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A Foundation for Chords (Part 2)

Here is a table that shows the basic Triads that we can make from all of the Notes within the Major Scales:

Function Root Position First Inversion (6) Second Inversion (64)
I 1-3-5 3-5-1 5-1-3
ii 2-4-6 4-6-2 6-2-4
iii 3-5-7 5-7-3 7-3-5
IV 4-6-1 6-1-4 1-4-6
V 5-7-2 7-2-5 2-5-7
vi 6-1-3 1-3-6 3-6-1
vii° 7-2-4 2-4-7 4-7-2

The Roman numerals represent Chords, and the regular numbers represent the Scale Degrees of the Notes within those Chords. Please do not get the two of them confused! Although they are sometimes used interchangably, Roman numerals and regular numbers usually represent different things. We will attempt to use them as consistently as possible here.

Let's look at the Intervals within each of these Chords:

Major Chords

Root: M3 + m3 = P5
First Inversion: m3 + P4 = m6
Second Inversion: P4 + M3 = M6

minor Chords

Root: m3 + M3 = P5
First Inversion: M3 + P4 = M6
Second Inversion: P4 + m3 = m6

diminished Chords

Root: m3 + m3 = dim5
First Inversion: m3 + Aug4 = M6
Second Inversion: Aug4 + m3 = M6

Notice that the Root Position of all of these Chords is made from a stack of Notes separated by an Interval of a Third. Therefore, these Chords are Tertian. After thoroughly learning the basic Triads, we can use them to generate larger Chords (i.e.: one's with more Notes in them).

More Roman Numerals

The next Tertian Chord is a Seventh Chord. This name comes from the fact that the lowest and highest Notes within the Chord are an Interval of a Seventh away from each other (when that Chord is in Root Position). We can think of each of these Chords as some combination of basic Triad and a Third Interval (with a couple of exceptions). These are the different types of Seventh Chord and how we represent them with Roman numerals:

Name of Chord How To Form It In Root Position Roman Numeral Representation
Major Seventh Chord a Major Triad with the Note a M3 Interval above it uppercase Roman numeral with M7 after it
Dominant Seventh Chord a Major Triad with the Note a m3 Interval above it uppercase Roman numeral with 7 after it
minor Seventh Chord a minor Triad with the Note a m3 Interval above it lowercase Roman numeral with 7 after it
half-diminished Seventh Chord a diminished Triad with the Note a M3 Interval above it lowercase Roman numeral with Ø7 or 7♭5 after it
fully-diminished Seventh Chord a diminished Triad with the Note a m3 Interval above it lowercase Roman numeral with O7 after it
diminished Major Seventh Chord a diminished Triad with the Note a P4 Interval above it lowercase Roman numeral with OM7 after it
minor-Major Seventh Chord a minor Triad with the Note a M3 Interval above it lowercase Roman numeral with M7 after it
Augmented Seventh Chord or Dominant 7♯5 Chord an Augmented Triad with the Note a M2 Interval above it uppercase Roman numeral with +7 or 7♯5 after it
Augmented-Major Seventh Chord an Augmented Triad with the Note a m3 Interval above it uppercase Roman numeral with +M7 or M7♯5 after it

As a shortcut, we can quickly get the top-most Chord Tone of each of these Chords in Root Position by Inverting the Seventh Interval:

Name of Chord Shortcut For Root Position
Major Seventh Chord The lowest and highest Notes of the Chord make a M7 Interval, so go up an Octave from the Root, and then go down by a Half-Step to get the top Note.
Dominant Seventh Chord The lowest and highest Notes of the Chord make a m7 Interval, so go up an Octave from the Root, and then go down by a Whole-Step to get the top Note.
minor Seventh Chord The lowest and highest Notes of the Chord make a m7 Interval, so go up an Octave from the Root, and then go down by a Whole-Step to get the top Note.
half-diminished Seventh Chord The lowest and highest Notes of the Chord make a m7 Interval, so go up an Octave from the Root, and then go down by a Whole-Step to get the top Note.
fully-diminished Seventh Chord The lowest and highest Notes of the Chord make a dim7 Interval, so go up an Octave from the Root, and then go down by a m3 Interval to get the top Note.
diminished Major Seventh Chord The lowest and highest Notes of the Chord make a M7 Interval, so go up an Octave from the Root, and then go down by a Half-Step to get the top Note.
minor-Major Seventh Chord The lowest and highest Notes of the Chord make a M7 Interval, so go up an Octave from the Root, and then go down by a Half-Step to get the top Note.
Augmented Seventh Chord or Dominant 7♯5 Chord The lowest and highest Notes of the Chord make a m7 Interval, so go up an Octave from the Root, and then go down by a Whole-Step to get the top Note.
Augmented-Major Seventh Chord The lowest and highest Notes of the Chord make a M7 Interval, so go up an Octave from the Root, and then go down by a Half-Step to get the top Note.

Like the Triads, the Inversions of entire Seventh Chords have their own notation too. For example:

Root Position First Inversion Second Inversion Third Inversion
V7 V65 V43 V42 or V2

Since there are four Notes within a Seventh Chord, it can be rearranged three times before coming back to Root Position.

Seventh Chords as Major Scale Degrees

Here is a table that shows the basic Seventh Chords that we can make from all of the Notes within the Major Scales:

Function Root Position First Inversion (65) Second Inversion (43) Third Inversion (2)
IM7 1-3-5-7 3-5-7-1 5-7-1-3 7-1-3-5
ii7 2-4-6-1 4-6-1-2 6-1-2-4 1-2-4-6
iii7 3-5-7-2 5-7-2-3 7-2-3-5 2-3-5-7
IVM7 4-6-1-3 6-1-3-4 1-3-4-6 3-4-6-1
V7 5-7-2-4 7-2-4-5 2-4-5-7 4-5-7-2
vi7 6-1-3-5 1-3-5-6 3-5-6-1 5-6-1-3
viiØ7 7-2-4-6 2-4-6-7 4-6-7-2 6-7-2-4

Instead of stacking another Note on top of a Triad, we can also think of the Major Seventh Chords as being made of the 1st, 3rd, 5th, and 7th Scale Degrees of the Major Scales. The Chord Tones made from the 3rd and 7th Scale Degrees are sometimes referred to as "Guide Tones" within this context. While all of the Notes involved in a Chord may contribute to its distinct sound, these two Notes in particular are what distinguish each of the Seventh Chords from one another.

[Generally, some of these Seventh Chords are used more frequently than others, and are associated with particular styles of music. For example, the Dominant Seventh Chords are common in Blues, while the minor Seventh Chords and Major Seventh Chords are common in Jazz.]