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Old 19th September 2008 , 08:44 PM
sphelan
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Default Music Theory 101

Music Theory 101 Part 3 Chords and Intervals

Before we talk about chords, which are the combination of notes, we need to consider intervals. An interval is the distance between two notes. We have already seen three types of intervals – semitone, tone and tritone. An interval is measured firstly by the number of lettered notes involved, e.g. C-D has two letters so the interval is a second, C-E has three notes (C, D and E) so it is a third.

Image:Interval numbers.gif - Wikipedia, the free encyclopedia

In a major scale, the intervals can be minor, major or perfect.

C-C Unison
C-D Major 2nd
C-E Major 3rd
C-F Perfect 4th
C-G Perfect 5th
C-A Major 6th
C-B Major 7th
C-C Perfect octave (8va)


As we know notes can be raised and lowered so we need to qualify more the actual distance between the notes, e.g. C-G, C-Gb and C-G# are all intervals of a fifth but there is clearly a difference between them. Making a major interval a semitone smaller, it becomes minor and vice versa a minor made one step bigger becomes a major. A perfect interval becomes diminished if made smaller and augmented if made bigger. Referring back to chromatic scales we can construct the full list of chromatic intervals.

Interval Notes
Unison C-C
Augmented unison C-C#
Minor 2nd C-Db
Major 2nd C-D
Minor 3rd C-Eb
Major 3rd C-E
Diminished 4th C-Fb
Perfect 4th C-F
Augmented 4th C-F#
Diminished 5th C-Gb
Perfect 5th C-G
Augmented 5th C-G#
Minor 6th C-Ab
Major 6th C-A
Minor 7th C-Bb
Major 7th C-B
Diminished 8va C-Cb
Perfect 8va C-C


While an interval is the combination of two notes, a chord is the combination of three or more notes. Basically we stack notes on top of each other – usually those that sound well together but also those that clash or provide dissonance.

The root is the foundation note of a chord and gives it its name, e.g. C. The most basic chord involves three notes, is called a triad, and is formed by putting the third and the fifth notes of the scale above the root, e.g. C-E-G.

http://library.thinkquest.org/15413/...ges/triad1.gif

The C major triad in root position (with the root of the chord in the bass)
http://library.thinkquest.org/15413/...ges/triad5.gif

http://www.musictheory.halifax.ns.ca...17_c_triad.GIF

And on the guitar:
Image:Cmajorguitar.png - Wikipedia, the free encyclopedia

We can build a chord on each degree of the major scale as follows.

http://library.thinkquest.org/15413/...es/romnum1.gif


We can therefore identify the types of chords created on each scale degree as follows.

Degree Major scale
I Major (C = CEG)
II Minor (Dm = DFA)
III Minor (Em = EGB)
IV Major (F = FAC)
V Major (G = GBD)
VI Minor (Am = ACE)
VII Diminished (Bdim = BDF)

Degree Natural Minor scale
I Minor (Am = ACE)
II Diminished (Bdim = BDF)
III Major (C = CEG)
IV Minor (Dm = DFA)
V Minor (Em = EGB)
VI Major (F = FAC)
VII Major (G = GBD)

Degree Harmonic minor
I Minor (Am = ACE)
II Diminished (Bdim = BDF)
III Augmented (C = CEG#)
IV Minor (Dm = DFA)
V Major (Em = EG#B)
VI Major (F = FAC)
VII Diminished (G# = GBD)


So, if I am playing guitar accompaniment to a song in C major, for example, I can expect to meet chords such as C, F, G, Dm, Em, Am and to a lesser extent Bdim. Similarly I can say the same if I play in A minor – only the different chords will have a different focus or importance.

Chords can be inverted which means that the bottom note can be placed on the top. If we take a chord of CEG and rearrange it as EGC’ (high C) then it’s called a first inversion. We notice that the 3rd of the chord (E) is the lowest note or is in the bass. If we rearrange if with the G or 5th as the lowest note, it is called a second inversion.

http://library.thinkquest.org/15413/...ges/triad7.gif

http://library.thinkquest.org/15413/...ges/triad8.gif


We can make chords more interesting by adding another note to make four note chords. Adding the note which is a seventh above the root gives us the following chords: major 7th, minor 7th, diminished 7th, half-diminished 7th (or minor seventh flat five – e.g. Dm7b5), dominant 7th.

Major 7th: Add the major seventh above the root in a major chord, e.g. CEGB
Minor 7th: Add the minor seventh above the root in a minor chord, e.g. ACEG or CEbGBb
Diminished 7th: Add the diminished 7th above the root in a diminished chord, e.g. BDFAb or CEbGBbb (B double flat)
Half-diminished 7th: Add the minor seventh above the root in a diminished chord, e.g. DFAbCb or CEbGbBb
Dominant 7th: Add the minor seventh above the root in a major chord, e.g. GBDF or CEbGBb

Similar to the triads we looked at above, we can also produce a set of seventh chords for each degree of the scale. These can also be used in inversions.

[B]Degree [/B]Major scale
I Major 7th (Cmaj7 = CEGB)
II Minor 7th (Dm7 = DFAC)
III Minor 7th (Em7 = EGBD)
IV Major 7th (Fmaj7 = FACE)
V Dominant 7th (G7 = GBDF)
VI Minor 7th (Am7 = ACEG)
VII Half-diminished 7th (Bdim7 = BDFA)


Degree Natural Minor scale
I Minor 7th (Am7 = ACEG)
II Half-diminished 7th (Bdim7 = BDFA)
III Major 7th (Cmaj7 = CEGB)
IV Minor 7th (Dm7 = DFAC)
V Minor 7th (Em7 = EGBD)
VI Major 7th (Fmaj7 = FACE)
VII Dominant 7th (G7 = GBDF)


Degree Harmonic minor
I Minor major 7th (AmM7 = ACEG#)
II Half-diminished 7th (Bdim7 = BDFA)
III Augmented major 7th (Cmaj7(#5) = CEG#B)
IV Minor 7th (Dm = DFAC)
V Dominant 7th (Em = EG#BD)
VI Major 7th (F = FACE)
VII Diminished 7th (G#dim7 = G#BDF)

In addition to the seventh chords, there are also chords where the sixth above the root is added. These, naturally are called sixth chords. We can play major sixth chords and minor sixth chords, e.g. C6 = CEGA and Cm6 = CEbGA.

There are many other types of altered chords, i.e. chords with notes added but I think this is a bit out our league at the moment and can be left until later.

How the chords are arranged between the instruments or voices is called chord voicing. This means that the notes of a chord may be spread between instruments such as in a string quartet consisting of two violins, viola, and cello. Here, typically the bass instrument, the cello, could play the root of the chord, the first violin could play the root as part of the melody and the other two instruments could complete the chord with the 3rd and the 5th.

Similarly, in a rock group, the bass guitar might play the root, the singer might sing the root or one of the other notes and the guitar could fill in the missing notes (and not necessarily play the whole chord). Counter melodies or pad sounds could also double some of the notes to fill out the sound.

The voicing of the chord will depend on the capabilities of each instrument used in the ensemble as well as on the position (root, 1st, 2nd or 3rd inversion).
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Last edited by sphelan; 20th September 2008 at 12:14 PM. . <
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