Music Theory - Basic, Intermediate, Advanced.pdf
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Music Theory
Basic Level
June 2005
Introduction .......................................................................................................................................... 3 Intervals................................................................................................................................................. 4 Theory................................................................................................................................................. 4 Usage .................................................................................................................................................. 5 Chords .................................................................................................................................................... 7 Theory................................................................................................................................................. 7 Triads .............................................................................................................................................. 8 Four-note chords .......................................................................................................................... 8 Usage .................................................................................................................................................. 8 The Major Scale.................................................................................................................................. 10 Theory............................................................................................................................................... 10 Usage ................................................................................................................................................ 13 The Minor Scales................................................................................................................................ 15 Theory............................................................................................................................................... 15 The Natural Minor Scale............................................................................................................ 15 The Harmonic Minor Scale........................................................................................................ 16 The Melodic Minor Scale............................................................................................................ 17 Usage ................................................................................................................................................ 17 References ............................................................................................................................................ 20
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Introduction This document is part of a compilation of a series of threads that deal with music theory and that were originally published by Eowyn on www.mysongbook.com. The compilation has been reorganized into three separate documents: •
Basic Music Theory – this document
•
Intermediate Music Theory
•
Advanced Music Theory
This has been done for two reasons: 1. The size of one single file was too large for download 2. The material covered by the different topics is of varying levels of complexity and targets different audiences. The text of the original threads has been modified and/or extended in several places where it was deemed appropriate for increased readability. The rather crude layout of the original text (due to the limitation of the forum) has also been improved. Finally, the text has been proof-read by Arnold and Blackiel. This is by no means an exhaustive treatise about music theory and harmony. Much more modestly, the purpose of this series of topics is to give those willing to better understand what they are doing with their guitar, the ability to get this knowledge into a quick and concise form. The underlying objective is lead work and improvisation in a rock music context (broadly speaking), but most topics are of a more general nature and they can also easily be adapted to other musical genres. There are numerous books and web sites about general music theory and more specialised topics. Interested readers will find a short reference list at the end of the document. Copyright Notice The information contained in this document and this document itself can be freely downloaded, used and copied for private educational purposes only. Selling of this document is strictly prohibited in all circumstances.
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Intervals Theory Intervals aren’t much fun to learn but they are essential and we'll need them: •
in the context of scales
•
in order to define chords
•
to help in analysing phrases and solos
and most importantly, we absolutely need to know how to play them. So please, bear with me and read on. As you probably know, the whole western musical system is built on 12 notes: C
D
C#/Db
D#/Eb
E
F
F#/Gb
G
G#/Ab
A
A#/Bb
B
Some points worth noting: •
Some notes have two names (e.g. C# - "C sharp", or Db - "D flat"). This is required for theoretical reasons that we will not go into but in practice they are one and the same note.
•
This ordered sequence of notes is called a scale; this particular one is the "chromatic scale". We'll get into scales in future topics.
•
Between any pair of consecutive notes in the scale above, there is an equal distance of a halftone (H); two halftones form a whole tone (W). Because of that equal distance of a halftone, this scale is called equal-tempered. Why there are only twelve notes and why there is that equal distance of a halftone between any pair of adjacent notes is a very complex subject that we won’t go into here.
The "distance" between two arbitrary notes is called an "interval". When the notes are played sequentially, the interval is called "melodic". When they are played simultaneously, it is called "harmonic". The name of an interval depends on the number of notes it contains, including the end notes; for example, the interval C - F contains 4 notes (C, D, E, F), and will be called a “fourth”. The type of an interval depends on the number of H's and W's that it contains. An interval can be "minor" (m), "major" (M) or “perfect” (P); in addition, intervals can be “augmented” (aug or # or +) (raised by an H) or “diminished” (dim or b) (lowered by an H). When nothing is specified, the interval is considered to be major or perfect. Here's a table of the intervals you should know: Name
M2
2
m3
3
4
b5
Distance
H
W
W+H
2W
2W+H
3W
3W+H
Example
C-
C-
C-Eb
C-E
C-F
C-
C-G
Db
D
Gb
5
M6
6
m7
4W
4W+H
C-
C-A
Ab
7
8
5W
5W+H
6W
C-
C-B
C-C
Bb
The “8” is not called a perfect eighth but a perfect octave or simply octave. Intervals can span more than one octave. A "9th" is a 2nd an octave higher, an "11th" in a 4th an octave higher and a "13th" is a 5th an octave higher. I've never seen intervals larger than a 13th being used in practice... and in blues and rock music, you'll rarely need more than the m7.
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And finally this: make sure you know the difference between a "chromatic" H and a "diatonic" H: •
A chromatic H is when you raise (or lower) a note by an H without changing its name. For example, C - C#, Db - D, Gb - G, A - A# are all chromatic intervals.
•
A diatonic H is when you raise (or lower) a note by an H and change its name. For example, C - Db, C# - D, F# - G, A - Bb are all diatonic intervals.
Please note: C - C# is musically identical to C - Db... but not theoretically. Damn theorists!
Usage We'll use intervals a lot when we'll talk about chords and scales. In standard tuning a guitar is tuned EADGBE from 6th string to 1st string (the 6th string being the low thick string). Interval-wise this means that between any two adjacent strings the interval is a perfect fourth (4), except between the G and B string, where there it is only a major third (3). As you probably know, whenever you move up (or down) by one fret on the fret board, the corresponding interval is an ascending (or descending) H. A distance of two frets on the fret board corresponds to a whole tone (W). As a guitarist (especially lead guitarist), you have to be able to instantaneously locate the m3, 3, 4, 5 and m7 with respect to any given note anywhere on the fret board. You will need this for fast and correct soloing! Let’s assume you are currently playing the 5th fret on the A string (that’s a D note), and let’s take that as the basis for our intervals: •
playing the note one fret higher gives you an D# note (or Eb); two frets higher gives you an E; one fret lower gives a Db (or C#); two frets lower gives a C.
•
playing the 5th fret on the D string represents a 4, and the resulting note is a G; playing the 4th fret on the D string results in a 3, and the note is an F#. Playing the 3rd fret on that string produces a m3 (an F).
•
playing the 5th fret on the G string (that’s two strings away) produces a m7 (a D)
The following diagram represents all this information graphically. This diagram is valid anywhere on the fret board, as long as you stay “under” the B string.
:
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Whenever the B string is involved (a note lands on the B string or the interval crosses that string) we need to remember that between the G string and the B string there is only an interval of a 3rd. That changes the shape of the interval patterns; for example:
I strongly recommend you do this exercise for yourself for all the strings at all the fret positions. Another useful exercise I recommend you do is intervallic analysis. Take any melody you know, but take a simple one to start with. Play that melody on the guitar. Now write down the sequence of intervals formed by the notes of the song, using a plus sign whenever the interval is ascending, and a minus sign otherwise. For example, if the melody goes C E G E G A G, the corresponding sequence of intervals will be (+3, +3, -3, +3, +2, -2). This form of intervallic analysis is useful in relating a melody (or a solo) to the fret board of the guitar, and makes it easier to memorize the melody.
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Chords Intervals are used to define chords. Needless to say, knowing chords and how to build them is very important for the rhythm guitarist. But chords are also very important for the lead guitarist, because the lead phrases must blend with the harmony and not clash with it. In other words, when improvising, you create a melodic line that needs to remain connected with the chord progression played in the background. What that means exactly is something we'll talk about in another section. For now, let's look at the chords themselves.
Theory You play a chord when you play at least three different notes simultaneously. Two notes played simultaneously don't really constitute a "chord" but rather a harmonic interval (sometimes called a “dyad”). There are of course many different ways to build chords; we'll stick to the most common approach of stacking up intervals of 3rds (m3 and/or 3) above a starting note called the "root" (R). The root gives its name to the chord. R + 3rd + 3rd = 3 notes chord, usually called a triad R + 3rd + 3rd + 3rd = 4 notes chord R + 3rd + 3rd + 3rd + 3rd = 5 notes chord ...etc... When the first third in the chord is a major third, the chord is major; when that first third is a minor third, the chord is minor. For each chord type, there is an equivalent formula, in which all the constituent notes are related to the root. For example, if the construction formula is R + 3 + m3, then the equivalent formula will be (R, 3, 5), because if you add a m3 on top of a 3 you get a 5 with respect to the starting note (i.e. the root). Triads are the most frequent chords (in rock music at least) and consist of a root (R), a 3rd and a 5th; there are four possible types of triads: major, minor, 5+ and b5. Four-note chords are less frequent in rock, but abound in classic, jazz and other genres. These chords consist of a root, a 3rd, a 5th and a 7th. There are seven possible types of four-note chords, but the most frequent ones are the dom7, m7, maj7 and dim7. Higher order extensions (chords with a 9th, an 11th or a 13th) can be found in blues, funk and jazz music, but very rarely in rock. Let's build the most important types of chords.
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Triads Type
Formula
Equivalent Formula
Example
Major Chord
R + 3 + m3
(R, 3, 5)
A = (A, C#, E)
Minor Chord
R + m3 + 3
(R, m3, 5)
Am = (A, C, E)
Power Chord
R + 5 + Octave
(R, 5, 8)
A5 = (A, E, A)
PLEASE NOTE: the power chord has no 3rd, and is therefore neither major nor minor!
Four-note chords Type Dominant 7
th
chord
Formula
Equivalent Formula
Example
R + 3 + m3 + m3
(R, 3, 5, m7)
A7 = (A, C#, E, G)
Minor 7th chord
R + m3 + 3 + m3
(R, m3, 5, m7)
Am7 = (A, C, E, G)
Maj7 chord
R + 3 + m3 + 3
(R, 3, 5, 7)
Amaj7 = (A, C#E,G#)
Diminished chord
R + m3 + m3 + m3
(R, m3, dim5, dim7)
Adim = (A, C, Eb, Gb)
PLEASE NOTE: in "Amaj7", the "maj" refers to the interval of a 7th; the chord itself is major! Musical conventions are not always consistent, and here we have an example where it isn’t! Usually, when nothing is specified, the interval is major. Here we have the opposite: A7 means “an A major chord with a minor 7th”, while Amaj7 means “an A major chord with a major 7th” and Am7 means “an A minor chord with a minor 7th”. In all the examples so far, we have assumed that the root is the lowest note in the chord; but this isn't necessarily the case. When the lowest note is not the root, the chord is said to be "inverted". There are as many possible inversions as there are notes in the chord. Inversions are notated with the "slash" notation. For example, C/G means a C chord with a bottom G. An inversion certainly changes the way a chord will sound, but does not change its quality: C/G remains a C chord.
Usage In order to build a chord on the guitar, proceed as follows: •
Find the chord's constituent notes first.
•
Next, select a string where you'll play the root (or lowest note in case of an inversion). This is typically the 6th, 5th or 4th string, but can also be the 3rd string.
•
Locate the 3rd of the chord on the next string, then the 5th of the chord, and so on. However, if fingering requires, you can change that order. In other words, it is not mandatory to play the notes of the chord in the order of the theoretical chord formula. You can also double up certain notes at the octave (but never double a 7th).
Here is an example: suppose we want to build a Dm7 (D – F – A – C) on the fret board, and suppose we want the 3rd (F) to be in the bass on the 5th string. We can work out a fingering pattern as follows: •
The F on the 5th string is at the 8th fret
•
The A is a minor third higher, which brings us on the 4th string at the 7th fret
•
The D can be played at the 7th fret of the 3rd string
•
Finally, there is a C note waiting to be played at the 8th fret of the 1st string
The resulting diagram is:
The B string should not be played. The actual way you decide to play the chord is called its voicing, and the way the various voices of the chords move when changing chords is called voice-leading. Excellent voicing and voice-leading skills are required for chord-based improvisations (frequent in jazz), and are also important in classical music.
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The Major Scale The chromatic scale is unquestionably the cradle of all scales, but the Major Scale is the mother of most of them!
Theory A scale is a sequence of notes organised in ascending pitch order. Let's start with the following scale: C
D
E
F
G
A
B
(C)
The first note of a scale is called the tonic, and gives its name to the scale - so this is a C scale. If the first 3rd of the scale (with respect to the tonic) is a major third (3), the scale will be "major"; if it is a minor third (m3), the scale will correspondingly be "minor". So the scale above is a "C Major scale". Although you may think that any scale is either major or minor, in fact this is not the case. Some scales are neither major nor minor because they contain a minor third and a major third! Other scales don’t contain any third. We'll get into to that later on. This C major scale is not the only possible C major scale; there are other major scales starting with C. However, this particular C major scale has become extremely important in what is called tonal music, and has acquired a dominant position over all the other major scales. This is why we will call it the C major scale (more on the other “major” scales later on). Instead of writing the notes of the C Major scale, let us write the intervals between each pair of consecutive notes in the scale; that gives us: W
W
H
W
W
W
H
and leads to the following extremely important definition: For a scale to be major, its notes must be laid out according to the interval pattern (W W H W W W H). With that definition we can build all the major scales we want. For example, let's build the G Major scale. First, we write down the plain notes: G
A
B
C
D
E
F
(G)
Next, we check that the interval between each pair of consecutive notes corresponds to the prescribed pattern. We find that this is almost the case; the only discrepancies are between E and F where we have an H instead of a W, and between F and G where we have the opposite situation. So, we need to sharpen the F note; the resulting scale is: G
A
B
C
D
E
F#
(G)
As you can verify, this scale now corresponds to the prescribed pattern.
In a G Major scale, the F note will always be sharp; on a music staff, this is indicated at the clef by placing a sharp sign on the F line. This is called the "key signature" and it immediately tells us that the tune is written in G Major (or a relative of G Major - more on this later). G Major (in this case) is the "key" or “tonality” of the tune. Building a major scale can sometimes be a tad bit more complicated; for example, let's build the F# Major scale. The plain notes are: F#
G
A
B
C
D
E
(F#)
Starting with the tonic, we inspect the scale, and sharpen up every note that needs it (according to the major scale pattern). The end result is: F#
G#
A#
B
C#
D#
E#
(F#)
Surprise! This scale contains an E# note! Isn't that strictly equivalent to F? Absolutely, but by convention in any scale, we can have only one occurrence of each note (name); if we wrote F and F#, we would violate this rule. So we "cheat" and we write E#! Finally, please note that not all major scales are build with sharps; sometimes you need to use flats instead. For example, the Ab Major scale is: Ab
Bb
C
Db
Eb
F
G
Ab
Bb
C
D
E
(F)
Similarly, the F Major scale is: F
G
A
Tip: in a scale, you can use sharps or flats, but not both! Since the chromatic scale contains twelve distinct notes, and since each note can become the tonic of a major scale, there are twelve different major scales; the following table lists them all: C major
C
D
E
F
G
A
B
C
G major
G
A
B
C
D major
D
E
F#
G
D
E
F#
G
A
B
C#
D
A major
A
B
C#
D
E
F#
G#
A
E major
E
F#
G#
A
B
C#
D#
E
B major
B
C#
D#
E
F#
G#
A#
B
F# major
F#
G#
A#
B
C#
D#
E#
F#
C# major
C#
D#
E#
F#
G#
A#
B#
C#
F major
F
G
A
Bb
C
D
E
F
Bb major
Bb
C
D
Eb
F
G
A
Bb
Eb major
Eb
F
G
Ab
Bb
C
D
Eb
Ab major
Ab
Bb
C
Db
Eb
F
G
Ab
In fact, this table only contains the most common forms of the major scales. In theory, there are 24 different notes, since each note has two different names (F# can be called Gb, for example, and C can be called B#). So theoretically there are 24 different major scales, and nor 12.
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We already talked about chords. Chords and scales are related in many ways. Here's one link between the two. Let’s take that C major scale again: C
D
E
F
G
A
B
(C)
Now, on each degree of the scale, we build a triad the way we did in the section on chords (i.e. stacking up 3rds), and we restrict ourselves to notes belonging to the scale (notes belonging to a scale are said to be diatonic to that scale; for example F# is not diatonic to C major, but is diatonic to D major). This gives us the following series of chords, called the harmonisation of the major scale: •
(C, E, G) = C
•
(D, F, A) = Dm
•
(E, G, B) = Em
•
(F, A, C) = F
•
(G, B, D) = G
•
(A, C, E) = Am
•
(B, D, F) = Bm(b5)
Let’s write them down in sequence: C
Dm
Em
F
G
Am
Bm(b5)
As you can see, the chords on the 1st, 4th and 5th degree of the scale are major; all the other chords are minor (and the chord on the 7th degree has a flatted 5th). This will clearly be the case for any major scale, since the notes of any major scale will correspond to the same interval pattern (make sure you fully understand this!!). So instead of writing the actual chord names, we write, in general: I
ii
iii
IV
V
vi
vii(b5)
In this convention the Roman numerals represent the degrees of the major scale (of any major scale, in fact); uppercase numerals indicate major chords, and lowercase numerals indicate minor chords (sometimes, you will also find minor chords notated IIm, IIIm, etc.). The Roman numeral notation is very convenient, and you should know this sequence by heart; it will let you anticipate the chords to be expected in any given key. For example, the harmonisation of the A Major scale produces the following triads: A
Bm
C#m
D
E
F#m
G#m(b5)
Instead of harmonising a scale with triads, we can also use four-note chords; in that case the chords are: Imaj7
ii7
iii7
IVmaj7
V7
Bm7
C#m7 Dmaj7 E7
vi7
vii7(b5)
F#m7
G#m7(b5)
In A major, we have: Amaj7
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Usage The first obvious usage of this information is transposition. Say you have a tune in A major, but that's too high for you to sing comfortably; you can "translate" it note for note and chord for chord in another key (e.g. D major): A Major Scale
A
B
C#
D
E
F#
G#
A Major
A
Bm
C#m
D
E
F#m
G#m(b5)
Harmonisation D Major Scale
D
E
F
G
A
B
C#
D Major
D
Em
F#m
G
A
Bm
C#m(b5)
Harmonisation So, each C#m chord in the key of A becomes an F#m chord in the key of D, and so on. A second usage is harmonising a melody. To obtain a basic harmonisation for a given melody: •
Concentrate on the strong beats (downbeats) of each bar. Those are the 1st and 3rd beat of each bar.
•
Identify the melody notes that fall on the strong beats
•
Pick up a chord from the scale harmonisation, such that the melody note is either the root, or the 3rd, or the 5th, or the 7th of that chord.
Finally, the major scale can be used for improvisation, especially if you're after long lyrical melodic phrases like in classical music. You'll probably find out that the Major Scale is actually much more difficult to use for soloing than you may think - it is very easy to sound "cheesy" with it! The following diagram represents a very simple and compact “implementation” of the major scale on the fret board (there are of course many other possibilities). This diagram is of course moveable along the fret board, and to make that obvious I have represented the degrees of the scale instead of the names of the notes.
13
Another possibility is as follows:
14
The Minor Scales After the Major scale, we explore the minor scales. Things are going to become slightly more complicated, and we’ll meet some new chords.
Theory The Natural Minor Scale A smooth an easy way to approach the minor scales is to start from… the major scale! Here is the C Major scale again: C
D
E
F
G
A
B
(C)
Let's build a scale whose tonic is located a m3 below the current tonic, or (equivalently) a 6 above it, and whose notes are the same as those of the current major scale; the note located a m3 below C is A, so the new tonic is the A, and the new scale becomes: A
B
C
D
E
F
G
(A)
This scale is called the "A natural minor scale"; it is minor by construction, since its first 3rd (A – C) is a m3. We say that this scale is a relative minor scale to C Major, which is (conversely) its parent major scale. Every major scale has a relative natural minor scale whose tonic is located a m3 below the tonic of the major scale and containing the same notes as the major scale. Conversely, every minor scale has a parent major scale whose tonic is located a m3 higher than its own tonic and containing the same notes as the minor scale. For example, the E natural minor scale is a relative minor scale to G Major, as follows: E
F#
G
A
B
C
D
(E)
So, given a major scale, we can always determine its relative natural minor scale. But we can also describe the structure of this scale, as we did for the major scale, by writing down the series of intervals between each pair of consecutive notes; in this case we find W
H
W
W
H
W
W
That gives us another mechanism for building natural minor scales. Simply write down the plain sequence of notes first, and then alter them so as to obtain the pattern above. For example, let’s build the D natural minor scale. We first write the plain notes: D
E
F
G
A
B
C
(D)
We see that the only discrepancy is between the A and the B, where we have a whole tone and we need a halftone instead. So we flatten the B, giving: D
E
F
G
A
Bb
C
(D)
15
This scales happens to contain the same notes as the F major scale, as expected (D is located a minor third lower than F). We can also harmonise the natural minor scale, with triads or four notes chords, as we did for the major scale: for example, in A minor we have Triads
Am
Bm(b5)
C
Dm
Em
F
G
Four notes
Am7
Bm7(b5)
Cmaj7
Dm7
Em7
Fmaj7
G7
Generalising that as we did for the major scale, and using the roman numerals notation: Triads
i
ii(b5)
III
iv
V
VI
VII
Four notes
i7
ii7(b5)
IIImaj7
iv7
v7
VImaj7
VII7
As you can see, these are just the exact same chords as for the major scale, but "shifted" by a m3. In the natural minor scale the 7th degree is located a m7 away from the tonic (or equivalently, a 2 below the octave); this has two main disadvantages: •
the W step from the 7th degree to the octave is relatively difficult to negotiate for a singer when going up the scale
•
compared with the major scale, the natural minor scale lacks a clear resolution from 7 to tonic. As we will discuss in a future topic, the ascending H melodic movement from the 7th degree to the tonic is one of the strongest and most conclusive ways to establish a tonality, and therefore one of the strongest features of the major scale. We lack this ability with the natural minor scale.
The Harmonic Minor Scale To compensate for this, early music theorists of the XVIIth century have invented the harmonic minor scale: it is similar to the natural minor scale, except it has a raised seventh; the harmonic A minor scale for example becomes: A
B
C
D
E
F
G#
W
H
WH
H
(A)
Interval-wise, we now have: W
H
W
A side effect of this modification is a more complex harmonisation of the scale; harmonising with triads gives us: Chord
I
ii(b5)
III(#5)
Iv
V
VI
vii(b5)
Formula
(R,m3,P)
(R,m3,b5)
(R,3,5+)
(R,m3,5)
(R,3,5)
(R,3,5)
(R,m3,b5)
Example
Am
Bm(b5)
Caug
Dm
E
F
Gm(b5)
Two things to note: •
the fifth degree now supports a major chord, as in the major scale
•
on the third degree we have an augmented chord, i.e. a chord with a raised 5th. This is a very unstable chord.
16
Harmonising with four notes chords gives: Chord
imaj7
ii7(b5)
IIImaj7(
iv7
V7
VImaj7
R,m3,5,m
R,3,5,m7
R,3,5,7
Vii dim
#5) Formula Example
R,m3,5,
R,m3,b5,
7
m7
Am(maj7)
Bm7(b5)
R,3,5+,7
7 Cmaj7(
R,m3,b5, m7
Dm7
E7
Fmaj7
G dim
#5) Again, a couple of remarks: •
the first degree supports a new chord: a minor chord with a major seventh
•
on the seventh degree, we have a fully diminished chord; this is dominant seventh chord (e.g. G7), in which all the notes except the root are lowered by a H (unlike the m7(b5) where only the 5th is lowered).
With the harmonic minor scale we have again this conclusive melodic H movement from 7th degree to tonic but we also have a nasty WH interval between the 6th and 7th degree! This was not considered very convenient, and has led to a third version of the minor scale.
The Melodic Minor Scale To address the nasty WH interval problem in the harmonic minor scale, the 6th degree of the harmonic minor scale was in turn raised by a H, giving birth to the melodic minor scale: A
B
C
D
E
F#
G#
(A)
F#
G#
(A)
Compare this scale with the A Major scale: A
B
C#
D
E
As you can see, the only difference is the flatted third - the melodic minor scale sounds very major, apart from the m3. The triad-based harmonisation of the melodic minor scale is: I
Ii
III aug
IV
V
vi(b5)
vii(b5)
R,m3,5
R,m3,5
R,3,#5
R,3,5
R,3,5
R,m3,b5
R,m3,b5
and the four-notes counterpart: imaj7
ii7
IIImaj7
IV7
V7
vi7(b5)
vii7(b5)
R,m3,5,7
R,m3,5,m7
R,3,#5,7
R,3,5,m7
R,3,5,m7
R,m3,b5,m7
R,m3,b5,m7
You will also often see i6 (R, m3, 5, 6) as the tonic chord; this chord is not build in thirds only, but highlights the sixth of the scale, which is characteristic of the melodic minor scale.
Usage As stated previously (and should now be obvious), the minor scales are significantly more complex than the major scale; but they also offer much more expressive power than the simpler major scale.
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The natural minor scale was very popular in the western middle-ages (as we will see later, it corresponds to the old Aeolian church mode). The two other minor scales are a more recent invention of the classical period; their usage was extremely codified: one would use the melodic minor scale only for ascending movements, and the natural minor scale for descending movements (for that reason, the melodic minor scale is sometimes called the ascending melodic minor scale). Nowadays, the rules for using the minor scales aren't so strict anymore. The natural minor scale enjoys a new popularity, so you won’t upset anyone by playing it. In fact, you are free to use and mix all these scales as you want. This gives you a lot of freedom. If you use triads, you have the following harmonic options: 1st Degree
2nd Degree
3rd Degree
4th Degree
5th Degree
6th Degree
7th Degree
I
ii(b5)
III
Iv
v
VI
VII
III aug
IV
V
vi(b5)
vii(b5)
If you use four-note chords, the possibilities are: 1st Degree
2nd Degree
3rd Degree
4th Degree
5th Degree
6th Degree
7th Degree
i7
ii7(b5)
IIImaj7(#5)
iv7
V7
VImaj7
VII dim
imaj7
ii7
vi7(b5)
vii(b5)
IV7
From an improvisation standpoint, the major scale and its relative minor scales are of course completely equivalent. You can therefore use a relative minor scale over a major harmony, and vice-versa. When the harmony is minor, you really have to take the harmonic constraints into consideration and choose the scale with care. For example you will probably find that the harmonic minor scale doesn’t sound very well, except over the V chord. Therefore, in practice, you will probably stick to the natural minor scale, and only use the harmonic minor over the V chord. The following diagram represents one way of playing the natural minor scale, and is a simple adaptation of the major scale pattern described previously:
Another fingering (similar to the second diagram of the major scale) is as follows:
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You can easily find the fingering patterns for the two other minor scales (harmonic and melodic).
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References Books: Clefs Pour l’Harmonie
-
Jo Anger-Weiler
Internet Sites www.schenkerguide.com www.tonalityguide.com www.teoria.com www.musictheory.net www.dolmetsch.com
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Music Theory
Intermediate Level
December 2005
Introduction .......................................................................................................................................... 3 Target Notes ......................................................................................................................................... 4 Theory................................................................................................................................................. 4 Characteristic Notes ..................................................................................................................... 4 Phrasing.......................................................................................................................................... 5 Usage .................................................................................................................................................. 6 Chord Progressions and Tonality...................................................................................................... 8 Theory................................................................................................................................................. 8 Diatonic Progressions .................................................................................................................. 8 Chord families ............................................................................................................................... 9 The role of the bass ................................................................................................................... 11 Non-diatonic progressions ........................................................................................................ 11 Dominant Substitutions............................................................................................................. 12 Usage ................................................................................................................................................ 13 Chord migration .......................................................................................................................... 13 Melodic Movements ........................................................................................................................... 15 Theory............................................................................................................................................... 15 Recommended Movements ...................................................................................................... 15 Forbidden Movements ............................................................................................................... 15 Tolerated Movements ................................................................................................................ 16 Usage ................................................................................................................................................ 16 Diminished and Augmented Chords .............................................................................................. 17 How to build them.......................................................................................................................... 17 Augmented chords ..................................................................................................................... 20 Pentatonic and Blues Scales............................................................................................................ 21 Theory............................................................................................................................................... 21 Pentatonic Major Scales ............................................................................................................ 21 Pentatonic Minor Scale .............................................................................................................. 21 Blues Scales................................................................................................................................. 22 Dominant 7th Pentatonic Scales............................................................................................... 23 Usage ................................................................................................................................................ 24 The CAGED system .............................................................................................................................. 25
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Introduction This document is part of a compilation of a series of threads that deal with music theory and that were originally published by Eowyn on www.mysongbook.com. The compilation has been reorganized into three separate documents: •
Basic Music Theory
•
Intermediate Music Theory – this document
•
Advanced Music Theory
This has been done for two reasons: 1. The size of one single file was too large for download 2. The material covered by the different topics is of varying levels of complexity and targets different audiences. The text of the original threads has been modified and/or extended in several places where it was deemed appropriate for increased readability. The rather crude layout of the original text (due to the limitation of the forum) has also been improved. Finally, the text has been proof-read by Arnold and Blackiel. This is by no means an exhaustive treatise about music theory and harmony. Much more modestly, the purpose of this series of topics is to give those willing to better understand what they are doing with their guitar, the ability to get this knowledge into a quick and concise form. The underlying objective is lead work and improvisation in a rock music context (broadly speaking), but most topics are of a more general nature and they can also easily be adapted to other musical genres. There are numerous books and web sites about general music theory and more specialised topics. Interested readers will find a short reference list at the end of the document. Copyright Notice The information contained in this document and this document itself can be freely downloaded, used and copied for private educational purposes only. Selling of this document is strictly prohibited in all circumstances.
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Target Notes I like to define improvisation as "instantaneous composition". In order to create a good solo it helps to be a good composer, with all the implied musical skills; but additionally you must be able to act on the spot in front of an audience – despite the stage fright and the stress! Those who have tried it know that this is far from easy, and poses two related challenges: •
Select the right notes at the right moment
•
Play as musically and meaningfully as possible
Music is and remains an art, and the theory is only there to acknowledge and establish what seems to work well. The rules are only there to provide guidance; in many cases they can be broken. But guidance is useful when you learn something new. And improvisation can be learned! I have broken down the theoretical aspects in three topics: •
In this topic we will address the problem of selecting the target notes of the solo based on the chord progression.
•
In the next topic we will explore chord progressions themselves.
•
In the topic after that we’ll discuss the general “rules” regarding melodic movements.
Theory Some solos are purely rhythmic and chord oriented. In most cases however, the lead player is expected to create a melodic composition that blends with the harmonic structure of the piece of music currently played by the band. This might be called constrained composition. When you are composing a piece of music, you are of course totally free to pick any harmony you want. As a lead guitarist, however, you will have to make do with the chord progression currently played by the band. The notes of the lead lines will inevitably interact with the chords played by the background and we want to make sure this interaction is as smooth and musical as possible. Fundamentally, this boil down to two separate but related aspects: •
Note selection (characteristic notes)
•
Phrasing
Characteristic Notes The characteristic notes of a chord are the notes that help uniquely identify and characterise that chord (hence the name). You will recall that chords are usually build by stacking up thirds, so the characteristic notes of the chord are the notes 1, 3, 5, 7, 9, etc., where the third and the seventh can be minor or major, the fifth can be perfect, augmented or diminished, and so forth. The root of the chord is a neutral tone. It is neutral because it remains the same in a very large number of chords: C, Cm, C7, Cmaj7, Cm7 all have the same root note C. The root does not characterise the chord very well. The 5th in the chord is called a second-order characteristic note; it is less uniform than the root, but still pretty stable across different types of chords. All the chords mentioned previously actually
share the same 5th (G) in addition to sharing the same root. But there are certainly C chords with a different fifth: Caug = (C,E,G#) and Cm(b5) = (C,Eb,Gb) are examples. The 3rd and 7th in a chord are the first-order characteristic notes of the chord; they give the chord its colour. The third immediately tells whether the chord is major or minor, while the seventh adds a lot of colour and accounts for totally different functions in the harmony. As we will see shortly, these notes play a fundamental role in improvisation. Higher order chord extensions such as the 9th (not to mention the 11th and 13th) are also considered first order characteristic notes, and are frequent in jazz music but you're not likely to see them as often in rock music.
Phrasing The impact of a note in a solo not only depends on its pitch and function, but also on its placement in the bar, its rhythmic value, and the effects applied to it. This together is called "phrasing".
Placement Rock music is predominantly 4/4 (four to the beat) music, so we'll focus on that. In a 4/4 bar, the 1st and 3rd beats (the downbeats) are strong (although the 3rd beat is slightly weaker than the 1st), while the 2nd and 4th beat (the upbeats) are definitely weak. This simply means that the 1st and 3rd beats get more emphasis than the other two beats. You can clearly hear that if you listen to a typical percussion track: bass drum on the 1st and 3rd beats, snare on the 2nd and 4th beats. In ¾, the first note of the bar is strong, while the other two are weak. The general rule when soloing is to place characteristic notes on the strong beats of the bar. These become your target notes. In other words, the theory requires you to try and place the 3rd or the 7th of the underlying chord on the downbeats, or else the 5th or the root. In rock music, you will typically (although not systematically) avoid the 9th and higher order extensions. In practice, you will want to handle the 7th with care: the major 7th may sound too jazzy, and the minor 7th may require an unwanted resolution (see next topic). On the other hand, the root, 3rd and 5th always sound right.
Rhythmic Value If a bump note is an 8th note or a 16th note, it will cause less aural damage than if it's a longer note, because it will resolve very quickly in harmonically more acceptable sounds and go almost unnoticed. •
Therefore, the rule above is of high importance for quarter notes and longer, and slightly more flexible for short notes (8th notes and faster).
5
•
Also, strictly speaking the rule above is only valid when the notes are within an interval of two octaves; beyond that, the distance becomes too large for the ear to be sensitive to the relationship between the notes.
However, if you’re not yet a seasoned lead guitarist I strongly recommend sticking to the rule, even for short duration notes and high pitches. A very effective trick when you’re not sure about the target notes is to start your musical phrases slightly after the downbeats, or downright on the upbeats. For example, when using 8th notes, you may decide to start on the second half of the first beat, or on the first upbeat. Even if the first note you play is off, its impact will be much less dramatic due to its more favourable position in the bar. Moreover, this technique produces a very driving effect. It is very commonly used in blues.
Effects We guitarists are happy to have several fretting-hand and picking-hand effects at our disposal: slides, hammers, pull-offs, bends, rakes, harmonics, muting, tapping, you name it! Again, applying effects on characteristic notes will dramatically enhance their role and importance. But beware of clichés.
Usage Granted, a solo should ideally flow naturally as an instant composition. You “think” the melody you want to play, and here it comes on the fret board… But as you will probably acknowledge if you have tried it, there is quite a distance between your brain and your fingers. Everybody needs to learn, so it will do no harm constructing your solo on the principles mentioned above. Fluency comes with practice. In general, when you're asked to play lead in a chorus: 1. Quickly analyse the harmonic progression (the chords you need to play over), and identify their characteristic notes. For mainstream rock music, you will probably want to stick with the root, 5th and 3rd of the chords, and only use 7th (especially major 7th) sparingly. Other genres will have their own stylistic requirements and opportunities. 2. Mentally select the characteristic notes you will play, and place them on the strong beats; this sequence of target notes becomes the melodic backbone of your solo. Try to locate and visualise those target notes on the fret board a little before you play them; that way you will always know where you are going. Don’t be discouraged if you find this hard to do: it is very hard to do and requires a lot of practice!
3. Fill in the "gaps" with short connection phrases - initially try to use as few notes as possible, and try to be consistent with the melodic flow of the target notes: you want to tell a story, not running up and down some scales. As you get comfortable with this, create longer and more complex phrases. Playing only long characteristic notes with expression and effects is much preferable over a waterfall of fast but meaningless notes!
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4. When working out your solos this way, you will occasionally produce very pleasant phrases; whenever that happens, repeat that phrase, exploit it and create all sorts of variations for it.
5. When the length and complexity of your solo phrases increase, it remains critical to select your starting notes carefully, but the importance of the other target notes decreases somewhat. This is because the human ear tends to remember the first note much more than the other notes, especially if the tempo is fast. Please make sure you only relax the rule when you have become sufficiently comfortable with it! Here is a very simple example. Suppose the chord progression of the song is: C - - - / Dm - - - / G7 - - - / C - - One possible backbone for the lead could be: e–g-/a---/g–d-/c--(lower case indicates notes, not chords). Based on this sequence of target notes, a simple melodic fragment using only quarter notes or longer could then be: efgb/a---/gad-/c--Another simple and very effective approach to soloing is to play arpeggios. An arpeggio is simply a chord whose notes are played sequentially instead of being played simultaneously. Take the same progression as above: C - - - / Dm - - - / G7 - - - / C - - It should be obvious that all the notes of a C chord (in whatever order) will work on the first bar; similarly, all the notes of a Dm chord (in whatever order) will work on the second bar, etc. Referring to chord theory (see Basic Level material), you will be able to enrich the arpeggios with compatible chord extensions. You may even decide to play chord substitutes; for example, when the band plays that C chord, you might decide to play an Em7 chord (E G B D). The combination of a C chord and an Em7 chord would produce a Cmaj7(9) chord – very jazzy indeed! We will explore all this in more details in the next topic.
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Chord Progressions and Tonality We are now going to discuss the "rules" that govern harmonic progressions, bearing in mind once again that in music theory most of the rules really come after the facts. Rules in music theory usually acknowledge best practices from their time, after the most successful musicians have established them (usually by breaking the existing rules!). Making technically acceptable music consists in following the rules; making innovative music consists in creatively breaking the rules! But as always, you have to learn how to walk before you can run. Please make sure you've read the sections on Major and Minor scales before moving on. In particular, remember the basic scale harmonisations: Major
Imaj7
ii7
iii7
IVmaj7
V7
vi7
vii7(b5)
Harmonic
imaj7
ii7(b5)
IIImaj7(#5)
iv7
V7
VImaj7
viidim
imaj7
ii7
IIImaj7(#5)
IV7
V7
vi(b5)
vii7(b5)
minor Melodic minor
Theory Before looking at the chord progressions themselves, here are three fundamental facts about tensions and note movements that you should be aware of: 1. a note always has a tendency (however faint) to move and resolve into another note located a 5th below it, or a 4th above it 2. in a major scale, the 7th degree (called the "leading tone") has a very strong tendency to move a halftone upwards towards the tonic 3. an augmented 4th interval (often called a tritone) such as F - B is extremely unstable (dissonant), and wants to resolve into a stable consonant interval, as follows: the lower end will move a halftone down, while the upper end will move a halftone up, stretching the augmented fourth into a perfect fifth; so for example the F - B interval will want to become an E - C interval These facts account for a large part in the theory of chord progression, and tonal harmony in general.
Diatonic Progressions We will concentrate on the major scale here, but the discussion below also applies to the harmonic (and melodic) minor scales. Remember that the harmonic minor scale was invented to benefit from the same sort of strong conclusive movements that are possible in the major scale, owing to the presence of the leading tone (the 7th degree of the scale, only a half tone away from the octave). In the harmonisation of the scale:
•
taken together, the triads on the 1st, 4th and 5th degrees contain all the notes of the scale (you may want to verify this). For that reason they are sometimes called "generator chords". They are self-sufficient: the simplest melodies can be harmonised with these three chords only.
•
the I chord is the strongest of the three; in the kingdom of tonality, the I chord rules. He very often opens the song, and almost always terminates it. He also shows up at regular intervals during the execution of the song, he himself or one of his delegates. All the chord sequences in the song tend to progress directly or indirectly towards the I chord. He represents the tone centre of the song.
The strongest supporter and herald of the I chord is the V chord. Whenever you hear the V chord, the I chord is usually on its way. Consider this: •
the root of the V chord calls for a resolution onto the tonic in a descending 5th movement or ascending 4th movement. For example: G -> C
•
the V7 chord contains the so-called tritone, a very unstable interval of an augmented 4th (and the only interval of its kind in the major scale); in C Major, this is the interval (F - B). Because of its instability, the tritone needs urgent resolution: its lower end will move down by an H, while its upper end will move up an H towards the tonic. The strongest way to establish a tonality is to play the progression V7 -> I
However, the I chord is also a bit suicidal: its own root is attracted a 4th upwards, towards the IV chord... In any scale, you will always have this power game between the I chord (who currently reigns), and the IV chord (who wants to take control).
Chord families The entire tonality is divided into three political parties, supporting one of the generator chords. 1. The iii7 and vi7 have several notes in common with the I chord, and the I chord itself can come in several varieties (I, Imaj7, I6, etc.). These chords are collectively called "tonic chords"; by definition they contain neither the 4th degree of the scale, nor the tritone. Therefore, they are very stable chords. 2. The chord on the 4th degree, called the subdominant chord, has one main supporter: the ii chord. These chords and their variants ( IVmaj7, ii7, etc.) are called "subdominant chords"; by definition they contain the 4th degree but not the tritone. Because they contain the subdominant, they are somewhat less stable (tonality wise) than the tonic chords. 3. The chord on the 5th degree (dominant chord) has one single supporter: the vii(b5) chord. They form the "dominant group"; chords in this group contain the sub-dominant as well as the tritone. They are very unstable in the sense that they imply a resolution on the tonic chord. All the other chords which are not build strictly out of thirds can always be associated with one of these three groups. For example, C6 (C – E – G – A) does not contain the 4th nor the tritone, and therefore belongs to the tonic group. Similarly, Dsus2 (D – E – A) also belongs to the tonic group, for the same reason.
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Harmonically, all the chords in a given group are equivalent. That means they can usually replace each other, and we can take advantage of that to: •
enhance a somewhat dull and boring chord progression, or
•
simplify an harmonically complex progression, for example in order to give the lead more room and emphasis.
Here are two examples. Example 1: Enrichment Suppose we have the following chord progression: G - - - / G - - - / C - - - / D7 - - - / G - - This is the (in)famous I – IV - V progression in G Major. But the progression dwells over the I chord for two bars, which is a bit dull. In order to make it more interesting, we could (for example) decide to replace the second bar with: Bm7 - Em7 which are equivalent tonic chords in G Major (they all belong to the tonic group). So the progression becomes: I - - - / iii7 - vi7 - / IV - - - / V7 - - - / I - - We could have chosen to highlight the subdominant chord (C) instead; in that case, we could have replaced the bar with the IV chord with ii7 - IVmaj7 Or we might choose to do both, giving: I - - - / iii7 - vi7 / ii7 - IVmaj7 / V7 - - - / I - - Of course, when you want to alter an existing harmonic progression, you need to do that in agreement with the other musicians! Simultaneously playing a chord and a substitute of that chord will usually not produce very good results! Example 2: Simplification Suppose we have the following chord progressions: Imaj7 – iii9 - / iii7 – vi7 - / IVmaj7 – ii7 - / V7 - - - / Imaj7 - - Such a rich harmony will not leave much room for the lead guitarist to be creative; so for the duration of chorus we may decide to simplify the harmony into the harmonically equivalent sequence: I - - - / I - - - / IV - - - / V7 - - - / I - - -
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The role of the bass The actual effect of a substitution will depend primarily on the movement of the bass (which does not need to be the root of the chord, of course): •
if the bass moves by a 4th, a 5th or an octave, substitutions have a very strong effect
•
if the bass moves by a 3rd or m3, the effect will be moderate
•
if the bass moves by a 2nd, the effect will be subtle
You can control this impact by carefully selecting the voicing of your chords: the larger the movement in the bass, the more dramatic the effect. Here's a progression that should be familiar to you: ii - - - / V7 - - - / I - - For example: Dm - - - / G7 - - - / C - - This progression (called "two five one") is pervasive in all musical genres, from classic to jazz. Let’s analyse its impact (assuming root position for all chords): •
the first chord change implies a strong movement of a 4th (from the 2nd to the 5th degree, that is from D to G in the example)
•
the second change implies a movement of a 5th - the strongest possible movement (from G to C in the example)!
The overall effect of this progression is quite strong. If you invert the V7 chord into a V7/5 (a V7 chord with its 5th in the bass, that is G7/D), the first movement disappears since the bass will stay on the D note, and the second movement is reduced to a second (from D to C). The effect is much less dramatic. If the ii chord is voiced ii/5 (A in the bass) and the V7 chord is voiced V7/3 (B in the bass), the amplitude of the bass movement is limited to seconds (from A to B to C), and the progression becomes very soft.
Non-diatonic progressions In the previous discussion, we have seen that the V - I progression is an extremely strong and effective way to establish a tonality. Progressions that enforce and establish a tonality are called "cadences". Using the basic principle of the V - I cadence, we can actually go a step further. Look at the following progression: C - - - / E7 - - - / Am - - - / A7 - - - / Dm - - - / G7 - - - / C - - -
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There is apparently something very wrong with it: it looks like a C major progression, but the E7 and A7 chords contain notes that don't belong to C Major (E contains a G# and A7 contains a C#)!!! What happens here is that some chords are preceded by their respective V7 chords, even though they are not diatonic to the original tonality. So, the Am chord is preceded by its own V7 chord in the A harmonic minor tonality (that is to say E7), and the Dm chord is preceded by its own V7 chord in the D harmonic minor tonality (that is to say A7). From a harmonic analysis standpoint, this will be represented as follows: I - - - | V7/vi - - - | vi - - - | V7/ii - - - | ii - - - | V7 - - - | I - - The main tonality is and remains C Major throughout, but we have introduced additional local tone centres in the harmonic progression. Everything happens as if Am and Dm temporarily became the new tone centres. Those foreign V7 chords are called "extended dominant chords". Now, if V7 -> I is a great way to establish a tonality, ii -> V7 -> I is even better! So how about also introducing the ii chord of the local temporary tone centre, and not just the V7? For the case above, that gives us (for example): C - - - / Bm7 – E7 - / Am - - - / A7 - - - / Dm - - - / G7 - - - / C - - Harmonically, we analyse this progression as follows: I - - - | ii7/vi - V7/vi | vi - - - / V7/ii - - - / ii - - - / V7 - - - / I
Dominant Substitutions We know that vii7(b5) is a dominant chord (it belongs to the dominant group) and it can therefore be a substitute for V7. However, this is not a very frequent substitution, because that vii7(b5) chord really doesn’t sound so good (although you may have a different opinion, of course). But look at this: C - - - / Dm - - - / Db7 - - - / C - - By the looks of it, Db7 replaces a G7: it is located at a place where you would expect a perfect cadence (i.e. V7 -> I), especially since it is preceded by the ii chord. But again, we seem to have a problem, in that Db certainly doesn't belong to C Major. And yet, this progression sounds great; the halftone bass movement in particular is very interesting and soft. Let's have a closer look at what happens here. The Db7 chord is made of the notes (Db, F, Ab, B).
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So this chord actually contains the (unstable) tritone in C Major (F – B), and as such calls for the urgent resolution we have already described. The Db and Ab notes being foreign to C Major will also be more than happy to resolve one halftone down onto C and G respectively. So this chord actually creates the same effect as a V7 chord, and is therefore functionally equivalent to it. In general, it is always possible to replace a V7 chord with a major chord rooted a halftone above the tonic of the current key. This is called a "substitution dominant". For example, in A major, you can replace E7 with Bb7, and the ii – V – I cadence then becomes Bm – Bb7 – A. We have seen above that it is possible to associate the local ii chord to an extended dominant; we can apply a similar trick with substitution dominants; for example: Cmaj7 - Dbm7 Gb7 / Fmaj7 - Bbm7 Eb7 / Dm7 - - - etc We analyse this harmonic progression as follows: •
The extended dominant for Fmaj7 (first chord of the second bar) is C7; the substitution dominant is Gb7.
•
Then Dbm7 is the ii7 in the tonality for which Gb7 is the dominant chord! Pfew!!
Usage As you can see, there are quite a few possibilities! All these extensions and substitutions and bass movements can be used to spice up the harmonic structure of a song. How much spicing is a matter of taste. Although you are ultimately the only judge, I suggest using these harmonic devices with care in mainstream rock music, because they will quickly start to sound very jazzy. At this point we also need to link back to the previous section (characteristic notes). We have concentrated on the chords and their progressions here, but you can't really dissociate the chords (harmonic background) from the melody. Melody notes do cause chord extensions (e.g. an A note over a C chord will actually create an overall C6 chord; similarly, a G note over an A chord will result in an A7 chord). The progression can be affected by these extensions, and you need to consider the whole thing globally. The target notes are always characteristic notes; since by definition they belong to the chords, they will always sound OK, at least technically. But you should also be careful to select the other notes so as to avoid chord migrations.
Chord migration We have seen that chords can be subdivided into three basic categories: tonic, subdominant and dominant. While chords of a given category can always be freely substituted for one another, they should never be replaced by chords of another category.
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Suppose the harmony is in C major and currently rests on a Dm chord; this chord belongs to the subdominant group. If we happen to play a long B note over that chord, we effectively transform it into a Dm6 chord, which belongs to the dominant group, since the chord now contains the tritone (the interval F – B is now part of the chord). This implies a resolution that is not likely to happen (the next chord the band is going to play is probably not a C); the harmonic effect of this is disastrous. Similarly, suppose the current chord of a C major progression is C. If we play a long F note over it, we make that chord a member of the subdominant group (since it now contains the subdominant) and the result will be far from pleasant, because the subdominant will clash with the 3rd. Please note that this is different from playing the 4th instead of the 3rd: in that case, you are playing a sus4 chord (whichever way you go after that). If the current chord is Em (another tonic chord), the subdominant note (F) will introduce the tritone and the chord will now belong to the dominant group. Let us now consider what happens when the current chord is the V7. Playing the tonic (C) over G7 will in effect resolve the chord and destroy the resolution effect that was planned by the band. So, to avoid chord migration, consider the following: •
On tonic chords, avoid the subdominant (4th)
•
On subdominant chords, avoid the leading tone (7th)
•
On dominant chords, avoid the tonic (because playing a tonic will unduly anticipate the resolution: you will be playing ahead of the harmony)
Again, these rules apply mostly for downbeats and relatively long notes.
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Melodic Movements While some melodies sound great others are just average (to say the least!). In this section we will try to analyse why this is the case, and what makes up a good melody. This is clearly useful to a lead guitarist who wants to play melodic solos; it is equally important to songwriters who want to write the next summer hit, and it is even important to bass players (we have already briefly touched upon this subject in the previous section). The “theory” of melodic movements is very old. Originally it aimed at determining which intervals would be considered appropriate (and feasible) for the human voice to sing, and for the human ear to hear. Some parts of this theory may be considered outdated by today’s standards, or applicable in specific genres only (mostly classic). But before breaking the rules, it is useful to at least understand them. This theory also constitutes the foundation for the study of harmonic movements or voice leading techniques (i.e. the melodic movements of several voices simultaneously). As this is a fairly complex subject, we will limit our study to the most important aspects.
Theory When two (or more) distinct notes are sung or played sequentially, the melody is said to make movements. There are two types of melodic movements:
• •
Step movement: the melody moves from one note to an adjacent note by a 2nd Leap movement: the distance between two consecutive notes is larger than a 2nd.
In general, step movements are preferred over leap movements; when the melody contains leaps, some intervals will be favoured, other intervals will be tolerated, and a few intervals will in principle be forbidden.
Recommended Movements All the movements implying intervals that are easy to sing are favoured; those intervals can be minor, major or perfect, but will typically be small or moderate (from the minor 2nd to the minor 6th). As an exception the octave is also accepted; despite being clearly very large, it is very easy to sing.
Forbidden Movements All movements implying large intervals (from major 6th upwards) or dissonant intervals (augmented 2nd, augmented 4th, major and minor 7th) must be avoided. Large intervals such as a 7th or a 9th should be broken down in two (or more) smaller intervals; if only one intermediate note is used, it is recommended that one of the two resulting intervals be a 2nd. For example, in C major, the ascending interval (C – B) should be broken down into (C – A –
15
B) (or possibly (C – D – B) although the first solution would probably be preferred by most listeners).
Tolerated Movements Chromatic movements (i.e. movements consisting of half tones) are accepted. The diminished 5th interval is in principle forbidden (see above) but it is tolerated if it resolves by a step movement onto a note belonging to that interval. •
For example, suppose the movement goes from B to F (aug 5th) in C major; as such, this movement is not acceptable. To make it tolerable, you need to “resolve” the dissonance onto an E (i.e. from the F you need to proceed to a note belonging to the interval F – B and located a step away).
•
Similarly, let us consider the (descending) movement F – B; this time you need to resolve the dim 5th on a C (a note located a step away from B and that is part of the interval).
The same tolerance and the same rule apply to the dim 4th (which you won’t find in the major scale but can occur in the harmonic and melodic minor modes), and also to the minor 7th (which is found in the harmonic minor mode); for example, in D harmonic minor (relative of F major), the movement C# - F needs to be resolved onto an E. As indicated above, the major 6th is in principle to be avoided (too large); however, when the movement is from the first degree of the tonality to the sixth degree then the interval is accepted (and only then). Double leaps implying larger intervals than the major 3rd should be avoided, except when the last note is an octave away from the first note. •
For example, in E major, (B – E – B) would be accepted, whereas (B – E – A) would not.
The leading tone (7th degree) should always be followed by the tonic, except when the next chord does not contain the tonic note, or if the leading tone does not belong to a V chord. •
For example, in C major, if B is part of a G chord, its normal resolution would be a C note. However, if B is part of an Em chord, or if the next chord is not a C chord, that B note is free to go anywhere it wants.
Usage It is extremely instructive to analyze existing melodies, and I suggest you do that for as many melodies as you can; you will find that most of them actually stick to the rules quite well. For example, take a look at Satriani’s “Always with me, always with you”, or at all the songs composed by the Beatles. You will find very few exceptions to the “rules” described above.
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Diminished and Augmented Chords When we harmonised the major scale we met a strange chord: the chord build on the 7th degree. It is a minor chord with a diminished 5th, and we have seen that it belongs to the dominant group. This chord is sometimes called semi-diminished. But here we will talk about his even stranger brother, the diminished chord, and his cousin the augmented chord. WARNING 1: if you're a mainstream rocker, don't even think of reading this!!! This is classical and jazz harmony stuff. WARNING 2: the explanations below can cause severe headaches. Please grab some tablets, just in case...
How to build them Easy: simply stack up minor thirds. The general chord formula for a dim chord is: (R, b3, b5, bb7) Note the notation (bb7) meaning yet a halftone lower than a minor 7th; the resulting interval with respect to the root is a diminished 7th. In practice, the note Bbb is of course equal to A. And there is more good news: there are really only three different dim chords, because all the other ones are inversions of those three! First Group: Cdim7 = (C, Eb, Gb, Bbb = A) Ebdim7 = (Eb, Gb, A, C) Gbdim7 = (Gb, A, C, Eb) Adim = (A, C, Eb, Gb) Second Group: Dbdim7 = (Db, E, G, Bb) This one gives birth to Edim7, Gdim7 and Bbdim7, as you can easily verify. Third group: Ddim7 = (D, F, Ab, B) giving birth to Fdim7, Abdim7 and Bdim7. Those dim chords are chromatic to the major scale, but diatonic to the harmonic minor scale. For example, G#dim7 = (G#, B, D, F) doesn't belong to C major, but is the vii in the A harmonic minor scale (which is a relative minor scale of C major, as you will remember).
17
But with these chromatic chords, we can create a whole lot of new functions in the major scale, and they will be written: Idim7 #Idim7 iidim7 #iidim7 iiidim7 IVdim7 #IVdim7 Or biidim7 biiidim7 bVdim7 ... So what’s the difference between a #iidim7 and a biiidim7?
•
A dim chord is written #Idim7, #iidim7, #iiidim7, etc. when it is part of an ascending
•
It is written biiidim7, biidim7, etc. when it's part of a descending cadence.
cadence
If this isn't 100% clear yet, read on, it will become clear in a moment - I hope! Now for the difficult part...
How to use them As approaching chords Any chord can always be approached from above or from below by a dim chord located a halftone away from it. Example: •
C - - - / F - - F#dim7/ G - - -
•
C - - Gbdim7/ F - - -
As passing chords Dim chords let you chromatically link two diatonic chords. The resulting bass movement of a halftone is smoother and harmonically richer than the whole tone movement between the bass notes of the diatonic chords (assuming root position, of course). For example: •
Dm7 - D#dim7 - Em7
•
Em7 Ebdim7 Dm7
Similarly, we could have: IVmaj7 #IVdim7 V7 or V7 bVdim7 IVmaj7 and so on and so forth. But of course, chords don't have to be in root position: they can be inverted. That opens up a can full of worms! For example: •
Dm7 D#dim7 C6/E where the dim chord resolves on the I/3.
18
•
Fmaj7 F#dim7 C6/G where the dim chord resolves on the I/5
•
Or even Em7 Ebdim7 G7/D where the dim chord resolves on a V7 chord.
As dominant chords This is a very frequent usage in jazz. To understand why that works, you have to realise that in a dim chord, there are always two tritones. For example, in Ddim7 = (D, F, Ab, B), the first tritone is (D - Ab) and the second is (F - B). This makes the dim chord very unstable, and capable of resolving in two different ways (can you predict these possible resolutions?). Now, please fasten your seatbelts... Take the following chord: A7(b9) = (A, C#, E, G, Bb) Remove the root from this chord; you obtain (C#, E, G, Bb) which is C#dim7 ( = Edim7 = Gdim7 = Bbdim7). But as a dominant 7th chord, A7(b9) resolves on a D or Dm chord (the fact that it is extended by a b9 doesn’t change its fundamental nature of dominant chord). So, if we had the progression: Cmaj7 - - - / Dm7 - - - / Em7 we could enhance it as follows: Cmaj - - C#dim7 / Dm7 - - D#dim7 / Em7 Where: •
C#dim7 is a subs for A7(b9), itself an extended dominant resolving in Dm7
•
D#dim7 is a subs for B7(b9), itself an extended dominant resolving in Em7 In general, in order to find all the equivalent V7 chords for a given dim chord, you take the dim chord located one halftone below it. Each note of that new chord becomes the root of a V7(b9) chord.
Example: Find all equivalent V7 chords for C#dim7. The dim chord 1/2 step below is Cdim7 = (C, Eb, Gb, A), and the resulting V7 chords are C7(b9), Eb7(b9), Gb7(b9) and A7(b9). Hence:
• • • •
C#dim7/C is equivalent to C7(b9) C#dim7/Eb is equivalent to Eb7(b9) C#dim7/Gb is equivalent to Gb7(b9) C#dim7/A is equivalent to A7(b9)
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You're still there??... Great. Then on to aug chords. They are a lot simpler.
Augmented chords An aug(mented) chord is simply a chord in which the 5th is raised a halftone. For example, Caug (or C+) is (C, E, G#). In other words, their formula is (R + 3 + 3); there is a constant interval between all the constituent notes. Consequently, they allow the same sort of permutations as the dim chords: C+ = E+ = G#+ Aug chords are used primarily as passing chords in a V - I cadence, as follows: V7 - V7+ - I For example: G7 - G7+ - C Let’s analyse this progression: G7 = (G, B, D, F) G7+ = (G, B, D#, F) C = (C, E, G) This makes the progression smoother as D moves to D# before resolving into E. Augmented chords can also be used in other progressions, such as: I - I+ - IV or in minor tonalities: i - iii+ - iii Pardon me? You've run out of headache tablets? No problem, we're done!
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Pentatonic and Blues Scales In this section we will talk about the pentatonic scales (and the so-called blues scales, which are derivatives of the pentatonic scales). These scales are at the heart of the blues and rock music. In the early days they were in fact used almost exclusively by the lead guitarists, and even today many top guitarists continue to build great solos with the pentatonic scales only.
Theory There are several pentatonic scales. In fact, there is an infinity of them! But we will stick to the most important ones.
Pentatonic Major Scales Let's start (again) with the major scale: T
2
3
4
5
6
7
8
If we drop the 4th and 7th degree from this scale, we are left with a new five notes scale, as follows: T
2
3
5
6
This scale is called the pentatonic major scale (it is a "major" scale since its first 3rd is a major third). For example, the C pentatonic major scale is: C
D
E
G
A
But, you may ask, why did we drop those two degrees specifically, and not say E and G? The answer to this question is not trivial. The most important reason is to be found in the very strong tonal function of the fourth and seventh degrees of a scale. Remember our discussion on chord progressions: in C major, the 4th and 7th degrees are F and B, which form the tritone F - B; this interval calls for a resolution to the I chord, and immediately drives the chord progression home. Whenever you hear F and B together, you want to hear a C chord immediately thereafter. However, many forms of ethnic music elsewhere in the world aren't tonal at all: they are modal. The pentatonic scale is the scale of choice for those musical genres: getting rid of the two most important tonal pivots in the scale helps a lot when you don't want to sound tonal (more on modes and modal music later).
Pentatonic Minor Scale Let's now start from the relative natural minor scale, for example A minor (relative of C major): A
B
C
D
E
F
G
(A)
From this scale, we drop the second and sixth degrees (i.e. the same 4th and 7th degrees we dropped from the parent major scale), leaving us with: A
C
D
E
G
Interval-wise (with respect to the tonic) we now have: T
b3
4
5
b7
This is the pentatonic minor scale (it is minor because the first third is a m3). For example, the E pentatonic minor scale is: E
G
A
B
D
(E)
The A pentatonic minor scale and the C pentatonic major scale are relative to each other, exactly as their heptatonic counterparts. Since they contain the same notes, they are completely interchangeable.
Blues Scales If we take the pentatonic minor scale, and add a flatted fifth (b5) as a passing note between the 4th and the 5th, we obtain the following scale: T
b3
4
(b5)
5
b7
This b5 note is called the "blue note" and is responsible for the unique bluesy sound of the scale. The pentatonic minor scale with an additional b5 is therefore often called the "blues scale". Please remember: the blue note is very dissonant and you always use it as a passing note: never dwell on it! In fact, the name "blues scale" is not very appropriate. Let's compare a pentatonic minor scale (with blue note) and the pentatonic major scale with the same tonic; for example in G: Pentatonic minor:
G
Bb
C
Pentatonic major:
G
A
B
(Db)
D
F
D
E
Merging these scales gives the following hybrid scale: G
A
Bb
B
C
(Db)
D
E
F
2
b3
3
4
(b5)
5
6
b7
Interval-wise: T
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This hybrid scale is the "real" blues scale, which is neither minor nor major, since it contains a minor third and a major third! In reality, this is only a western simplification: in the genuine “blues scale” (as originally "imported" from Africa) the "third" is a note somewhere between the minor 3rd and the major 3rd! This note doesn't exist in our scale system, but if we arbitrarily decide to call it "3*", we can write the "real" blues scale as follows: T
2
3*
4
(b5)
5
6
b7
This ambiguous third interval can be simulated by playing the b3 and the 3 often in the same solo, one quickly after the other. But on a guitar, we can also actually play this undetermined third interval by bending up the b3 a little (e.g. 1/4 of a tone)! The minor/major ambiguity is also reflected by the characteristic harmonic structure of a typical twelve bar blues. In G, you would have the following chord progression: G7 - - - / G7 - - - / G7 - - - / G7 - - - / C7 - - - / C7 - - - / G7 - - - / G7 - - - / D7 - - - / C7 - - - / G7 - - - / D7 - - - / This is puzzling, because in terms of classical harmony we seem to have three different tonalities! The chords G7, C7 and D7 indicate the tonalities of C, F and G respectively, since these are the only tonalities having those dominant 7th chords. In fact, in blues the progression (G7 C7 D7) remains fundamentally a I7 IV7 V7 progression in the tonality of G. What happens is: •
the G7 chord (G B D F) reminds us to the fact that the blues scale contains a b7 degree (F)
•
the C7 chord (C E G Bb) reminds us to the fact that the blues scale "also contains" a b3 degree (Bb)
•
the D7 chord (D F# A C) is the real dominant 7th of the tonality, and allows us to "turn around" into G
The fact that the I7 and IV7 chords don't resolve into a I chord is another peculiarity of the blues!
Dominant 7th Pentatonic Scales A final pentatonic scale that turns out to be useful in practice is the dominant 7th pentatonic scale. This scale is defined as follows: T
2
3
5
b7
In fact, it is nothing but the pentatonic major scale where the 6 is replaced by a b7. For example: G
A
B
D
F
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Usage By definition, pentatonic scales only contain five notes. When you run up or down a pentatonic scale, you will therefore play intervals larger than the whole tone. Take the G pentatonic major scale: G
A
B
D
E
The interval between the 3rd and 4th degree of the scale is a third, not a second. This “gap” helps breaking the monotone linearity of the scale, and is one of the big advantages of this type of scales. Another advantage of the pentatonic scale is the fact that its fingering is typically easier and more compact than the corresponding major scale. This not only makes it easier to play, but also allows a more energetic play, very welcome in rock music!
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The CAGED system There are many interesting theoretical patterns and symmetries on a guitar fret board, and they can help us visually keep track of where we are and where we need to go. One of those patterns is called the CAGED system. Here is a fret board with a C chord in its most fundamental position:
That same C chord can also be played as a barre chord at the 3rd fret, as follows:
As you certainly recognize, this is actually the shape of an open A chord played three frets higher. The next possibility is to play the C chord as follows:
This is a G shape barred at the 5th fret. Next, we’ll have an E shape barred at the 8th fret, as follows:
The final shape will be a D chord played at the 12th fret and barred at the 10th fret The sequence C – A – G – E – D is what gives its name to the system.
25
In fact, this sequence and its regular permutations are absolutely general: if you start with a major chord in G shape somewhere up the neck, the next shape will be an E shape three frets higher and the previous shape is an A shape two frets lower. The CAGED system is useful from an improvisation perspective for several reasons. First, it tells where you are on the fret board and it gives you anchors. Here are all the 5 fundamental positions of the C chord; please note the position of the root (C) in each of them:
Next, knowing the location of the root in each shape, you can easily locate the most important notes from an improvisation perspective, i.e. the 3rd, the 5th and the 7th (characteristic notes). This boils down to knowing the position of those notes in the basic chord shapes C, A, G, E and D. Finally, the CAGED system allows you organize your solo around chord shapes, so you can very easily play arpeggios and also extend the harmony. Suppose for example that we are improvising in C major, around the E shape at the 8th fret. Knowing the shape (i.e. the root, 3rd and 5th) not only allows us to securely locate the characteristic notes, but also to very quickly and visually spot all the other extensions. For example, if you want to play a C7 chord, you can easily spot the required note by comparison with an E7 basic form. The CAGED system as such only works for major chords, but there is nothing to stop you from turning the major 3rd into a minor 3rd and voilà! You have a CAGED system for minor chords as well. The CAGED system also makes it visually clear that you can very easily connect the shapes to obtain complete freedom across the neck. There are two basic connecting moves: •
Connecting shapes on the same string
•
Connecting shapes across strings
In order to connect shapes on the same string, you only have to remember that: •
A displacement of one fret up our down corresponds to a half-step
•
A displacement of two frets up our down corresponds to a whole step
Of course, the same half-step and whole step movement can also be performed between strings, as such: Whole step movement:
26
Half step movement:
The diagrams above show the note located a whole tone or half tone higher than the corresponding note on the previous string, fifth fret; this is of course general and true anywhere on the neck. The half-step movement across the strings is clearly not very easy to play, but remember that in most cases you don’t have to actually play that. Those shapes are only there for you to visualize, so you never loose track of where you are. Using the shapes of the C major chord as visual references and applying the fundamental moves as explained above, we can “wipe” the fret board in an infinite number of ways. For example:
You may find that the chord shapes are not very apparent anymore in this continuous scale diagram. This is true, and is a perfect illustration of the duality between chords and scales!
27
Music Theory Advanced Level
June 2005
Defining modes .................................................................................................................................... 4 Theory................................................................................................................................................. 4 Most Important Modes ................................................................................................................ 5 Summary ........................................................................................................................................... 7 Using Modes for Improvisation ......................................................................................................... 9 Theory............................................................................................................................................... 10 A. Recap ....................................................................................................................................... 10 B Choosing appropriate modes ............................................................................................... 11 Using Modes for Composition.......................................................................................................... 16 Usage ................................................................................................................................................ 18 The Dorian Mode................................................................................................................................ 19 The Phrygian Mode ............................................................................................................................ 22 The Lydian and Mixolydian Modes ................................................................................................. 24 Lydian Mode .................................................................................................................................... 24 Mixolydian mode ............................................................................................................................ 25 The Locrian Mode............................................................................................................................... 27 Usage ............................................................................................................................................ 27 Modulation........................................................................................................................................... 29 Modulating into the parent key ................................................................................................... 29 Modulating into an adjacent key................................................................................................. 30 Modulating into remote keys ....................................................................................................... 31 Inter-tonal Exchanges................................................................................................................... 32
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Introduction This document is part of a compilation of a series of threads that deal with music theory and that were originally published by Eowyn on www.mysongbook.com. The compilation has been reorganized into three separate documents: •
Basic Music Theory
•
Intermediate Music Theory
•
Advanced Music Theory – this document
This has been done for two reasons: 1. The size of one single file was too large for download 2. The material covered by the different topics is of varying levels of complexity and targets different audiences. The text of the original threads has been modified and/or extended in several places where it was deemed appropriate for increased readability. The rather crude layout of the original text (due to the limitation of the forum) has also been improved. Finally, the text has been proof-read by Arnold and Blackiel. This is by no means an exhaustive treatise about music theory and harmony. Much more modestly, the purpose of this series of topics is to give those willing to better understand what they are doing with their guitar, the ability to get this knowledge into a quick and concise form. The underlying objective is lead work and improvisation in a rock music context (broadly speaking), but most topics are of a more general nature and they can also easily be adapted to other musical genres. There are numerous books and web sites about general music theory and more specialised topics. Interested readers will find a short reference list at the end of the Basic Level document. Copyright Notice The information contained in this document and this document itself can be freely downloaded, used and copied for private educational purposes only. Selling of this document is strictly prohibited in all circumstances.
3
Defining modes Modes... A very controversial topic that seems to confuse the hell out of many people... Opinions vary from "Modes are completely useless - the major and minor scales are all you need" all the way to "The next best thing since sliced bread!" In fact, many people fail to make the distinction between a number of fundamentally different concepts such as "modes", “scales”, "modal music versus tonal music" and others. I'll try my best to be as concise and accurate as possible, and yet remain simple! In this topic, we will simply define modes (even that is often controversial!), leaving their practical usage for later topics.
Theory We define a mode as follows: a musical mode is an ordered series of intervals with respect to a starting note (whose absolute pitch is not specified). In other words, a mode simply defines a series of relative pitches; for example: 1
2
b3
4
5
6
b7
8
What this example mode definition says, is the following: given the (unspecified) starting note (1), the second note is a major second away from it (2), the third note is a minor third away from it (b3), the fourth note is a perfect fourth away from it (4), etc. An equivalent way of defining a mode consists in enumerating the sequence of intervals between the various relative pitches (as opposed to their definition with respect to a starting note); for the example mode above that would be: W
H
W
W
W
H
W
The example above happens to be a seven note mode, and it just so happens that Western music deals primarily with those, but of course you can define an infinite number of modes using an arbitrary number of constituent notes. Many traditional Indian and Chinese modes use 5 notes, for example. A mode is different from a scale! The mode is completely abstract, since it does not impose a starting pitch. If you specify the starting note by its absolute pitch, and apply the definition of the mode, you obtain a scale. The scale can be thought of as the melody of the mode once you indicate the starting note. For example, starting with the note C, the mode above becomes: C
D
Eb
F
G
A
Bb
(C)
4
If you start with A, you get: A
B
C
D
E
F#
G
(A)
The mode is the same, but the scales are clearly different. Modes have been dominant in Western music until the late Middle-Ages. Pope Gregorius is known for his complete and sophisticated theorisation of the musical systems to be used by the church, and still known today as Gregorian Chant or Plain Chant. In that system, the definition of the various modes consisted as much in the specification of the relative pitches (as we did) as in the rigorous definition of the melodic organization and prescribed cadences (that we don’t need to worry about for now). The Gregorian modal system is heavily based on the Pythagorean system, and the names of the various modes come from the ancient Greek names (although Gregorius had them all mixed up!). We still use these names today (see below), but our names are again different from what they used to be in the Middle-Ages.
Most Important Modes In order to be able to theorize about modes, it is convenient to be able to name them. Below is a list of the most important modes and their definitions. Remember: in these definitions, the symbols represent intervals with respect to the starting note, which is always notated “1”. Group I Ionian
1
2
3
4
5
6
7
Dorian
1
2
b3
4
5
6
b7
Phrygian
1
b2
b3
4
5
b6
b7
Lydian
1
2
3
#4
5
6
7
Mixolydian
1
2
3
4
5
6
b7
Aeolian
1
2
b3
4
5
b6
b7
Locrian
1
b2
b3
4
b5
b6
b7
1
2
b3
4
5
b6
7
1
b2
b3
4
b5
6
b7
1
2
3
4
#5
6
7
1
2
b3
#4
5
6
b7
1
b2
3
4
5
b6
b7
Group II Harmonic Minor Altered Locrian Altered Ionian Altered Dorian Altered Phrygian
5
(Major Dominant Phrygian) Altered
1
#2
3
#4
5
6
7
1
b2
b3
b4
b5
b6
bb7
1
2
3
#4
5
6
B7
Lydian Altered Myxolyian
Group III Bartok
These tables may seem like an overwhelming amount to memorise. In fact, it is rather easy. The modes of Group I are the so-called “modes of the major scale”. By now you should realise that there is no such thing as the mode of a scale, but we nevertheless use this expression as a convenient shortcut to remember the definitions of the modes. The Ionian mode is nothing else but the major scale. You obtain the Dorian mode by “starting a major scale from its second degree”. For example: D
E
F
G
A
B
C
D
is D Dorian and is a C major scale started from D (second degree of the C major scale) Similarly, the scale: A
B
C
D
E
F#
G
A
is A Dorian, and is a G major scale “started from the A”. The double quotes are there to show that this is just short hand convention. We will omit them from now on. The modes of Group I are obtained as follows: •
The Ionian mode is the same as the major scale itself
•
The Dorian mode is a major scale started from the second degree
•
The Phrygian mode is a major scale started from the third degree
•
The Lydian mode is a major scale started from the fourth degree
•
The Mixolydian mode is a major scale started from the fifth degree
•
The Aeolian mode is a major scale started from the sixth degree
•
Finally, the Locrian mode is a major scale started from the seventh degree
Looking at the modes defined in Group I, you will notice that three of them are major (Ionian, Lydian, Mixolydian) since their third is major, and four of them are minor (Dorian, Phrygian, Aeolian, Locrian) since their third is minor.
6
The modes of Group II can all be related to the harmonic minor mode, in a way similar to what we did for the modes of Group I. The first mode of Group II is the harmonic minor mode; the Altered Locrian mode is derived from the harmonic minor mode by starting from the second degree. The Altered Ionian mode is a harmonic minor mode started from the third degree, etc. The modes of Group II are obtained as follows: •
The Altered Locrian mode is a harmonic minor scale started from the second degree
•
The Altered Ionian mode is a harmonic minor scale started from the third degree
•
The Altered Dorian mode is a harmonic minor scale started from the fourth degree
•
The Altered Phrygian mode (also known as Major Dominant Phrygian) is a harmonic minor scale started from the fifth degree
•
The Altered Lydian mode is a harmonic minor scale started from the sixth degree
•
The Altered Mixolydian mode is a harmonic minor scale started from the seventh degree
Finally, Group III contains the modes derived from the melodic minor scale; however, there is only one mode that is really worth mentioning: the Bartok mode, which is the fourth mode of the melodic minor scale. This mode is named after the Hungarian composer Belà Bartok, and is one of the most popular modes in the East-European music.
Summary Modes have been used in music long before the Western world started to favour harmony, and settled for the major and minor scales. Most other popular musical systems in the world are still mostly modal. Modes can be defined at will, and don’t have to be based on seven notes; this just happens to be the most useful set in Western music. Although the modes are in fact defined completely independently from each other, it is convenient to related them to the major and minor scales: The Ionian mode is the first mode of the major scale. The Dorian mode is the second mode of the major scale. The Phrygian mode is the third mode of the major scale. The Lydian mode is the fourth mode of the major scale. The Mixolydian mode is the fifth mode of the major scale. The Aeolian mode is the sixth mode of the major scale (and equal to the natural minor mode). The Locrian mode is the seventh mode of the major scale. The Altered Locrian mode is the second mode of the harmonic minor scale. The Altered Ionian mode is the third mode of the harmonic minor scale. The Altered Dorian mode is the fourth mode of the harmonic minor scale. The Altered Phrygian mode is the fifth mode of the harmonic minor scale. The Altered Lydian mode is the sixth mode of the harmonic minor scale. The Altered Mixolydian mode is the seventh mode of the harmonic minor scale.
7
The Bartok mode is the fourth mode of the melodic minor scale.
8
Using Modes for Improvisation In the previous section, we defined all sorts of modes; we will now discuss how they can be used in practice: improvisation (in this topic) and composition (in future topics). Using modes for improvisation requires that you clearly understand the relationship between modes, scales and tonality. One of the dominant features of modal (church) music in the Middle-Ages is the fact that it was purely monodic (a single melody line sung at unison). In the late Middle-Ages, with the birth of counterpoint (several melodic lines sung simultaneously but independently), and at the Renaissance when music became downright polyphonic (several melodic lines simultaneously at rest to form chords), the modes were gradually abandoned and replaced by the tonal system. However, two modes were kept: the Ionian mode (major) and the Aeolian mode (minor). The Aeolian mode itself further evolved (for tonal reasons) to give birth to the harmonic minor scale and later the melodic minor scale. In contrast, most traditional musical systems in the world have kept the modal characteristics, and are still modal, even today. This is notably the case of the East-European music, African music, Indian music, Chinese music, and so forth. As said, the original modal music was monodic: each song consisted of a single melody played or sung at unison. There were no chords. The melody was more or less free to move, but severe rules would impose specific cadences (depending on the mode being used). One of them was that any song should always terminate on the tonal centre, or finalis. Later, music gradually became polyphonic, and that changed the picture completely. By definition, a chord consists of several notes played simultaneously. However, notes have a variable affinity with each other; when played together, some combinations of notes seem to produce a feeling of rest and fulfillment, while others seem to flee each other and require an urgent resolution onto a more relaxing combination. Careful observations of this phenomenon, along with fashion effects and cultural habits have progressively resulted in the theory of harmony, rooted in the so-called tonal system (see Intermediate Theory). In this system the tone center is imposed by the chords and their progressions. The more rich and complex the chords, the more strictly defined the mode will be. This has two dramatically important (and often overlooked) consequences: •
When playing lead on top of a harmonic background, the actual fingering pattern (scale pattern) used by the lead guitarist has typically little or no effect on the mode of the song (since the latter is imposed by the chord progression). Put differently: the mode is decided upon at composition time, not at improvisation time. If the song is in C major, the fact that you start the C major scale on a D does not mean the song now all of a sudden becomes D Dorian
•
When playing harmonised modal music, the rules governing chord progressions will have to be different in order to escape from tonal habits
Over any chord or chord progression you can always use any scale pattern (fingering pattern) that is compatible with it; depending on this chord progression, you may in fact have more or less flexibility in choosing the appropriate scale pattern(s). •
with diatonic four notes chords (and more), you will usually have no choice other than that imposed by the chords
•
with triads, you may have more flexibility
•
with power chords, you will typically be able to pick several compatible scale patterns; in that case the notes you decide to play will have a large impact on the harmonic color of the music
We will now explore these different possibilities in detail.
Theory A. Recap In the previous topic, we have listed several modes and for convenience we have related them to the major and minor scales. Specifying the intervals with respect to the starting note we had: Ionian
1
2
3
4
5
6
7
Dorian
1
2
b3
4
5
6
b7
Phrygian
1
b2
b3
4
5
b6
b7
Lydian
1
2
3
#4
5
6
7
Mixolydian
1
2
3
4
5
6
b7
Aeolian
1
2
b3
4
5
b6
b7
Locrian
1
b2
b3
4
b5
b6
b7
The table above defines each degree of the modes as an interval with respect to the starting note. Comparing each mode with the Ionian mode, you can easily determine what you need to do to obtain any other mode. In order to transform the Ionian mode into the Dorian mode (for example), you need to lower the 3rd and the 7th of the Ionian scale. Raising the 4th would transform it into a Lydian scale. And so on and so forth. For example, let’s find the A Mixolydian scale: •
We start from A major: A B C# D E F# G# (A)
•
We apply the Mixolydian pattern, meaning we lower the 7th; the result is A B C# D E F# G (A)
Of course, you can also work out the Mixolydian mode by remembering that it is a major scale started from the fifth degree; the major scale whose fifth degree is A is D major, i.e. A B C# D E F# G; starting that scale from A gives us A B C# D E F# G as above.
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It is a good idea to memorise this information or keep the chart handy, as we will need it further on.
B Choosing appropriate modes If there is no chord progression (i.e. there is only one chord over a long series of bars) the mode is implied (we will come to that later). If there is a chord progression, there will usually be a tonal centre towards which the progression moves (although this is not always the case). The first and most important thing to do is to identify that tonal centre. This will give you the resolution chord (I chord). Identifying the tonal centre can be difficult, so here are a few strategies to help you along: •
the last chord is usually the resolution chord;
•
the first chord is often (but not always) the resolution chord;
•
identify recognisable cadences (such as ii-V-I or I-IV-I);
•
watch the movements of the roots of the chords - they often imply typical cadences;
•
use your ears!!
1. Four Notes Chords Take the following simple progression: Cmaj7 - - - / F - - - / C - - This looks (and sounds) like a I - IV - I progression in C major (i.e. the tonal centre here is clearly C). Let's write down the constituent notes of these chords as we find them: Cmaj7:
C-E-G-B
F:
F-A-C
Sorting these notes in ascending pitch order gives us: C
?
E
F
G
A
B
(C)
3
4
5
6
7
(8)
or written in intervals 1
?
We still have an "unknown" second degree, which is not directly imposed by the harmony; but looking at the reference chart above, we find that the only mode that accommodates our case is the Ionian mode: C
D
E
F
G
A
B
(C)
1
2
3
4
5
6
7
(8)
You can play any of these notes in any order over any of the chords of the progression: that will have no impact on the mode of the song. (But please remember that the best melodic result will usually be obtained whit characteristic notes on the downbeats – see Intermediate Theory tutorial).
2. Triads The chord progression above contained a maj7 chord; what if it didn't? Say the progression was: C---/F---/C---
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Writing down the notes as they are imposed to us by the chords being used, we find: C:
C-E-G
F:
F-A-C
This results in the following scale: C
?
E
F
G
A
?
(C)
1
?
3
4
5
6
?
(8)
Now we have two "unknowns" (two notes that are not imposed by the harmony) and from the reference chart we see that we can choose to play a B note or a Bb note. Depending on that choice we will end up playing the Ionian mode or the Mixolydian mode. The tonal centre is still strictly defined (C), but the mode is less strictly defined than in the previous case. Since the chords don’t impose the mode, you as the lead are free to pick the one you want. (In fact, you may want to be careful if you play C Mixolydian, because a Bb in a C chord makes it C7, which is the V7 of F, so you could very easily cause a transposition into the F key!) In general, very rich harmonies define modes much more strongly than “lighter” harmonies. In the first example above, we had a Cmaj7 implying a B note; in the second example, we had a plain C; that left some more room.
3. Power Chords If the harmonic background consists of power chords (R + 5th + R), no thirds are played. Consequently, the harmonic content of the song is much less strongly defined, and you, the lead player, have a big responsibility in determining that content and the resulting color. Power chords also usually imply a tonal centre, but it is often suggested more than it is imposed. Let's take a simple example to start with. Suppose we have the following progression: E5 - - - / C5 - - - / D5 - - - / B5 - - - / E5 The question is: which mode(s) are you going to use to improvise? In this case, the progression "sounds" like it resolves into E5. This assumption is supported primarily by the final bass movement B - E which strongly establishes E as the tonal centre (since it suggests a V – I cadence). Therefore, some sort of E scale will do for our solo. But which one exactly? Let's write down the E major scale: E
F#
G#
A
B
C#
D#
(E)
1
2
3
4
5
6
7
(8)
Now let's write down the notes implied by each power chord in the actual progression, and place them at their proper location in the E scale: E5:
E
?
?
?
B
?
?
E
C5:
E
?
G
?
B
C
?
E
D5:
E
?
G
B
C
D
E
B5:
E
F#
G
B
C
D
E
A A
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Compared with the major scale (Ionian mode), we actually have: 1
2
b3
4
5
b6
b7
8
This is the signature of the Aeolian mode. E Aeolian is therefore the theoretically correct scale for this progression. For contrast, here is another example: E5 - - - / A5 - - - / B5 - - - / E5 - - For the same reason as above, the tonal centre is E. Let's work out the scale as above. E5:
E
?
?
?
B
?
?
E
A5:
E
?
?
A
B
?
?
E
B5:
E
F#
?
A
B
?
?
E
?
4
5
?
?
The signature is 1
2
with three undefined intervals. Therefore all the following modes of E major will fit this progression: •
E Ionian:
1234567
•
E Dorian:
1 2 b3 4 5 6 b7 (equivalent to D major)
•
E Mixolydian:
1 2 3 4 5 6 b7 (equivalent to A major)
•
E Aeolian:
1 2 b3 4 5 b6 b7 (equivalent to G major)
So you can use any one of them (or all of them), depending on •
how you "hear" the progression (rather minor or rather major)
•
what the rest of the band is currently playing
•
the overall context of the song
All the examples above assume that there is only one tonal centre. Of course this isn't always the case. Suppose we have the following triad progression: E - - - / C - - - / D - - - / B7 - - - / E Working out the notes as above reveals some conflicts: •
G# in the E chord conflicts with G in the C chord
•
D# in the B7 chord conflicts with D (root of the D chord)
So, what do we do? •
One possibility is to adapt to the changing tonal centers, and develop a chord oriented solo. For example, you could play a C and D arpeggio on the corresponding chords
•
Another possibility could be to treat the first three chords (E, C and D) as an A melodic
•
Or you could use pentatonic scales; for example, it is possible in this case to play E
minor sequence, modulating into E major (more on modulation later on) pentatonic minor throughout (please verify this!)
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4. Vamps A final interesting case is when the band keeps on repeating the same chord for a long period of time (this is called a "vamp"). Depending on the type of that chord, you may have a lot of freedom or no freedom at all in choosing the mode. Power Chord Since all the modes of the major scale accommodate a given power chord (except the Locrian mode which has a b5 and would conflict with the 5 of the power chord), the lead can vary modes and colors at will. This is in fact what Joe Satriani calls his “pich axis” theory. Triad or Seven-Note Chord If the chord is a triad or a seven note chord (or more complex chord), the mode is implied. The lead has little or no freedom at all. To understand why the lead has no options in the second case above, we need to revisit the relationship between chords and scales. Let’s take a C major chord: its constituent notes are (C E G). A Cmaj7 chord would contain (C E G B); a Cmaj7(9) contains (C E G B D), etc. Starting with the latter chord, we can continue to enrich it by adding more thirds; the most complex C chord we can make this way is (C E G B D F A). Map back all these notes within the boundaries of an octave, sort them by ascending pitch order, and you end up with: C
D
E
F
G
A
B
In other words, the C major chord is a shortcut of the C major scale, or Ionian mode; the richer the chord becomes, the better it approximates the corresponding scale/mode. Similarly, starting with a Dm chord and stacking up thirds you obtain (D F A C E G B), or D
E
F
G
A
B
C
D
This is a D Dorian scale. If you do this for all the degrees of the major scale, you will find out that: •
The Ionian mode corresponds to the I chord
•
The Dorian mode corresponds to the ii chord
•
The Phrygian mode corresponds to the iii chord
•
The Lydian mode corresponds to the IV chord
•
The Mixolydian mode corresponds to the V chord
•
The Aeolian mode corresponds to the vi chord
•
The Locrian mode corresponds to the vii chord
In other words, whenever a vamp is played with a triad or more complex chord, the mode is implied by the chord. Once again, if the chord is part of a tonal sequence, the mode is implied by
14
the chord progression, not by the fingering pattern you happen to use to play the notes of that tonality. If you remember this, you will avoid most of the confusion around modes and patterns.
15
Using Modes for Composition As discussed in the previous topic, the choice of a scale pattern has typically very little impact (if any at all) on the mode of the song. If the song is in G major, it will remain in G major no matter in what order you happen to play the G major scale. The only exception worth mentioning is when the harmony consists of power chords, as we have seen. In other words, the mode of a song is normally determined when you compose the song. So, how do we use modes for composition then?
Theory One of the distinct features of the key-based functional musical system is its so-called "faithfulness to the tonic". The degrees of the scale and the chords build on them are organized to form a hierarchical functional system, collaborating to revolve around and resolve into the tonal centre. Faithfulness to the tonic is a concept that also applies to modal systems that have eventually led to the tonal system. However, since the various modes are characterized by different interval sequences with respect to the tonic, they will feature distinct and unique cadences. In the original modal system of the early Western music, the principal note of the mode was called finalis because any piece based on that mode would always terminate on that node. The intervals of all the other notes with respect to the finalis fully defined the mode; the main cadences available to fall back from these notes onto the finalis would further define the way the mode should be used. This musical system survives today in a large number of ethnic genres. Another distinct feature of modal melodies is that they are usually diatonic to the mode. In other words, they only use intervals from that mode (unlike melodies in the major or minor keys, where chromatic fills and passing notes are frequent). Here are again the modes of the major scale as we defined them earlier: Ionian
1
2
3
4
5
6
7
Dorian
1
2
b3
4
5
6
b7
Phrygian
1
b2
b3
4
5
b6
b7
Lydian
1
2
3
#4
5
6
7
Mixolydian
1
2
3
4
5
6
b7
Aeolian
1
2
b3
4
5
b6
B7
Locrian
1
b2
b3
4
b5
b6
B7
As you can see, they form two groups: - The Ionian, Lydian and Mixolydian modes all have a major third and form the major modes - The Aeolian, Dorian, Phrygian and Locrian modes all have a minor third and form the minor modes. The third is therefore the first differentiator between modes. But in order to further differentiate
the modes within each group, we need a second note called characteristic modal note. The characteristic modal note is extremely important in modal compositions, because it is the note that establishes the unique feel of the mode. Modal melodies and harmonies therefore use it extensively as a way to clearly underline the mode being used. We will take the Ionian mode as reference mode for the major group, and the Aeolian mode (natural minor scale) as the reference for the minor group (this is of course completely arbitrary, but very common). We will then determine the characteristic modal note by comparing each mode with the reference mode of its group. A. Major modes Lydian mode: As you can see, the #4 is what differentiates the Lydian mode from the Ionian mode; the #4 is therefore the characteristic modal note of the Lydian mode. Mixolydian mode: The b7 is what differentiates the Mixolydian mode from the Ionian mode; the b7 is therefore the characteristic modal note of the Mixolydian mode. B. Minor Modes Dorian mode: The major 6th is what differentiates the Dorian mode from the Aeolian mode; the 6 is therefore the characteristic modal note of the Dorian mode. Phrygian mode: The b2 is what differentiates the Phrygian mode from the Aeolian mode; the b2 is therefore the characteristic modal note of the Phrygian mode. Locrian mode: The b5 is what differentiates the Locrian mode from the Aeolian mode; the b5 is therefore the characteristic modal note of the Locrian mode. Here is a summary of the fundamental rules governing modal composition: 1. The I chord (which of course contains the third) is the tonal centre, and is therefore the most important chord (faithfulness to the tonic). It will usually open the song (first chord used), and will always end it (last chord used). In true modal composition this is a strict rule. 2. The characteristic modal note will be used extensively, in the melody AND in the harmony, to help establish the distinctive mood of the mode. This means that the chords
17
containing the characteristic modal note will be favored. 3. Modal melodies are usually diatonic to the mode. 4. All the chord sequences and cadences typical of the corresponding major scale (Ionian mode) must be avoided at all costs, because they convey the feeling of the major scale, and will destroy the modal feel.
Usage A typical modal trick is the drone. A drone (or pedal, or ostinato) is a note that gets repeated over and over during the song. In modal music, this drone is usually the mode tonic. Think of Celtic music (Scottish bagpipes, for example), or the so-called African desert blues. In modal rock tunes, the drone is usually played by the bass. A special case drone is when a particular chord gets repeated over and over again (vamp). We have seen that this chord implies a particular mode, as follows: Chord
Mode
I
Ionian
ii
Dorian
iii
Phrygian
IV
Lydian
V
Mixolydian
vi
Aeolian
vii
Locrian
We will further explore the various modes from a composition perspective in the next topics.
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The Dorian Mode The Dorian mode has been around for a while. We know that the Ancient Greek already used it, and it was one of the most frequent church modes in the early Middle-Ages. The Dorian mode is also extremely frequent in Celtic and African music; it is therefore often used in folk tunes, and of course in rock music, which was strongly influenced by all these genres. Dorian melodies are often played against a drone (which is always the tonic).
Usage A. Harmonisation Compared to the major scale (W W H W W W H), the pattern of the Dorian mode is: W
H
W
W
W
H
W
or, in terms of intervals with respect to the tonic: 1
2
b3
4
5
6
b7
8
Its characteristic modal note is the 6 (in the Aeolian mode we have a b6). If you remember the major scale, we harmonized it by stacking up thirds, and we came up with the following series of four note chords: Imaj7
ii7
iii7
IVmaj7
V7
vi7
vii7(b5)
Let's harmonise the Dorian mode; this gives the following chord system: i7
ii7
bIIImaj7
IV7
v7
vi7(b5)
bVIImaj7
Please note: this notation is in reference to the major scale. For example, bIII means that the chord build on the third degree of the Dorian mode has its root a halftone lower than in the major scale, and is major. We will use this convention consistently during our discussions of the various modes, so it is important to get used to it. Let’s take D Dorian; as you, this is the second mode of C major, so D Dorian will have the exact same chord system as C major, but shifted: C major:
Cmaj7 Dm7
Em7
D Dorian:
Dm7
Fmaj7 G7
Em7
Fmaj7 G7 Am7
Am7
Bm7(b5)
Bm7(b5)
Cmaj7
Bm7
C#m7(b5)
Let us now write the chord system for D major: Dmaj7 Em7
F#m7 Gmaj7 A7
Comparing D Dorian with D major, degree by degree, we have: i7
ii7
bIIImaj7
IV7
v7
vi7(b5)
bVIImaj7
This gives us a way to immediately obtain the harmonisation of the Dorian mode knowing that of the Ionian mode. Example: A major
Amaj7
Bm7
C#m7
Dmaj7
E7
F#m7
G#m7(b5)
A Dorian
Am7
Bm7
Cmaj7
D7
Em7
F#m7(b5)
Gmaj7
Finding the harmonisation of the mode is in fact very easy, since the chords are the same as those for the parent major scale - but "shifted". In the example above, the chords for A Dorian are the same as those for G major (since A Dorian is a G major scale started from the second degree). The harmonisation given here is in four notes chords, but you can easily find the corresponding triad harmonisation. The tonic chord is of course i. The characteristic chords are by definition those containing the characteristic modal note; they are the chords build on the 2nd, 4th and 6th degrees (ii, IV and vi(b5) ). These chords will be used extensively, except the chord build on the 6th degree, which is a vi7(b5) chord. This semidiminished chord is extremely unstable because it contains the tritone. For that reason, it is usually avoided in modal songs. (This will be true in every mode except Locrian). B. Typical cadences The cadences most often found in Dorian are: i - - - / ii7 - - -
(e.g. Cm - - - / Dm7 - - - )
i - - - / IV7 - - -
(e.g. Cm - - - / F7 - - - )
i - - - / bVIImaj7 - - -
(e.g. Cm - - - / Bbmaj7 - - - )
i - - - / ii7 - bVIImaj7 -
(e.g. Cm - - - / Dm7 - Bbmaj7 - )
A cadence that should be avoided (because it sounds "major"): IV / bVII
(e.g. F7 / Bbmaj7)
That sounds like a V / I in Bb major. Homework 1. Drop-tune the low E string of your guitar to D. Now play the D Dorian scale linearly and slowly against a repeating low D note, until you begin to "feel" that Dorian sound. That may take a while... Finally start improvising melodic fragments; play slowly at first, and make sure you keep that constant D bass on all the beats. Hit the 6 and tonic frequently and always terminate on the tonic
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(but I bet you'll do that quite naturally). 2. Listen to the song "Scarborough Fair" from Simon and Garfunkel. It is a typical example of the Dorian sound. In fact, lots of old English folksong ballads are in Dorian. 3. Listen to Malian desert blues. A typical example is the music of Ali Farka Toure, who recorded "Talking Timbuctu" with Ry Cooder. Tune up the low E to G (light gauge strings preferred!), and start jamming in A Dorian as if you'd be playing blues.
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The Phrygian Mode The Phrygian mode is a very colorful mode, with a touch of "Arabic" or Spanish-like flavor. The Phrygian mode is very frequently used as a melodic improvisation device - and has been used as such by many rock guitarists. But it does sound rather exotic, so you're not likely to hear it often in Western European melodies, except in Raï music and of course Spanish flamenco, where it is either used as such, or in the form of the "altered Phrygian" - in which the third degree is raised a halftone (see topic on mode definitions). Unlike other modes, the Phrygian mode is less often played against a drone. This is because the b2, which is a characteristic modal note of this mode, creates an unpleasant friction when played against the tonic.
Usage A. Harmonisation Compared to the major scale (W W H W W W H), the pattern of the Phrygian mode is: H
W
W
W
H
W
W
or, in terms of intervals with respect to the tonic 1
b2
b3
4
5
b6
b7
8
Its characteristic modal note is the b2 (in the natural minor mode we have a regular 2). Harmonising this mode gives the following chord system (please see the section on the Dorian mode for an explanation of the notation): i7
bIImaj7
bIII7
iv7
v7(b5) bVImaj7
bvii7
C Major
Cmaj7
Dm7
Em7
Fmaj7
G7
Am7
Bm7(b5)
C Phrygian
Cm7
Dbmaj7
Eb7
Fm7
Gm7(b5)
Abmaj7
Bbm7
The chords for C Phrygian are in fact the same as those for Ab major, but shifted. The tonic chord is of course i. The characteristic chords are by definition those containing the characteristic modal note; they are the chords build on the 2nd, 5th and 7th degrees. These chords will be used extensively in Phrygian compositions, except the chord build on the 5th degree, which is the unstable semidiminished v7(b5) chord. B. Typical cadences
The cadences most often found in Phrygian are: i - - - / i - - - / bIImaj7 - - - / bIImaj7 - - - / i - - - / i - - - / iv - - - / bIImaj7 - - i7 - - - / bvii7 - - - / i7 - - - / bvii7 - bIImaj7 - / As always, you should avoid the cadences that sound major: bIImaj7 -> bVImaj7
sounds like IVmaj7 -> Imaj7 in major
bvii7 -> bIII7
sounds like ii7 -> V7 in major
In fact, in Phrygian, the bIII7 chord should generally be avoided, because it has a very strong tendency to go towards the major tonic chord, or one of its substitutes. Consider this: bIII7 -> i
sounds a lot like V7 -> iii in major
bIII7 -> iv7
sounds a lot like V7 -> vi7 in major
bIII7 -> bVImaj7
sounds like V7 -> Imaj7 in major
What you can do, is replace the bIII7 chord by a bIII7(sus4). Since the latter is a subdominant chord, it is much more stable.
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The Lydian and Mixolydian Modes In this section we'll look at the two other major modes besides Ionian: the Lydian mode and the Mixolydian mode.
Lydian Mode The Lydian mode has been used extensively in classical music of the 20th century, and also in jazz and fusion. Some musicians have heavily advocated the Lydian mode. Ornette Coleman, for example, considers that #4 to be a much better choice than the 4 as a subdominant, because unlike the perfect 4, it splits the major scale into two exact halves. This reduces its tendency to compete with the tonic as the tonal centre. However, this #4 is a rather dissonant tone, making the Lydian mode relatively difficult to use. As far as I know, it is of limited usage in rock (at least as a composition mode).
Usage A. Harmonisation Compared to the major scale (W W H W W W H), the pattern of the Lydian mode is: W
W
W
H
W
W
H
5
6
7
or, in terms of intervals wrt the tonic 1
2
3
#4
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Its characteristic modal note is of course the #4. The harmonization of this mode produces the following chord system: Imaj7
II7
iii7
#iv7(b5)
Vmaj7 vi7
vii7
Example: C Major
Cmaj7
Dm7
Em7
Fmaj7
G7
Am7
Bm7(b5)
C Lydian
Cmaj7
D7
Em7
F#m7(b5)
Gmaj7
Am7
Bm7
The chords for C Lydian are in fact the same as those for G major, but shifted. The tonic chord is of course I. The characteristic chords are by definition those containing the characteristic modal note; they are the chords build on the 2nd, 4th and 7th degrees. These chords will be used extensively, except the chord build on the 4th degree, which is the unstable semi-diminished v7(b5) chord.
B. Typical cadences The cadences most often found in Lydian are: Imaj7 - - - / - - - - / vii7 - - - / - - - Imaj7 - - - / - - - - / iii7 - - - / vii7 - - Imaj7 - - - / iii7 - vi7 - / Imaj7 - - - / vii7 - - I - - - / II - - - /I - - Avoid: Vmaj7 -> Imaj7
sounds like a Imaj7 -> IVmaj7 in major
II7 -> Vmaj7
sounds like a V7 -> I in major
In the latter case, use the triad II instead of the II7 - the triad is more stable than the four-note chord because it doesn't contain any tritone.
Mixolydian mode Unlike the Lydian mode, the Mixolydian mode is used extensively in pop, rock and folk music, but also in Celtic and African music. In fact, it is THE alternative to the Ionian mode. It is essentially a plain old major scale, but the b7 gives it a bluesy feel.
Usage A. Harmonisation Compared to the major scale (W W H W W W H), the pattern of the Mixolydian mode is: W
W
H
W
W
H
W
or, in terms of intervals with respect to the tonic 1
2
3
4
5
6
b7
8
Its characteristic modal note is of course the b7. The harmonisation of this mode produces the following chord system: I7
ii7
iii7(b5)
IVmaj7
v7
vi7
bVIImaj7
Example:
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C Major
Cmaj7
Dm7
Em7
Fmaj7
G7
Am7
Bm7(b5)
C Mixolydian
C7
Dm7
Em7(b5)
Fmaj7
Gm7
Am7
Bbmaj7
The chords for C Mixolydian are in fact the same as those for F major, but shifted. The tonic chord is of course I. The characteristic chords are by definition those containing the characteristic modal note; they are the chords build on the 3rd, 5th and 7th degrees. These chords will be used extensively, except the chord build on the 3rd degree, which is the unstable semi-diminished m7(b5) chord. B. Typical cadences The cadences most often found in Mixolydian are: I - - - / v7 - - - / I - - - / bVIImaj7 - - I - - - / vi7 - v7 - / I - - - / ii7 - bVIImaj7 I7 - - - / bVII - - Be careful with I7! It easily slips away into a major tonality!
Homework As said, you'll find that the Mixolydian mode is used very often. Listen to "Norwegian Wood" for a good example.
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The Locrian Mode The Locrian mode is by far the darkest and strangest mode of all! It is completely absent from the classical repertoire, and playing it in the Middle-Ages would have resulted in your being convicted to death and publicly burned at the stake! Consider this: •
In the Locrian mode the tritone is placed between the tonic and the dominant!
•
The tonic chord is an unstable m7/b5 chord!
No wonder it has always been considered an absolute no-no… Recently however, a number of extreme metal bands have started to use it extensively (and more or less successfully).
Usage A. Harmonisation Compared to the major scale (W W H W W W H), the pattern of the Lydian mode is: H
W
W
H
W
W
W
b5
b6
b7
or, in terms of intervals wrt the tonic 1
b2
b3
4
8
The characteristic modal note is of course the b5. The harmonisation of this mode produces the following chord system: i7(b5) bIImaj7
biii7
iv7
bVmaj7
bVI7
bvii7
Example: C Major
Cmaj7
Dm7
Em7
Fmaj7
G7
Am7
Bb7(b5)
C Locrian
Cm7(b5)
Dbmaj7
Ebm7
Fm7
Gbmaj7
Ab7
Bbm7
The chords for C Locrian are in fact the same as those for Db major, but shifted. The tonic chord is of course i7(b5). The characteristic chords are by definition those containing the characteristic modal note; they are the chords build on the 1st, 3rd and 5th degrees. All these chords will be used extensively. B. Typical cadences The cadences most often found in Locrian are:
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im7(b5) - - - / bV5 - - im7(b5) - - - / biii7 - - i(b5)5 - - - / bii5 - - - / bV5 - - -
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Modulation So far we have always assumed that a given piece of music remains in a given key (tonality). In practice this is rarely the case, except for the simplest songs. In fact most songs change tonality one or more times during execution. This is typically done to change the atmosphere of the song, or to wake up the listener’s interest. As a lead guitarist, you need to be aware of this: •
If the background modulates into another tonality, some notes will be altered and you need to play them as such
•
If you modulate during your improvisation, you need to clearly indicate that to the background (especially the bass) for the harmony to keep on doing sensible things
For all these reasons, it is important to study the theory of modulation although, as usually, the rules may seem exaggeratedly dogmatic and will frequently be broken in contemporary music. One thing to be aware of is that it is not necessarily easy to establish a particular tonal centre, but once established it is equally difficult to leave it. In order to establish a key, you need to use all the harmonic devices that we studied in the Intermediate volume, particularly cadences. If you want to leave that key, and establish another tone center, you will have to give your listener ears the time to adjust; therefore you will need at least three or four bars for the modulation to take over. Another thing to be aware of is that the ear is used to a particular tonal center, and will usually be unpleasantly surprised by an abrupt change. Therefore, many modulations will need to be prepared. Modulation can be more or less difficult, depending on how far apart the two keys are in the circle of fifths: •
The only difference between C major and G major is that in G major the note F is sharp (F#); therefore, C major and G major share a lot of chords, and switching from one to the other should not be too difficult
•
Similarly, the only difference between C major and F major is that in F major the note B is
•
The only difference between G major and D major is that in D major the note C is sharp
flat (Bb). These two keys are again very close to each other (C#); this makes G major and D major neighbors, but modulating from C major into D major will be slightly more complicated because the two keys are wider apart.
Modulating into the parent key This type of modulation involves a key and one of its relative minor keys. For example, modulating from C major into A natural minor, or from G major into E harmonic minor.
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Modulating into the relative natural minor key is straightforward, since the notes of the two tonalities are exactly the same. Simply make the modulation apparent by insisting on the new tonic; this role is usually devoted to the bass. Modulating into the relative harmonic or melodic minor key is slightly more difficult, because you need to manage at least one alteration. For example, in A harmonic minor, the G note is sharp and will clash with the natural G note of C major: C major:
C
D
E
F
G
A
B
(C)
A harm minor: A
B
C
D
E
F
G#
(A)
From a chord progression perspective, the new tonality is often introduced by its V of V7 chord followed by the new I chord. For example, in order to modulate from C major into A harmonic minor you would play an E7 chord followed by an Am chord (V – I cadence). From an improvisation perspective, the modulation is often made apparent with an ascending half tone approach resolving into the new tonic. For example, the lead phrase G – G# - A would indicate a modulation from C major into A harmonic (or melodic) minor. Modulating into the relative melodic minor key is similar to the harmonic minor case, except that there is an additional sharp: A mel minor:
A
B
C
D
E
F#
F#
(A)
Always read the score before playing, and try to spot these types of modulations: they will usually be indicated by the presence of “foreign” chords with respect to the original tonality.
Modulating into an adjacent key This type of modulation concerns two adjacent keys in the circle of fifths; for example C major and G major, or A major and E major, or F major and Bb major, etc. As indicated above, this type of modulation is relatively easy because the two tonalities have much in common. Let’s consider the triad harmonization of C major and G major: C major
:
C
Dm
Em
F
G
Am
Bm(b5)
G major
:
G
Am
Bm
C
D
Em
F#m(b5)
These two keys have the following chords in common: C, Em, G, Am Each one of these can therefore be used as pivot between the two tonalities. But there is a better way… You may recall from the section on tonality in the Intermediate volume, that the fourth and seventh degrees of a tonality play an extremely important role. We have seen that the seventh
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degree (called leading tone) and the fourth degree (called sub-dominant) are separated by a tritone, and that the presence of this very unstable interval in a chord (the V7 chord) mandates a resolution onto the tonic chord. The idea, then, is to use this V – I cadence to establish the new tonality. Suppose are in C major; altering the 4th degree (F) makes it a F#, and puts us in the G major tonality, where it becomes the 7th degree. Similarly, altering the leading tone (B) makes it a Bb and puts us in F major, where it becomes the 4th degree! a) So, in order to modulate from C major into G major, we only need to transform the F note into a F# note; we can do that by playing D or D7 chord. If we then immediately play a G chord, we have an unambiguous cadence that establishes G major as the new tonality. In order to make the transition smoother, we can prepare the D or D7 chord by preceding it with a Dm chord, as in the following progression: C - - - / G - - - / C - - - / Dm – D - / G - - The first G chord followed by a C chord says: “We are in C major”. But the D chord followed by a G chord says we are in G major now. Modulating back from G major into C major would also rely on the 4th degree: in G major, we will play a F chord, followed by a C chord; ce can then round off the modulation by playing the V – I cadence G – C. b) Modulating from C major into F major follows the same principles, but here we will alter the B note and make it a Bb. One way we can do this is by playing a G chord followed by a Gm chord, followed in turn by a F chord. But this is a rather soft transition. A better approach is to use the V – I cadence; therefore, we will play a C chord, followed by a C7 chord, itself followed by a F chord: C - - - / G - - - / C – C7 - / F - - The same principle applies to all modulations between adjacent tonalities, and also to modulations from a key into a relative minor of an adjacent key (for example, from C major into E harmonic minor - relative of G major, or from C major into D harmonic minor - relative of F major). For example, the following progression modulates from C major into E harmonic minor: C - - - / F - - - / C - - - / B7 - - - / Em - - - / D - - - / B7 - - - / Em - - -
Modulating into remote keys Modulating into a distant key is usually more complicated before there are fewer common notes and fewer chords that can be used as pivots.
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The same general principle discussed above applies in this case: the V or V7 chord of the new tonality can be used to modulate, but this V7 chord might itself need some preparation. Here is an example of a modulation from C major into E major by means of a V – I cadence: C - - - / F - - - / C - - - / B7 - - - / E - - - / A - - - / C#m - - - / B - - This sequence is very similar to the previous example, and this is normal since E harmonic minor (in the previous example) and E major (in this example) share the same tonic and the same dominant chord. How do you handle this from a lead perspective? There are two options: •
You can play a B(7) arpeggio on the B7 chord: in doing so you stick very closely to the
•
You can also smooth out the modulation by applying some mode theory. On the C major
harmony, and you make the modulation immediately apparent part, you obviously play with the C major scale. But on the last C chord of the C major part we can already prepare the modulation and announce the new tonic (E) by stressing the E note (which is the third of the C chord and is therefore an excellent note to play on that chord). So to speak, you play an E Phrygian fingering pattern – but remember that this doesn’t affect the “Ionianality” of the harmony. On the B7 chord, we can again stress the third, which is now D#, in the tonality of E major – in other words, play a D# Locrian fingering pattern. Finally, on the first E chord we finalize the modulation by playing an E Ionian pattern. Essentially, we have prepared and approached the modulation with a chromatic note sequence E – D# - E; if this chromatic sequence is supported by the bass line, the modulation will be very melodic and musical. In practice, modulations in Hard Rock, Fusion and Metal are often unprepared harmonically: the chord progression abruptly switches into the new tonality. However, even in that case the modulation is often “prepared” by other tricks such as a percussion roll, a rest, an acceleration, etc.: all these tricks are meant to make the transition more acceptable. Ultimately, it is up to you to decide what you like best.
Inter-tonal Exchanges We have seen that a modulation consists in changing tonics; this always implies the usage of new chords not belonging to the old tonality. The reverse is not true: the appearance of non-diatonic chords in a progression does not necessarily imply a modulation. We have already talked about this is the Intermediate volume (e.g. extended dominant chords). This principle can be extended and generalised into what is usually called inter-tonal exchanges, which was first advocated by Belà Bartok.
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Let’s consider two widely separated tonalities: C major and Gb major. The diatonic triad harmonization of these tonalities consists of the following chords: I
ii
iii
IV
V
vi
C major:
C
Dm
Em
F
G
Am
vii Bm(b5)
(C)
Gb major:
Gb
Abm
Bbm
Cb
Db
Ebm
Fm(b5)
(Gb)
(Note the profusion of flats in the latter scale, in particular the theoretically correct Cb!) The principle of inter-tonal exchange states that it is ok to use functionally equivalent chords from any tonality into any other tonality. For example, the following progression in C major: C - - - / Dm - - - / F - - - / G - - - / C - - - / Em - - - / Am - - - / Dm - - - / G - - - / C might be rewritten as follows: C - - - / Dm - - - / F - - - / G - - - / C - - - / Bbm - - - / Am - - - / Abm - - - / G - - - / C because Bbm and Abm are functionally equivalent to Em and Dm (they are chords on the same degrees in both scales). As you can see, the bass line is potentially deeply impacted by this, and if you remember the discussion on melodic analysis (Intermediate volume), you will agree that this is quite an interesting change. The only constraint for doing this sort of inter-tonal exchanges is that the new chords may not clash with the melody (in other words, the melody note must remain a characteristic note of the chord, or be a valid extension). Although such inter-tonal exchanges are more frequent in jazz and fusion than in mainstream rock music, there are often an interesting way to harmonise or re-harmonise a theme.
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