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Just Enough Music Theory
Road Map for the Week
Monday
Masters of the musical university – the octave, scales, keys
Tuesday
Intervals in music and how to create chords
Wednesday
Choosing chords – Circle of 5ths
Thursday
Chord substitution - chord alternations - chord extensions
Friday
Arranging – composing – where to go from here
GOALS
By the end of the week you should be able to:
 Understand the overtone series and its use
 Spell the chords on the diatonic scale
 Know how to create chord progressions
 Know how to interpret chord symbols
 Use chord extensions to create the sound you want
The Handouts you don’t have!
www.BillTroxler.com
Handouts
Just Enough Music Theory
Reach me at:
[email protected]
A WONDERFUL reference book for this subject is
Edly’s Music Theory for Practical People
http://www.edly.com/ locally or Amazon
Music Begins when something vibrates
air…….a reed…..human lips…..vocal cords…..a string….
an animal skin….metal plate…block of wood
The vibrations are perceived by the brain as sound –
musical tones. We order those tones based upon how fast or
slow the vibrations occur – in cycles per second or Hertz (Hz)
 A musician's job is to manipulate the four major auditory
attributes of musical tones:
pitch - loudness - duration - timbre
Musical tones are psychoacoustic. That’s why music is SO powerful and so memorable
The Range of Musical Tones
Name of Tone
Hertz
C0
16
C1
32
C2
64
C3
128
C4 (middle C)
256
C5
512
C6
1,024
C7
2,048
C8
4,096
C9
8,192
C10
16,384
The table is in “scientific” not “musical” pitch. C4 in musical pitch is 261.63 Hz
Masters of the Musical Universe
The Octave – range of tones
The interval between one musical pitch and another with half or double its
frequency is called the OCTAVE. The octave is sometimes called the “diapson”.
Scales - order or tones
A scale divides the octave into a specific number of tones or pitches –
usually between 5 and 31 pitches. A scale ALWAYS imposes a specific
order to the pitches it contains
Keys - A sense of belonging - population without order
Keys tell you which tones within the octave are used in a piece of music.
The scale we select within a key determines the relationships among the
tones of that key and thereby allows us to construct melody and its supporting
harmony.
Masters of the Musical Universe – the Octave
The term “octave” comes from the Latin word “octavus”
which means “eighth”.
“Octave” describes this doubling of frequency because that
span of frequencies natural divides into eight parts:
Do - Re - Me - Fa - So - La - Ti - Do
These eight divisions of the octave are a phenomenon of nature.
They are the basis for all Western music
The Overtone Series
Look at how guitar strings vibrate
Listen to the Overtones Across Six Octaves
The Overtone Series Used in Music – 2001 –Close Encounters - NBC
Sunrise begins with a sustained low C the double basses, contrabassoon
and organ. Prelude to the brass fanfare of "dawn" motif - in intervals of a
fifth and octave, as C1–G–C2 - also called the Nature-motif
The motif is a part of the first five notes of the natural overtone series:
The major third is immediately changed to a minor third, which is the first note
played in the work (E flat) that is not part of the overtone series
The Music
Close Encounters
Sunrise in Performance
NBC
The Musical Scale
A scale divides the octave into a number of tones - Scales exhibit these characteristics:
Order
Scales arrange their pitches in a specific order
Number
In theory there is no limit to the number of pitch divisions that can be applied
to an octave. The number of divisions used in Western music ranges from
five to twelve. Experimental work is being done with as many as 31 divisions.
Indian classical music divides the octave into 22 divisions.
Western music describes the divisions of the octave as “steps”. These steps may
be whole steps or half steps. Look at a piano key board. The black and white keys
are these whole and half steps.
The first tone of a scale is called the “tonic” or “root”. It usually is the name of the key
CENTS
 The cent is a unit of measure used for musical intervals.
 The octave can be divided a chromatic scale of 12 semitones.
 Each of these twelve semitones is further divided into 100 cents.
 One cent is too small to be heard between successive tones.
 Humans can discern about 5 cents and no smaller intervals.
That's about 1/10 of a semitone.
Cents
Cents across the octave
Whole & Half Steps
The pattern of steps in a major scale is:
W W H W W W H
More Scales than a Fish!
Review the handout on the website to see the vast number of possible scales
Melodic players should master these scales …………
Ionian mode scales in the keys of C, D, G, A and E major
In the key of “C” that’s: C D E F G A B
Natural minor Scales in the keys of Eminor, A minor, D minor and G minor
In the key of “A minor” that’s: A B C D E F G
Major Pentatonic in the keys of C, G, D, A, E and F
In the key of “C” that’s: C D E G A
More info here……..
Intervals
Pitches on scales are given two kinds of names.
 letter names [A- B – C – D – E – F - G].
 a number that describes their relationship the tonic pitch
Scale
do
re
Interval Unison Second
name
2nd
me
Third
3rd
fa
so
Perfect Perfect
fourth
fifth
4th
5th
la
Sixth
6th
ti
do
Seventh Octave
7th
Intervals
What about the black keys?????
 The major intervals become minor intervals
 The perfect intervals become diminished intervals
Scale
do
ra
Interval
name
Unison
Minor
Second
2nd
me
mi
Se
le
tie
Minor Diminished Diminished Minor Minor
Third
fourth
fifth
Sixth Seventh
3rd
4th
5th
6th
7th
do
Octave
Making Chords
A chord is a stack of at least three tones played simultaneously.
When chords are built on the diatonic scale used in most
traditional music, three forms are created:
major - minor - diminished
These stacks of three tones are called “triads”.
Additional tones are often added to the basic triads.
These additional tones are called “Chord Extensions”.
The sounds created by chord extensions are the essence of many styles of music
Chord Formulas: The Major Chord
To form a major chord
Begin with the tone that names the chord.
Add a major 3rd above that fundamental tone
Add a perfect 5th above the fundamental tone.
Examples:
The C-major chord is [C or Cmaj ] is spelled C – E – G.
The G-major chord [G or Gmaj ] is spelled G – B - D
The D-major chord [CD or Dmaj ] is spelled D – F# - A
OR….. A major chord is a major 3rd PLUS a minor 3rd
Chord Formulas: The Minor Chord
To form a minor chord
Begin with the tone that names the chord.
Add a minor 3rd above that fundamental tone
Add a perfect 5th above the fundamental tone.
Examples:
The C-minor chord [Cm or Cmin] is spelled C – Eb – G.
The G-minor chord is spelled [Gm or Gmin] G – Bb - D
The D-minor chord is spelled [Dm orDmin] D – F - A
OR…. A minor chord is a minor 3rd PLUS a major 3rd
Chord Formulas: The Diminished Chord
To form a diminished chord
Begin with the tone that names the chord.
Add a minor 3rd above that fundamental tone
Add a diminished 5th above the fundamental tone.
Examples:
The C-diminished chord [Cdim or C°] is spelled C – Eb – Gb.
The G-diminished chord is spelled [Gdim or G°] G – Bb - Db
The D-diminished chord is spelled [Ddim or D°] D – F - Ab
OR…. A diminished chord is a minor 3rd PLUS a minor 3rd
Chord Formulas: The Augmented Chord
To form an augmented chord
Begin with the tone that names the chord.
Add a major 3rd above that fundamental tone
Add an augmented 5th above the fundamental tone.
Examples:
The C-augmented chord [Caug or C+] is spelled C – Eb – Gb.
The G-augmented chord is spelled [Gaug or G+] G – Bb - Db
The D-augmented chord is spelled [Daug or D+] D – F - Ab
OR…. An augmented chord is a major 3rd PLUS a major 3rd
Chord Symbols
Major Chords: Maj M
Gmaj GM
Δ
GΔ
Minor Chords: min
Dmin Dm D-
m -
Diminished Chords: dim
o °
Adim Ao A°
Augmented Chords: aug +
Slash Chords
Sometimes a specific tone is to be played as the lowest tone
In the triad.
To indicate this a slash “/” is used following the chord name.
C/B means play a C chord with “B” as the lowest tone.
A walking bass on guitar is often notated this way:
C
C/B C/A C/G and then off to a new chord
Chord Nomenclature
Music notation often uses the letter names of the chords:
In C major – C Dm Em F G Am Bdim
In conversation, in studio work and in text, chords symbols are used.
The symbols used are Roman numerals representing the interval
of the scale on which the chord is built
In C major - I ii iii IV V vi vii°
Chord Progressions
Chord Progression…… Chord Changes….. Harmonic Motion…..Harmonic Rhythm
The most basic chord progression in a major key is
I – IV - V
Key of C major: C - F - G
Key of G major: G - C - D
The “circle of 5hts” is a tool for determining chord progressions in any key
Circle of 5ths
Circle of 5ths –
Key Signatures
Add one sharp to each
Key as you move
clockwise around
the circle.
Which sharp to add is
determined by the
scale pattern of:
WWHWWWH
The order of sharps to
add is:
F# C# G# D# and so forth
CIRCLE OF 5THS –
KEYS
Anticlockwise the
movement is in 4ths.
Add flats instead of
sharps.
More info here…….
Circle of 5ths – Relative Minors
Circle of 5ths – the chord box
The Circle of 5ths – Chord Progressions
What you need to know is here!
There is much more to say about chord progressions.
Chord extensions and use of intra-modal chords really enliven a
performance. But, those topics are beyond a week long class.
We’ll take just a peek at these two subjects
Suspended and other useful chords
A suspended chord replaces the 3rd with either a 4th or a 2nd.
Dsus4 is spelled” D G A
Often this chord will be played as D7sus4 spelled D G A C
Dsus2 is spelled” D E A
Often this chord will be played as D7sus4 spelled D E A C
The “minor 7th chord is often useful.
An example is Dm7 spelled D F A C
Rearrange the tones of the Dm7 chord in this order – F A C D – and the
chord gets a new name: F6. What to call it depends upon the key
Chord Extensions
Often a fourth tone is added to the triad.
It’s most often the flatted 7th of the scale.
These are called “7th chords “ and written as C7, D7, G7.
Or as numeric notation as V7. We say “ C seven” to identify the chord
On occasion the major 7th of the scale is added.
These chords are called “major 7th chords”.
They are written as Cmaj7, Dmaj7, Gmaj7.
More tones can be added to a chord beyond 7th of the scale.
These are called “chord extensions”.
Chord Extensions – 9th, 11,th,13th
A 9 chord is spelled: 1, 3, 5, b7, 9
A C9 chord is spelled: C E G Bb D
An 11 chord is spelled: 1, 3, 5, b7, 9
A C11 chord is spelled: 1, 3, 5, b7, 9, 11
A C13 chord is spelled: 1, 3, 5, b7, 9, 11, 13
A C13 chord is spelled: 1, 3, 5, b7, 9, 11,13
Chord extensions can sound “muddy”. To fix that some tones
are often left out of the chord. Those chords are call “add chords”
Add Chords
If any tone other than the 7th is included in a chord
the result is called an “add chord”
A Cadd9 chord or C+9 is spelled: C E G D
A Cadd11 chord or C+11 is spelled: C E G F
ANY of the twelve tones of the chromatic scale
may be added to a basic triad
The G7+b5 chord is spelled: G B Db F(natural)
Intra-Modal and Mixed Mode Music
The musical scale does not have to start on DO.
It can start on any tone of the diatonic scale
When a scale begins on a tone other than DO the result is called
“a mode of the diatonic scale”.
The seven modes of the scale are titled:
Ionian, Dorian, Phrygian, Lydian, Mixolydia, Aeolian, and Locrian
Each mode has a unique sound and chord selection
Music can shift modes and mix modes.
One mode can borrow chords from another mode.
Hear and learn about the modes
Ionian Mode
Tone
C
Step
Solfege do
D
whole
E
whole
re
F
half
me
G
whole
fa
Sample 1 of Ionian Mode - Visitors
A
whole
so
B
whole
la
half
ti
Aeolian Mode
Solfege
la
ti
do
re
me
fa
so
A-Aeolian
A
B
C
D
E
F
G
E-Aeolian
E
F#
G
A
B
C
D
B-Aeolian
B
C#
D
E
F#
G
A
Step
whole
half
Sample 1 Aeolian Mode
whole
whole
half
whole
Sample 2 Aeolian Mode
whole
That’s it!!!!
Hope you enjoyed the class and will find a place
in your music for the information!!!
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WWW.BillTroxler.com
[email protected]