Music theory
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[edit] The Chromatic Scale
Traditional western music is based on a 12 pitch system, known as the chromatic scale. The notes in the chromatic scale, starting on the note C, are as follows: C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B, and finally C (As C has already been listed it is a repeated note not and counted as an additional note, however it is important to remember that the scale begins to repeat at this point). It may appear that 17 notes have been listed, but this list only contains 12 notes. The notes with a slash between them are “enharmonic”, meaning they represent the same sound with two different names. For example C# and Db are actually the same pitch (sound) with different names. Though it may seem silly now there is actually a very good reason behind this, as you will later learn.
From the twelve notes of this chromatic the majority of western music has emerged. Just about every western scale and chord, and many non-western scales and chords, are based on these twelve notes.
Other Notes
There are enharmonic notes other than the ones listed here, these are as follows: Cbb(Bb), Cb(B), Cx(D), Dbb(C), Dx(E), Ebb(D), E#(F), Ex(F#), Fbb(Eb), Fb(E), Fx(G), Gbb(F), Gx(A), Abb(G), Ax(B), Bbb(A), B#(C), Bx(C#)
The symbol "x" means "Double Sharp", the symbol "bb" means "Double Flat".
[edit] The Intervals of the Chromatic Scale
Basic Intervals
Just as the chromatic scale has 12 notes it also has 12 of what are called intervals. An interval, by definition, is the space between two different pitches. The intervals of the chromatic scale are, in this order: Unison, Minor 2nd, Major 2nd, Minor 3rd, Major 3rd, Perfect 4th, Augmented 4th or Diminished 5th (enharmonic intervals), Perfect 5th, Minor 6th, Major 6th, Minor 7th, Major 7th and Perfect Octave. It may seem like I have listed 14 intervals, but the Unison and Perfect Octave are considered to be the same interval and the Augmented 4th and Diminished 5th are enharmonic intervals.
Each of these intervals has a universal abbreviation (with the exception of the unison, which has many different abbreviations), they are as follows: Minor 2nd – m2, Major 2nd – M2, Minor 3rd – m3, Major 3rd – M3, Perfect 4th – P4, Augmented 4th – +4 (also commonly seen as “aug4”), Diminished 5th – °5 (also commonly seen as “dim5”), Perfect 5th – P5, Minor 6th – m6, Major 6th – M6, Minor 7th – m7, Major 7th – M7, Perfect Octave – P8.
This intervals relate to the chromatic scale, in this order, from whatever the starting note of the scale happens to be. If we use the scale previously written, we have a good example of this. The scale started on the note C, the next note was a C#/Db, the relationship between these two notes is a m2. The next note in the scale is a D, the relationship between C and D is a M2. The next note is D#/Eb, the relationship between this note and C is a m3. The pattern continues this way until you reach C and C, which is a P8.
Complex Intervals
Though this is not an actual musical term, it does serve the purpose of describing the subject. There are other intervals than those listed here, but they are the more easily learned once you have a solid grasp of the basic intervals and enharmonic relationships, however they should be explained.
There are two types of these complex intervals, the first are augmented and diminished basic intervals, and the second are what are known as “compound intervals”, which are basic intervals after the octave.
The first type are as follows: +1, °2, +2, °3, +3, °4, +5, °6, +6, °7, +7, °8, +8
These intervals are enharmonic spellings of our basic intervals, but are used in a unique way. For example, the interval of a m2 is the same interval as a +1, but they are used in different ways. Using our previous example, the interval of C to C#/Db, we can see an example of this. The interval of C to Db is a m2, while the interval between C to C# is actually an +1. The reason for this becomes a little more clear once you understand the concept scale degrees.
The second type of complex intervals, compound intervals, are as follows, m9, M9, m10, M10, P11, +11 or °12, P12, m13, M13, m14, M14.
These intervals are exactly the same as the basic intervals, but are used when referring to notes past the octave. For example a m2 past the octave is called a m9, a M2 is called a M9 and so on.
[edit] Major Scale
The chromatic scale and all of the intervals contained with the chromatic scale provide a means of describing any pitch in traditional, written Western music. This generality, however, is not necessary nor helpful in many musical situations. To simplify, one often chooses to limit one's musical context to a reduced set of pitches within the chromatic scale. A very common simplification of the chromatic scale is the Major scale. In fact, the Major scale is so common in most genres of Western music that, unless otherwise specified, it is the assumed form of the scale being used.
The Major scale employs only eight of the twelve notes in the chromatic scale. The scale is composed of the root of the scale (unison), the Major 2nd, the Major 3rd, the Perfect 4th, the Perfect 5th, the Major 6th, and Major 7th, and the octave. It is this pattern of intervals that gives the Major scale its unique sound and it is what differentiates the Major scale from other scales (such as the Minor scale).
As an example, if we choose C to be the root, the Major scale would be C, D, E, F, G, A, B, C [1] 
Listen source
Another way to describe the Major scale is to describe the "steps" between each note of the scale. Using this language, the distance from one note to the next in a chromatic scale is defined to be a "half step". By extension, a "whole step" is equal to an interval equal to two "half steps", or two notes on the chromatic scale. Expressed in terms of "half steps" (H) and "whole steps", the Major scale can be described as WWHWWWH. This way of describing the Major scale is completely equivalent to using the interval names as employed earlier.
One creates a Major scale by first choosing a certain pitch as the starting point, or "root". Because it started on "C", the C Major scale was shown as an example above. Other major scales can be created by starting on other notes and then by following the pattern of WWHWWWH from that root. Any note from the chromatic scale can be used as the root of a Major scale.
Some major scales are redundant in the sense that they sound the same as their enharmonic counterparts (e.g. Gb-major sounds the same as F#-major). Some redundancies are more common while others are not. Generally, if one has to go beyond the use of single sharps or flats, then one has created a redundant scale which can be more simply expressed (e.g. Gbb-major: Gbb, Abb, Bbb, Cbb, Dbb, Ebb, Fb, Gbb is redundant compared to F-major: F, G, A, Bb, C, D, E, F).
[edit] Minor Scale
The minor scale is derived from the sixth mode of the major scale, (the aeolian mode). Like the Major scale, the Minor scale employs only 8 notes from the chromatic scale. The Minor scale is generally differentiated from the Major scale by the pitch of the third note of the scale -- the Minor scale employs the minor 3rd while the Major scale employs the major 3rd. The rest of the notes in the Minor scale vary depending upon which "flavor" of minor scale being used. There are generally three permutations of the 'minor scale', which are described below:
The 'Natural' Minor
This is exactly the same as the aeolian mode, and can be represented by the pattern WHWWHWW (where W represents whole-steps and H half-steps). The descending melodic minor scale also follows this pattern. With A as the root the scale is formed thus.
A B C D E F G (A')
The Harmonic Minor
For the purposes of musical composition, from (approximately) the late 1500s, the harmonic minor scale came into use in order to produce more satisfying chord progressions (in order to better emphasize a stronger dominant-tonic relationship). It is the same as the 'natural' minor scale, but the seventh degree is raised by one half step, and can be represented thus, WHWWH(W+H)H. Note the large Whole+Half Step (3 semitone) jump between the 6th and 7th note of the scale.
When A is the root, the scale runs
A B C D E F G# (A')
It is in some ways an amalgamation of the final two steps of the major scale and the aeolian mode, giving the seventh degree a inevitable 'drive' towards the root (this raised seventh is known as the leading-note). When writing works in harmony (i.e. in two or more parts), most composers prefer not to use this scale in the outer (more prominent) voices (melody and bass), writing for solo voice or melody instrument due to the awkwardness of the leap between the sixth and seventh degrees (an interval of an augmented second). For this purpose the melodic minor scale is often employed:
The Melodic Minor
Due to the above mentioned 'unattractiveness' to the ear of the harmonic minor scale, the melodic minor is used foremost in harmonic writing, in the most prominent, outer parts i.e. the melody line (usually the soprano in four part writing) and the bass. It has two forms, ascending and descending, which are used respectively according to rise and fall of the melody. In traditional theory and practice, the descending scale is the same as the aeolian mode, and can be expressed thus WWHWWHW, or where the root is A:
A' G F E D C B (A)
The ascending scale is close to the aeolian mode, but the sixth and seventh degrees are raised, giving the pattern WHWWWWH, i.e. where the root of the scale is A:
A B C D E F# G# (A')
In contemporary styles of music, such as jazz, the ascending version of the melodic minor scale is used exclusively.
[edit] Chords
Chords: three or more notes sounded at the same time. They are named based on the intervals they contain relative to the root. The convention for naming the intervals is based on the major scale. For example 1, 3, 5 means the chord contains the root, the third note of the major scale and the fifth note of the major scale. 1, b3, 5 means the chord contains the root, a flat third and a fifth.
Some chord formulas for triads are as follows:
| Chord type | Formula | Example in C |
|---|---|---|
| Major Chord | 1 3 5 | C E G |
| Minor Chord | 1 b3 5 | C Eb G |
| Diminished Chord | 1 b3 b5 | C Eb Gb |
| Augmented Chord | 1 3 #5 | C E G# |
| Major b5 Chord | 1 3 b5 | C E Gb |
| Minor #5 Chord | 1 b3 #5 | C Eb G# |
Some Examples of Chord Formulae for 7th Chords
| Chord type | Formula | Example in C |
|---|---|---|
| Major 7th | 1 3 5 7 | C E G B |
| Dominant 7th | 1 3 5 b7 | C E G Bb |
| Minor 7th | 1 b3 5 b7 | C Eb G Bb |
| Minor Major 7th | 1 b3 5 7 | C Eb G B |
| Half-Diminished 7th | 1 b3 b5 b7 | C Eb Gb Bb |
| Fully-Diminished 7th | 1 b3 b5 bb7 | C Eb Gb Bbb |
