Music Theory
Basic Level
2
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
3
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.
4
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 C#/Db D 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 5 M6 6 m7 7 8 Distance H W W+H 2W 2W+H 3W 3W+H 4W 4W+H 5W 5W+H 6W Example C-Db C-D C-Eb C-E C-F C-Gb C-G C-Ab C-A C-Bb C-B C-C
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.
5 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.
6 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.
7
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.
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 Formula Equivalent Formula Example
Dominant 7th chord 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
9 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.
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)
11 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
Similarly, the F Major scale is:
F G A Bb C D E (F)
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 E F# G D major 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.
12 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 vi7 vii7(b5)
In A major, we have:
13
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 Harmonisation A Bm C#m D E F#m G#m(b5) D Major Scale D E F G A B C# D Major Harmonisation D Em F#m G A Bm C#m(b5)
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.
14 Another possibility is as follows:
15
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:
16 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# (A)
Interval-wise, we now have:
W H W W H WH H
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.
17 Harmonising with four notes chords gives:
Chord imaj7 ii7(b5) IIImaj7(
#5)
iv7 V7 VImaj7 Vii dim
Formula R,m3,5, 7 R,m3,b5, m7 R,3,5+,7 R,m3,5,m 7 R,3,5,m7 R,3,5,7 R,m3,b5, m7
Example Am(maj7) Bm7(b5) Cmaj7(
#5)
Dm7 E7 Fmaj7 G dim
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)
Compare this scale with the A Major scale:
A B C# D E F# G# (A)
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.
18 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 IV7 vi7(b5) vii(b5)
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:
19
20
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
Music Theory
Intermediate Level
2
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 7
thPentatonic Scales... 23
Usage ... 24
The CAGED system ... 25
3
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.
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
5 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).
6 • 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 aspossible, 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!
7
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:
e f g b / a - - - / g a d - / 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.
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
minor
imaj7 ii7(b5) IIImaj7(#5) iv7 V7 VImaj7 viidim Melodic
minor
imaj7 ii7 IIImaj7(#5) IV7 V7 vi(b5) vii7(b5)
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).
9 • 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.
10 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:
11
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:
12 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.
13 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.
14 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)
15
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 –
16 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.
17
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).
18 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 cadence•
It is written biiidim7, biidim7, etc. when it's part of a descending 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:
19 • 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)20 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
