Snippets Of Music Theory
The following covers a number of subjects in music theory
INDEX
1. Diminished and Augmented Chords
2. Suspended chords
3. Seventh chords
4. Why sharps and flats?
5. Simplifying the subject of chord symbols
6. Relative major and minor keys
7. Unravelling complex chords
8. Simplifying key signatures
9. Understanding intervals
10. Interval inversions
11. Critical intervals
12. Seventh intervals
13. Seventh chord substitution
14. Major chord types
15. Dominant chord types
16. More about chord families
17. Chord families and modes
18. The II V I sequence and basic chord substitution
1. Diminished and Augmented Chords
The terms 'Diminished' and 'Augmented' often frighten guitarists.
I think this is because like everything else to do with chord formulas, they are ideas that are easier to understand on the keyboard rather than on the fretboard.
A good way to think of the term 'diminished' is as 'even more minor than minor' and augmented: 'even more major than major'
Example: Major chords use the 1st, 3rd and 5th notes of the major scale (1,3,5). To augment the chord you 'stretch it' by sharping the 5th (1,3,#5)
Similarly: Minor chords use the 1st, flatted 3rd and 5th notes of the major scale (1,b3,5). To diminish the chord you 'shrink it' by flatting the 5th (1,3,b5).
Suspended chords are sometimes a cause of confusion. Just what are they and from which part of your anatomy are you supposed to suspend them?
The unique thing about suspended (or sus) chords is that they
exclude the 3rd.
All other chord types have the 3rd note of the major scale or
(in the case of minor and diminished chord types) the flatted 3rd
(b3).
By replacing the 3rd with the 4th you create the sus4 chord.
The ear really wants to hear a 3rd of some description so by
doing this you hold your audience in 'suspense' waiting for the
chord to resolve back to major.
Likewise if you replace the b3rd in the minor chord with the 2nd
you create the sus2 chord and similarly keep your audience in
suspense until you resolve back to the minor chord.
It should be noticed that there are other chord types that use
the 4th note (11ths, add11ths, min11ths, maj11ths) and the 2nd
note (9th, add 9, 6/9, min9, maj9 etc..). None of these count as
suspended though because they include 3rds or b3rds.
There are 10 types of seventh chord in all, but unless you're teaching at a fairly advanced level you will mainly be concerned with these three chord types:
Dominant 7th
Major 7th
Minor 7th
Their formulas are as follows:
Dominant 7th = 1,3,5,b7
Major 7th = 1,3,5,7
Minor 7th = 1,b3,5,b7
Confusion arises when jazz musicians meet rock musicians.
To a jazz musician a 7th chord generally means Major 7th chord because the major 7th type is more commonly used in jazz than the dominant 7th.
The jazz musician will usually refer to the dominant 7th by its full name (that's if they haven't already substituted a dominant 13th chord for it!)
To a rock/blues/pop/country or folk guitarist a 7th chord usually means dominant 7th because major 7ths are used less frequently in these genres. When major 7th chords do crop up they tend to give them the full title of 'Major Seventh'.
4. Why the need for Sharps and Flats?
Occasionally a bright student will ask this question:
Why do we have to have both sharps(#s) and flats(bs)?"
It's an innocent enough question, but the answer lies buried quite deep in the traditions established during the evolution of musical notation.
The simplest answer is that in any one key you must include just one of each of the letter names (from A-G).
One way to derive the notes in any key is to apply the major scale formula: Tone, Tone, Semi-tone, Tone, Tone, Tone, Semi-tone to the chromatic scale starting on the key note. Suppose we do this starting on D:
Chromatic scale: D D# E F F# G G# A A# B C C# D
Major Scale: D E F# G A B C# D
Telling us that the key of D major has 2 #s: F# & C#
Note: There is one of each letter name used in this scale.
No problem.
But now try it in the key of F:
Chromatic scale: F F# G G# A A# B C C# D D# E F
Major Scale: F G A A# C D E F
We have violated the rule that in any one key you must include just one of each of the letter names (from A-G).We have both A and A# in the same key and we are missing a B. So to satisfy this rule we call the note that sounds like A# by it's enharmonic name of Bb (B flat). Enharmonic is a fancy way of saying: 'sounds the same as'):
Chromatic scale: F F# G G# A A# B C C# D D# E F
Major Scale: F G A Bb C D E F
Now we have one of each letter name. I should stress that there are other perfectly valid answers to this question, but this is probably as far as you need go in answering your student's question unless you have already taken them through the circles of fourths and fifths, relative major and minor keys, naming of intervals etc. etc.
5. Simplifying the subject of Chord Symbols
Chord symbols can appear quite daunting especially when you start looking at typical jazz harmonies. Things like: F#m7b5, A7+add9, Gbmaj7#9#13 ... etc.. What does it all mean?
There are literally hundreds of different chords, but a good place to start understanding chord theory is with triads (3 note chords) because:
a) There are only six of them to learn and
b) Almost every other chord you ever come across is an extension of one of these six triads.
Here they are together with their formulas (or spelling) which is simply a reference to steps on the Major scale:
Major Triad = 1 3 5 (example C major = C E G)
Minor Triad = 1 b3 5 (C minor = C Eb G)
Suspended 4th Triad = 1 4 5 (C sus4 = C F G)
Suspended 2nd Triad = 1 2 5 (C sus2 = C D G)
Augmented Triad = 1 3 #5 (C aug = C E G#)
Diminished Triad = 1 b3 b5 (C dim = C Eb Gb)
6. Relative Major and Minor keys
All major keys have a relative minor key.
Relative keys share the same key signature as each other.
The relative minor key is based on the sixth note of its relative major key.
Examples:
Key of C major (no #s no bs) move up 6 notes - C D E F G A
Relative minor = Key of A minor (no #s no bs).
Key of D major (F#,C#) move up six notes - D E F# G A B
Relative minor = Key of B minor (F#,C#)
A useful application of this is in choosing scales with which to improvise over certain keys.
It's worth remembering that:
The C major scale - C D E F G A B - contains the same notes as
the A natural minor scale - A B C D E F G - similarly:
The C major pentatonic scale - C D E G A - shares its notes with
the A minor pentatonic scale - A C D E G - and
The C Country scale - C D Eb E G A contains the same notes as
the A blues scale - A C D Eb E G
Some of the more complex chords are quite easy to remember if you think of them in terms of combinations of simpler chords.
What do I mean by that? Take a look at the ninth chord:
Its formula is 1 3 5 b7 9
So C9 would be made up of C E G Bb D
A simple way to work with a ninth chord is to think of it as a major chord:
C E G = C major - with a minor chord built on the end of it -
G Bb D = G minor
So by adding a G minor chord to a C major you get a C9 chord!
Here are some other similar ideas:
11th chords (1 3 5 b7 9 11) = major chord plus another major chord built on a note one tone lower than the root, for example: G11 = G B D F A C (G major plus F major)
13th chords (1 3 5 b7 9 13) = relative minor chord (minor chord built on a note 6 up from the root) plus a minor chord built on the fifth note of the key example: G13 = G B D F A E (E minor plus D minor)
See if you can think of some more!
Major scales (and by derivation, major keys) always include notes using one of each of the letter names from A to G.
This is one of the few rules in music that has no exceptions.
One useful application of this rule is to determine whether a key should have a sharps (#s) key signature or flats (bs) key signature.
Example: Key of B major:
1.Write out letter names: B C D E F G A B
2. Apply sharps to space notes according to major scale formula (Tone, Tone, Semitone, Tone, Tone, Tone, Semitone):
B (t) C# (t) D# (s/t) E (t) F# (t) G# (t) A# (s/t) B
3. No problem! B major has 5 #s
But what if we tried D# major?
1. Write out letter names: D E F G A B C D
2. Apply sharps to space notes according to major scale formula (Tone, Tone, Semitone, Tone, Tone, Tone, Semitone):
D# (t) E# (t) F## (s/t) G# (t) A# (t) B# (t) C## (s/t) D#
3. We have had to go to extraordinary lengths to preserve the formula by using double sharps. Life is complicated enough without having to try and play something in a key like that!
So we decide to use the enharmonic equivalent key of Eb instead (this is a fancy way of saying that Eb sounds the same as D#)
In the key of Eb
1. Write out letter names: E F G A B C D E
2. Apply flats to space notes according to major scale formula (Tone, Tone, Semitone, Tone, Tone, Tone, Semitone):
Eb (t) F (t) G (s/t) Ab (t) Bb (t) C (t) D (s/t) Eb
3. We now have a much simpler key signature - 3 flats (bs) which will sound identical to the exotic key of D# major (9 sharps). Of course we can still tell our audience we're playing in D# major!
Understanding intervals is a vital key to unlocking the mysteries of music theory.
An interval always concerns two notes.
Interval names have two parts: a number (from 1 to 13) and a type. Special names are given to the number 1 and 8 intervals (unison and octave).
The number part of the interval name always refers to where the notes are found on the Major Scale if you consider the lowest note in the interval to be the key note.
For example the interval C to E is a 3rd because in the C major scale E is the third note.
The unison, 4th, 5th and Octave intervals are described as 'perfect'.* All other intervals on the major scale (2nd, 3rd, 6th and 7th) are called 'major'
If you reduce a major interval by one semitone it is called 'minor' If you reduce a perfect or minor interval by a semitone it is called 'diminished' If you increase a perfect or major interval by a semitone it is called 'augmented'
So here are the intervals from the note C in order of magnitude:
C to C = Unison
C to Db = minor 2nd
C to D = major 2nd
C to Eb = minor 3rd
C to E = major 3rd
C to F = perfect 4th
C to F# = augmented 4th
C to Gb = diminished 5th
C to G = perfect 5th
C to G# = augmented 5th
C to Ab = minor 6th
C to A = major 6th
C to Bbb = diminished 7th
C to Bb = minor 7th
C to B = major 7th
C to C1 = perfect Octave
This is a brief look at quite a complex part of the subject. Some bits of it may seem a little odd (Bbb for example), but these become clearer as you study chord construction theory.
*The reasoning behind the use of the word 'perfect' is researchable via this site which we recommend you visit.
Continuing our discussion on the subject of intervals.
What happens when you turn an interval upside down? The correct musical term for this is inversion.
Example : C to G
E------------------------------
B------------------------------
G------------------0----------
D------------------------------
A--------3--------------------
E------------------------------
Is a perfect 5th interval
C D E F G
1 2 3 4 5
But G to C
E------------------------------
B--------------1--------------
G--------0--------------------
D------------------------------
A------------------------------
E------------------------------
Is a perfect 4th interval
G A B C
1 2 3 4
So although they contain the same notes these two intervals are named differently according to which way up they are.
Here are the rules about inversions of intervals:
Octave becomes unison
Unison becomes octave
Minor second becomes major seventh
Major seventh becomes minor second
Major second becomes minor seventh
Minor seventh becomes major second
Minor third becomes major sixth
Major sixth becomes minor third
Major third becomes minor sixth
Minor sixth becomes major third
Perfect fourth becomes perfect fifth
Perfect fifth becomes perfect fourth
Augmented fourth is unchanged when inverted
Diminished fifth is unchanged when inverted
Points to note:
Pairs of intervals and their inversions tend to add up to 9.
The sound quality of intervals and their inversions are the same
(ie: they are enharmonic)even though their tonality alters
(minor changes to major and vice versa).
Continuing our discussion on the subject of intervals. There are two groups of intervals that seem to be more critical in their effect than the others - these are the 3rd and 7th intervals.
The 3rd interval determines the overall tonality of a key, scale, chord or phrase: Major third produces major tonality a Minor 3rd produces Minor tonality.
If you combine both tonalities you get a very disturbing sound. An excellent example of this is the 7#9 chord which features strongly in many of Jimi Hendrix' classic songs. The formula for this chord is 1 3 5 b7 #9 The major 3rd is obvious enough, but the minor 3rd is disguised as #9(Remember the 9th note is the same as the 2nd and if you sharpen a 2nd you'll get the same note as if you'd flatted a 3rd!)
Blues and Rock 'n' Roll licks rely heavily for their effect on using the transition from minor to major 3rd. Check out this simple blues lick in G; if you were playing against a G major chord you would play this:
E---------------3-----------------------
B----------------------------------------
G-----3-h-4------3-h-4-p-3-h-4----
D----------------------------------------
A----------------------------------------
E----------------------------------------
i.e the final note is a B (major 3rd in the key of G)
But if you were playing this lick against a Gm chord you would make sure you ended the phrase on the Bb (minor 3rd in the key of G):
E------------3---------------------------
B-----------------------------------------
G--3-h-4------3-h-4-p-3-h-4-p-3--
D-----------------------------------------
A-----------------------------------------
E-----------------------------------------
Try it out!
Continuing our discussion on the subject of intervals.
The 7th interval has a very strong effect on how a particular chord or arpeggio will blend with another chord or arpeggio or a particular scale.
Generally speaking if a chord includes a Major 7th interval (eg. Amaj7, Amaj9) then it will work best with Major scales, or with other major chords and arpeggios.
If a chord includes the minor 7th interval (flatted 7th) then it will work best with dominant chord types (E7, E9, E13 etc..) or with minor chords (Bm7, Bm9 etc.) or with the Mixolydian scale.
There is one notable exception which is the chord known by the somewhat confusing name of minor major 7th (sometimes called minor natural 7th). Its formula is 1 b3 5 7 so Amin/maj7 would comprise the notes A C E G#. This chord effectively contains both minor (b3) and major (natural 7) tonality which gives the chord a special inner tension all of its own!
The b3 interval really dictates that it gets treated as a minor chord and this is reinforced by the fact that it is nearly always used as a passing chord linking a minor chord to a minor 7th:
Example:
4
4 Am |AminMaj7 |Amin7 | Amin6 :||
E ---5-------5----------5----------5-------------
B ---5-------5----------5----------5-------------
G ---5-------5----------5----------5-------------
D ---7-------6----------5----------4-------------
A ---7-------7----------7----------x-------------
E ---5-------5----------5----------5-------------
13.Seventh chord substitution.
The FIFTH chord in any minor or major key can almost always be substituted by a Seventh Chord type:
Example:
Key of C major:
||: C | Am | F | G :|| ...could be played as:
||: C | Am | F | G7 :||
Key of Dm:
| Dm |F | G | Bb | | Dm |F | A | A || ...could be played as:
| Dm |F | G | Bb | | Dm |F | A7 | A7 ||
This is a very low-risk substitution which means it works almost every time.
If you substitute the FIRST or FOURTH chords in a Major key with a Seventh chord type you will often get away with it, but you will find that you have definitely altered the flavour of the song in a bluesy direction:
Compare:
Key: C major:
| C |F | C | F || with:
| C7 |F7 | C7 | F7 ||
If you substitute the SECOND, THIRD or SIXTH chords in a major key by a Seventh type chord you will find a very strong sense of alteration which will sound country-like or trad-jazzy according to the context:
Compare:
Key of G major:
| G | Am | C | D7 || with:
| G | A7 | C | D7 || or:
| G | Em | C | D7 || with:
| G | E7 | C | D7 ||
Many and complex are the rules governing chord substitution.
The subject can be greatly simplified however if you take the view that most chords fit into one of three families.
The first of these types is the MAJOR chord type. Major chords are built on the basic major triad (1 3 5) to which may be added the Major 6th or Major 7th notes. These remain unaltered. Further notes may then be added such as the 9th, 11th and 13th, any of which may be altered by sharping (#) or flatting (b) them.
Some examples of Major chords are:
C Maj 7 (1 3 5 7)
C Maj 6 ( 1 3 5 6)
C Maj 9 ( 1 3 5 7 9)
C Maj 7b9 ( 1 3 5 7 b9)
C Maj 9 b13 ( 1 3 5 7 9 b13)
Major chords do not have b3rds nor do they have b7ths
Continuing with the idea that the subject of chord substitution can be greatly simplified if you take the view that most chords fit into one of three types or families...
The third of these types is the DOMINANT chord type.
Dominant chords are built by taking the basic Major Triad (1 3 5)and adding the FLATTED SEVENTH note to make a DOMINANT SEVENTH CHORD.
The formula for the seventh chorde is therefore
1 3 5 b7
The family of Dominant Chord Types is made up of chords built on the Dominant Seventh chord. To the dominant seventh may be added notes such as the 9th, 11th and 13th, any of which may be altered by sharping (#) or flatting (b) them.
Some examples of Dominant chords are:
C7 (1 3 5 b7)
C6/7 ( 1 3 5 6 b7)
C9 ( 1 3 5 b7 9)
C7b9 ( 1 3 5 b7 b9)
C9b13 ( 1 3 5 b7 9 b13)
C7#9 (1 3 5 b7 #9)
Dominant chords do not have minor 3rds although this rule is broken in effect by the 7#9 chord where the #9 can be heard as a b3 in the next octave up. The existence of both the major 3rd and Minor 3rd in the same chord is what gives it a particular sense of angst much exploited by Jimi Hendrix (The E7#9 features as the main chord in 'Purple Haze', 'Voodoo Chile' and 'Foxy Lady').
Continuing with the idea of simplifying chord substitution principals - we have talked about how chords fit into one of three main families:
The MAJOR chord type
The MINOR chord type
The DOMINANT chord type
Say we want to take a basic 'vanilla' chord sequence and jazz it up a bit. The first step is to classify each chord according to type. Lets take the chords of 'House of the Rising Sun'
Here's the 'vanilla' sequence:
Am C D F
Am C E E
Am C D F
Am E Am E
So we classify Am as MINOR
C, D and F as MAJOR
And E as DOMINANT (the fifth chord in the key is always DOMINANT)
We can then substitute chords from the same family as follows:
Am7 CMaj7 DMaj6add9 FMaj7
Am7 CMaj9 E13 E7#9
Am7 CMaj7 DM9 FMaj6
Am7 E9 Am7 E7#9
(Note: If you don't know all these chords you'll find a useful chordfinder site on our links page under utilities.)
This will give you a nice sleazy Jazz version of the song using chords that open up extra possibilities for walking bass lines and improvised counter-melodies.
Of course this is just one of many thousands of possible permutations. Try it out for yourself - Jazz is all about experimenting.
NB. If this article sounds confusing spend a bit of time researching modes and II-V-I chord relationships.There are loads of sites that have great information on this. You can access some from our links pages
Continuing with the idea of simplifying chord substitution principals lets look at a connection between the three Chord Families and three of the modes:
The MAJOR chord type is primarily associated with the IONIAN mode
The MINOR chord type with the DORIAN mode
The DOMINANT with the MIXOLYDIAN mode
This idea is based on a theme that runs through most music forms, but is especially prevalent in Jazz, the II-V-I chord relationship.
Try this exercise. Play the following chords rooted at the fret shown on brackets after each chord:
4
4||:Am7(12) | D7(10) | GMaj7(10) | GMaj7(10) |
Gm7(10) | C7(8) | FMaj7 (8)| FMaj7(8) |
Fm7(8) | Bb7(6) | EbMaj7(6) | EbMaj7(6) |
Ebm7(6) | Ab7(4) | DbMaj7(4) | DbMaj7(4) |
Dbm7(4) | F#7(2) | BMaj7(2) | BMaj7(2) |
Bm7(2) | E7(12) | AMaj7(12) | AMaj7(12) :||
Learn the sequence thoroughly then record yourself playing through it at a reasonably slow tempo. Alternatively get a friend to play it live.
So using the sequence as a backing try improvising lead over it using the three scales as follows:
Over the IIm7 chord use the Dorian mode (b3,b7)
Over the V7 chord use the Mixolydian mode (b7)
Over the I chord use the Ionian mode (same as major scale)
This exercise has a lovely sound and feel to it and is a great way to get students into Jazz guitar, providing they are already quite proficient at playing rock, blues or classical guitar first.
18.The II-V-I sequence and basic chord substitution
NB. If this article sounds confusing spend a bit of time researching modes and II-V-I chord relationships. There are loads of sites that have great information on this. You can access some from the links pages.
Continuing with the idea of simplifying chord substitution principals lets look at the exercise from last month and how we might use it to develop our basic chord substitution skills.
Here's the basic exercise again (root note fret numbers in brackets):
4
4||:Am7(12) | D7(10) | GMaj7(10) | GMaj7(10)|
Gm7(10) | C7(8) | FMaj7(8) | FMaj7(8) |
Fm7(8) | Bb7(6) | EbMaj7(6) | EbMaj7(6) |
Ebm7(6) | Ab7(4) | DbMaj7(4) | DbMaj7(4) |
Dbm7(4) | F#7(2) | BMaj7(2) | BMaj7(2) |
Bm7(2) | E7(12) | AMaj7(12) | AMaj7(12) :||
Notice that each line is in a different key. The key chord is the one in the last two bars of each line. Each line represents the chord relationship II-V-I.
As a broad general rule, in a major key the II chord can be substituted by any chord of the MINOR family (m6, m7, minMaj7, m9, m11, m7b9, m7#5 etc. etc..).
Likewise the V chord can be substituted by any chord in the DOMINANT family (6/7, 7/9, 7, 9, 11, 13, 7#9b13, etc..)
The I chord can be substituted by any MAJOR type chord (6, Maj7, Maj9, Maj13, Maj7#9#11 etc).
It must be said that some combinations have a better natural flow to them than others. This is where experimentation comes in. Try various ideas out using the above exercise as a testbed.
For example you might start out with:
4
4||:Am9(12) | D13(10) | GMaj7(10) | GMaj9(10) |
Gm9(10) | C13(8) | FMaj7(8) | FMaj9(8) |
…etc..etc…
If you are a budding Jazz guitarist it is well worth investing hours and hours into these exercises because what you are doing is getting your fingers, ears and musical instincts used to the chord relationships that exist at the heart of almost all Jazz standards. You are also working with raw application of music theory in an intelligent way which should provide you with a very clear understanding of chord and scale relationships.