pleasant by normal standards. Atonality is often coupled with widely varying time signatures and tempo.

'[t[2]Bitonality and Polytonality (or polymodality)'[/t]
'[b]Bitonality'[/b] is the use of two key signatures, or two "tonalities" across different parts at the same time (also referred to as vertical harmony). This can be achieved by having one part or set of instruments in one key signature (for example, C major), and other part or set in a different, often contrasting key signature (for example, F♯ Major). Combining different chords or key signatures can produce a range of different effects in a piece. Two consonantly related keys/chord (for example, tonic and dominant) can produce lush or more pleasant sounding chords, whereas less closely related chord combinations (tonic and supertonic) can be more clash-y and very dissonant.

Igor Stravinsky's Rite of Spring is a good piece to study for this sort of technique. The first dance combines both an E major and E♭7 chord in the lower strings to produce a brilliantly dissonant sound. 

Bi/polymodality is based on the same principle, except you're combining "modes" rather than scales or key signatures. One example of this would be combining a pentatonic scale starting on E with a whole tone scale in another instrument.

'[#[The Science of Sound]
So how does this all work? I mean, on the most fundamental level, how does it really work?
When something makes a sound, it is quite literally sending vibrations out from the energy produced by the action creating the sound. It sends off these vibrations through the air, where your ear picks them up.
To explain we have to venture into human anatomy. In the human ear (and many animal ears in general), sound is perceived through a construct in the inner ear called the '[b]eardrum'[/b], which is very sensitive to vibration, and amplifies any vibrations received from the air, to another construct called the '[b]cochlea'[/b].
The cochlea is filled with fluid, which vibrates as well. The cochlea is a tube which is spiraled up, and on one side there are hairs lining the tissue, and when these hairs vibrate, our brains perceive this sensation as sound. There is a point in the cochlea for middle C, and every pitch from roughly 20 Hz, to 20kHz.
A '[b]sine wave'[/b] is the most basic of sounds, and the fundamental building block of all other sounds! Its vibration is just a round wave of vibration. Sine waves are what our brain actually perceives when it processes sound! Every sound you will ever hear is just sine waves at different volumes, stacked on top of each other. (See Section VII)
An '[b]overtone'[/b] is a frequency our brain combines with a lower frequency to synthesize a new sound.
These sine wave overtones, when the highs and lows match nicely, are consonant, and when they do not, they fall out of step with each other, and are considered dissonant. For example, an A5 (880Hz) has exactly two high points for every high at A4 (440Hz). These notes meld together well, and are consonant.
The '[b]overtone sequence'[/b] are the notes produced by diminishing ratios to a given frequency. Let's take a note, say C. A frequency that is half the length from high to high is also double the Hz. Therefore, this note is also C. What about a note which is a third the length? Turns out, this note is G. A quarter? Another octave up, C! A fifth, and we get E! Hey, wait a moment, we just deduced the major triad! If we kept going in this pattern, we would deduce the entire chromatic scale!

'[#[Timbre, Sound Design, and Production]
'[b]Timbre'[/b], with pitch and tempo, are the three needed components to make music. White noise is not music, because as it contains timbre, it has no discernible pitch or tempo. Timbre is defined as the synthesis of a pitch and its overtones to create a different sound. A guitar, and a piano may play the same pitch at the same tempo, but they have different timbres.

'[b]Sound design'[/b] is the process of creating or altering a specific timbre.
'[b]Production'[/b] is the refinement of a sound or piece.

'[b]Velocity'[/b] is the volume at which a note is played.
'[b]Attack'[/b] is the rate at which the beginning of the note reaches its full velocity.
'[b]Sustain'[/b] is how long a note stays at its peak velocity.
'[b]Decay'[/b] is how long a note takes to inch down from its peak velocity.
'[b]Delay'[/b], or '[b]echo'[/b], is a sound being repeated, slowly fading out.
'[b]Reverberation'[/b], or simply '[b]reverb'[/b], is when a sound lingers for a bit after being made. Reverb is usually used to make electronic music sound more 'natural', or give the effect of being in a large room.
'[b]Compression'[/b] is the consolidation of pitch and volume in a sound to a more uniform level, not to be confused with '[b]normalization'[/b], or the (de)amplification of pitch to a certain point.
'[b]Chorus'[/b] is the layering of sounds on top one another.
'[b]Amplification'[/b] is the process of artificially making a sound louder, or seem louder.
'[b]EQ'[/b], or '[b]equalization'[/b], is the amplification or deamplification of certain frequencies in a sound.
'[b]Pitch Correction'[/b], colloqially known as '[b]autotune'[/b], the the act of electronically altering a voice or instrument to be on key in a piece.

In a piece, '[b]dynamics'[/b] are how varied a song is in volume. The act of compressing a song's volume and then amplifying it to the point of '[b]clipping'[/b], or losing data because it went over the volume threshold, has been the most controversial issue in music production for the past few decades. Scientific studies have proven people pay more attention to, and even are more favorable towards, music that is perceived as louder. Since '[b]sound cards'[/b], devices that render electronic data as acoustic sound, and speakers can only reach a certain volume, this technique is used. Many people enjoy a dynamic piece, and therefore dislike the so-called '[b]loudness wars'[/b].

'[#[Miscellaneous Tips and Tricks]
First of all, you need to keep trying. Don't ever give up.
And try new things! Listen to new music, get out of your shell!
Mess up intentionally now and again, you might do something you like!
Remember, simplicity is your friend! Lou Reed famously stated that one chord is fine, two is pushing it, and three is getting into jazz!
With that being said, complexity is not your enemy.
Don't regret things! Regret something, accomplish nothing! People do poorly sometimes, but that's just part of the fun!

'[#[Helpful Links and References]
'[[Music Theory - Case Examples and Analysis]
'[[Music Theory - History of Modern Theory and Tonality]
http://www.youtube.com/watch?v=i_0DXxNeaQ0 - A great video explaining the fundamentals of timbre and sound design!
http://hooktheory.com - fantastic for testing melodies and chord progressions!
http://musictheory.net - interactive, graphical music theory lessons!
http://www.everythingisaremix.info/ - the modern Bible on the process of creation in general, with some musical examples.