In western music, there are several tonalities which can be used to construct scales and chords.
Tonalities are perceived, and can be used as a starting point, but are not necessary to understand music theory.
The primary tonality is "Major." The major tonality is best represented by the major scale.
Major = I = 1 3 5 (7)
The strongest tones in the major tonality are the root or tonic, the major third, and the perfect fifth. Secondary to that is the tone of the major seventh. Tertiary tones in major tonality are usually the major ninth, major sixth, and rarely the major eleventh and major thirteenth (the thirteenth is enharmonically equivalent to the major sixth in standard tuning anyway),
Major chords are represented by capital roman numerals, capital letters, or sometimes by a triangle or the letters "maj." For example, the C major chord, which is C E G C, can be written C, C maj, or CΔ.
Use major chords to demonstrate a happy or contented feeling, as they provide little to no musical tension. It is very common for tension to resolve to a major tonality.
The second most important tonality is called "minor." Minor tonality is less strictly defined than major. It contains the minor third and perfect fifth. Secondarily, it may contain a seventh, usually minor, but often major or even diminished sevenths can be used with other scales.
Minor = i = 1 b3 5 (b7 or sometimes 7)
The C minor chord is spelled C Eb G C. It can be written Cm, Cmin, c, or C-. The chord may also be represented by a lower case roman numeral.
Common minor scales are the natural minor, harmonic minor, melodic minor, dorian, and phrygian scales.
Minor tonalities are used to express sadness, anger, frustration, and melancholy. They provide little musical tension, but are more emotive than major tonalities. Many tensions resolve to minor tonalities, but the resolution to minor is considered less pleasing than the resolution to a major tonality.
The third important tonality is called "dominant." It is based loosely off of the harmonic series of tones in mathematics, and sounds very pleasing on a basic level.
Dominant = I7 = 1 3 5 7 (sometimes 9, b9, #9, 11, #11, b11, 13, or b13)
Dominant tonalities can be built off of the mixolydian scale. The dominant chord is like a major chord, but contains the dominant seventh. In standard tuning and in notation the dominant seventh is represented the same way as the minor seventh, but it should be noted that in higher level microtonal tunings and in barbershop quartets, the minor seventh and dominant seventh are not the same.
The C dominant chord is spelled C E G Bb, and can be represented as C7 or C dom 7 or sometimes C dom. The capital roman numeral with the arabic number seven is used in general cases.
Dominant chords have an addative convention, such that C9 = C7 plus the ninth, C E G Bb D. C13, for instance is spelled C E G Bb D F A. Not all of the notes are necessary, but they may all be present. Depending on the bass, the root of the chord may even be ommited by the performer forming the chord, so long as the root is implied by bass or even by context.
The dominant tonality is used to provide some musical tension without the sad, angry, or melancholy feel. It can remain unresolved, but usually resolves to a major tonaility. It is commonly used in blues and funk music to give a more energized mood than minor keys.
Suspended tonality is a little more difficult to define. It is when the case is ambiguously major or minor. There are two common suspended forms: suspended second and suspended fourth.
In a suspended form, the third is replaced by either the second or the fourth interval.
Suspended Second = I sus2 = 1 2 5
Suspended Fourth = I sus4 = 1 4 5
The seventh can be added, and may be either major, minor or dominant. The notation for the suspended chord is typically a capital roman numeral with "sus," and the C suspended chord would be noted as Csus, Csus2, or Csus4. The C suspended second chord is spelled C D G C and the C suspended fourth chord is spelled C F G C.
Suspended chords should not be confused with add nine chords, like Cadd9 and Cmadd9, which would be spelled C E G D and C Eb G D, respectively. Add nine chords contain the third and are types of major and minor chords, while suspended chords do not contain the third interval.
The suspended chord is very tense and likes to resolve to either major or minor tonality. Many old Baroque songs ended tritely with a Isus4 - Isus2 - I, sometimes even when the rest of the composition was in a minor tonality.
There are three other important tonalities, but these are encountered much less frequently than the three above, and are extremely rare as the root tonality of a musical composition. Rather, they are used to build tension and to transition between keys.
The diminished tonality is defined by the minor third and the diminished fifth. There is a fundamental split between two subsets of diminished tonalities, full diminished and half diminished. The full diminished tonality is assumed when the qualifier is absent. The diminished tonality contains the diminished seventh, while the half diminished tonality contains the minor seventh.
Diminished = viio = 1 b3 b5 bb7
Half Diminished = viiø = 1 b3 b5 b7
The diminshed chords are noted by lower case roman numerals with a circle for diminished and a circle with a line through it for half diminished. You may see diminished chords marked C dim, C dim 7, Co, Co7, Cd, Cd7, and possibly other ways. Half diminished chords are noted as Cm7b5, Cø, Cø7, and other ways.
The C half diminished chord is spelled C Eb Gb Bb, and the C diminished chord is spelled C Eb Gb Bbb.
The augmented tonality is defined as a major third and augmented fifth. It is perhaps the least common of the well described tonalities in western music.
Augmented = I+ = 1 3 #5
The chord is represented by a capital roman numeral with a plus sign, and C augmented may be written in the following ways: C aug, C+, C+5, Cmaj#5, etc.
The C augmented chord is spelled C E G# C.
Color
Color is addition of intervals that are not crucial to the tonality,
To review the standard tonalities' key intervals:
Major: 1 3 5
Minor: 1 b3 5
Dominant: 1 3 5 b7
Suspended: 1 (2 or 4 ) 5
Half Diminished: 1 b3 b5
Diminished: 1 b3 b5 bb7
Augmented: 1 3 #5
A color is an interval outside of these in addition to the above sets of intervals. For example, a major seventh chord, such as Cmaj7, is a major tonality with the seventh interval added. A C minor seventh contains the minor seventh interval upon the minor tonality. Hybrids are allowed, however, in standard tuning, a major minor seventh chord is the same as a dominant chord, therefore will be always called a dominant chord unless there is strong reason not to do so.
Common color intervals are:
Imaj7: 1 3 5 7
Im7: 1 b3 5 b7
Iadd9: 1 3 5 9
Imadd9: 1 b3 5 9
I9: 1 3 5 b7 9
Imaj9: 1 3 5 7 9
Im9: 1 b3 5 b7 9
I11: 1 3 5 b7 (9) 11
I13: 1 3 5 b7 (9) (11) 13
Imaj6: 1 3 5 6
Im6 1 b3 5 b6
There are many more, and some might have ambiguous interpretations as written. With experience, you should become comfortable enough to decide these cases based on context or even taste. For instance, A C13 chord can be spelled a few different ways, depending on whether or not you wish to include the ninth and eleventh intervals. Maybe you will even omit the perfect fifth, if context is strong enough to imply it. A common guitar shape incorporates the root, dominant seventh, third, and thirteenth.
Shifting Tonalities
Many musical pioneers are not afraid to shift from one tonality to another. This takes quite a bit of finesse to do tastefully.
Many Baroque composers shifted tonality in a very predictable way by using the Melodic Minor Scale. The scale matches the natural minor when descending, but has a major sixth and major seventh when ascending.
For example, the song "Dog Pound Hop," a twelve bar blues jam used as the theme song for Nickelodeon's Ren and Stimpy show follows the chord structure:
I13 - IV9 - I13 - V7#9 - IV7b9 - I13
These chords imply the dynamic scale:
1 2 3* (b3) 4 5 6* (#6) b7* (7)
This is the dominant scale (mixolydian) when the chords are in root position, but is the Dog Pound scale when the chords are off center.
12-7-66-336/Dominant Scale/Mixolydian
1 2 3 4 5 6 b7
12-7-40-303/Dog Pound Scale
1 2 b3 4 5 #6 7
This type of tonality shift can be more succinctly described by using blue note terminology. Use the dominant scale, but allow the blue notes for b3, #6 and 7 with judgement.