Tonal Harmony by Stephen Kotska
Chapter three – Introduction to Triads and Seventh Chords
Tonal harmony makes use of tertian (built of thirds) chords. The fundamental sonority is the triad, a three-note chord consisting of a fifth divided into two superimposed thirds. There are four possible ways to combine major and minor thirds to produce a tertian triad.
Chords are built off of a single note, called the root.
A major triad (or major chord) is built with a major third and a perfect fifth from the root.
The first triad of a major scale will always be major, the second and third triads will always be minor, etc.
Use this chart to reference the diatonic triads in each scale:
Every major and minor scale has seven diatonic seventh chords.
Example in C major Scale:
• The first chord is C–E–G–B, a major triad and a major seventh. Therefore, it is a major seventh chord.
• The second chord is D–F–A–C, a minor triad and a minor seventh. Therefore, it is a minor seventh chord.
Let’s see now the fifth chord is A-C-E-G, a minor triad and a minor seventh. Therefore, it is a minor chord with minor seventh.
Finally, the seventh chord is B–D–F–A, a diminished triad and a minor seventh. Therefore, it is a half-diminished seventh chord.
IMPORTANT: The first seventh chord of a major scale will always be a major seventh, the second and third seventh chords will always be minor sevenths, etc.
Inversion of the chords
Like triads, seventh chords can be inverted by moving the lowest note up an octave.
Root position is the same as a triad – the root is the lowest (bass) note.
Let's invert the chord:
First inversion is also the same – the third is the lowest note.
Let's invert the chord again. The Second inversion is also the same – the fifth is the lowest note.
Let's invert the chord again. Now, the seventh is the lowest note of the chord. This is called third inversion.
Use this chart for reference to seventh chord inversion:
Inversion Symbols and Figured Bass
In music analysis, each diatonic triad is identified by a Roman numeral. Upper-case numerals represent major triads, lower-case numerals represent minor triads.
Upper-case numerals with a small plus sign represent augmented triads.
Lower-case numerals with a small circle represent diminished triads.
Use this chart to reference the Roman numerals for each scale, using C major as example:
The Roman numeral system can indicate inversions.
First inversion is represented by a small 6 after the numeral. This is due to the root being a generic sixth above the bass note.
Second inversion is represented with both a small 6 and 4. This is due to the root and third being a generic sixth and fourth above the bass note.
Inversion on the seventh chords
Seventh chords also can be inverted. Here's a chart describing an example in C Major and Minor Scale:
Symbols of inversions in Seventh Chords
• The 7 identifies a root position seventh chord.
• 6 and 5 identify a first inversion seventh.
• 4 and 3 identify a second inversion seventh.
• A lone 2 identifies a third inversion seventh chord.
IMPORTANT: The inversion numbers are in numeric order from 7 to 2.
Sometimes also called "pop symbols", they were developed for use in jazz in order to facilitate the notation process and served to provide sufficient information to allow the performer to improvise within certain bounds.
Chapter Four – Diatonic Chords in Major and Minor Keys
The Minor Scale
While there is only one major scale, three different variations of the minor scale exist.
The first minor scale that will we discuss is natural minor. It is constructed with this formula.
A Natural Minor is: A, B, C, D, E, F, G, A.
Another example, C natural minor:
C natural minor is: C, D, E-flat, F, G, A-flat, B-flat.
To convert any natural minor scale into harmonic minor, raise the seventh note by a half step.
Let's convert C Natural Minor into C Harmonic Minor.
Simply raise the seventh note (B-flat) by a half step, resulting in B.
C harmonic minor is: C, D, E-flat, F, G, A-flat, B.
To convert a natural minor scale into melodic minor, raise both the sixth and seventh notes by a half step.
For example, to convert C Natural Minor into C Melodic Minor, simply raise the A-flat and B-flat a half step to A and B.
C melodic minor is: C, D, E-flat, F, G, A, B.
Usually, melodic minor is used only when ascending.
When descending, composers prefer to use the natural minor scale.
Diatonic Triads in Major
Upper-case numerals represent major triads
Lower-case numerals represent minor triads
Upper-case numerals with a small plus sign represent augmented triads
Lower-case numerals with a small circle represent diminished triads
Example in C Major Scale
Roman numerals to the C natural minor scale
Roman numerals to the C harmonic minor scale
Roman numerals to the C melodic minor scale
Diatonic Seventh Chords in Major and Minor