Introduction
In our last lesson, we established the fundamental building blocks of harmony, the triads, by stacking major and minor third intervals. We also connected their structure to the simple integer frequency ratios found in the natural harmonic series, explaining why major and minor chords sound so stable. Now, we will extend this principle by adding another layer of complexity and color.
Today's lesson addresses the next step in our study of chord construction: building the five primary types of seventh chords. The learning outcome is for you to be able to construct major 7th, minor 7th, dominant 7th, half-diminished, and fully-diminished 7th chords. We will achieve this by stacking one more third on top of the triads you already know. True to your interest in the "why," we will then investigate the physical properties of these new chords, exploring how concepts like frequency ratios and wave interference give them their unique sonic character and function, which are pivotal in the harmonic language of everything from house to techno.
From Triads to Seventh Chords
A seventh chord is, at its core, a four-note chord. The name comes from the fact that, in its basic or "root" position, the interval between the lowest and highest notes is a seventh. While our previous lesson focused on four types of triads, there are five common types of seventh chords that form the backbone of Western harmony.
The simplest way to conceptualize them is as a combination of a triad and a specific type of seventh interval (major, minor, or diminished) above the root. The following short video provides a concise overview of this concept.
Seventh Chords - Music Theory Crash Course
In "Seventh Chords - Music Theory Crash Course," the Odd Quartet channel gives a quick, high-level summary of how the five main seventh chords are formed.
Watch the video from the beginning to the end. Notice how each seventh chord is defined as a specific triad (major, minor, or diminished) plus a specific seventh interval. This is a great mental framework to start with.
As you saw, the five essential seventh chords are:
- Major Seventh: Major Triad + Major Seventh
- Dominant Seventh: Major Triad + Minor Seventh
- Minor Seventh: Minor Triad + Minor Seventh
- Half-Diminished Seventh: Diminished Triad + Minor Seventh
- Fully-Diminished Seventh: Diminished Triad + Diminished Seventh
The Stacking of Thirds, Continued
Just as triads are stacks of two thirds, seventh chords are stacks of three thirds. This systematic approach is a powerful and reliable method for construction. Each of the five chord types corresponds to a unique sequence of major and minor thirds.
The next video provides a detailed, step-by-step breakdown of how to build these chords using both the scale formula method (e.g., 1-3-5-7) and by analyzing the stack of thirds.
Intervals in 7th Chords - Music Theory
The video "Intervals in 7th Chords" by Gracie Terzian offers an excellent, methodical exploration of each chord type. For each chord, she explains its construction, its internal intervals, and even the half-step counts, which will be familiar from our previous lessons.
Please watch the following segments. For each one, focus on the "stack of thirds" recipe and the underlying triad that forms the chord's foundation. Major Seventh (Maj7): Built on a major triad. Dominant Seventh (7): Also built on a major triad, but with a different seventh. Minor Seventh (m7): Built on a minor triad. Half-Diminished Seventh (m7b5): Built on a diminished triad. Fully-Diminished Seventh (dim7): Also built on a diminished triad, but with a different seventh. You can also watch her demonstrate the sound of each chord from the keyboard playthrough.
Let's consolidate what you've learned into a single table. This is your master reference for constructing these chords. Notice the addition of the "Minor-Major Seventh" chord, which was also covered in the video—a less common but harmonically rich sound used in jazz and film scoring.
| Chord Name | Formula (vs. Major Scale) | Underlying Triad | Added Interval | Stacked Thirds (from root) |
|---|---|---|---|---|
| Major 7th | 1 - 3 - 5 - 7 | Major | Major 7th | M3 + m3 + M3 |
| Dominant 7th | 1 - 3 - 5 - b7 | Major | Minor 7th | M3 + m3 + m3 |
| Minor 7th | 1 - b3 - 5 - b7 | Minor | Minor 7th | m3 + M3 + m3 |
| Half-Diminished 7th | 1 - b3 - b5 - b7 | Diminished | Minor 7th | m3 + m3 + M3 |
| Fully-Diminished 7th | 1 - b3 - b5 - bb7 | Diminished | Diminished 7th | m3 + m3 + m3 |
| Minor-Major 7th | 1 - b3 - 5 - 7 | Minor | Major 7th | m3 + M3 + M4 (or augmented 3rd) |
Note on the Minor-Major 7th: Its stack of thirds is m3 + M3 + M3. The interval from G to B is a major third.
The Physics of Seventh Chords: Dissonance and Beating
Now that you can construct these chords, we can analyze why they have such distinct characteristics. Why does a dominant 7th feel so tense and unstable, while a major 7th sounds relaxed and "open"? The answer lies in the physics of their harmonic content, a topic perfectly suited to your background.
A paper on the spectral analysis of harmonies provides a quantitative look at this. We will examine how these chords behave in different tuning systems.
[PDF] Spectral analysis of different harmonies Implemented by Equal ...
This paper applies a scientific lens to harmony, analyzing chords based on their frequency components and deviations between tuning systems.
Focus on the tables under the heading "Tuning Implementaion". Examine the data for the Dominant seventh, Diminished seventh, and Half diminished seventh chords. Note the different frequency ratios proposed for Just Intonation (JS) and Overtone-based (OV) tunings. For instance, in the dominant seventh chord, the minor seventh is represented by a 16/9 ratio in JS, but by a 14/8 = 7/4 ratio in OV tuning. This 7/4 ratio corresponds to the 7th harmonic, which is significantly flatter than the equal-tempered version and gives the chord a very different, "bluer" color.
The most striking feature of the dominant 7th chord in equal temperament is its inherent tension. This isn't just a subjective feeling; it's a direct result of wave interference, or beating, between the harmonics of the chord's constituent notes.
Your physics coursework on wave phenomena is directly applicable here. When two sound waves with slightly different frequencies and are played simultaneously, the resulting amplitude fluctuates at a rate equal to their difference, . This is the beat frequency. In the context of a chord, these beats are created by near-coincidences in the overtone series of each note.
The same paper provides a fantastic analysis of this phenomenon.
[PDF] Spectral analysis of different harmonies Implemented by Equal ...
This section dives into the physical reason for the dominant seventh's instability in equal temperament.
Read the section titled "Results". The author explains that for an A dominant 7th chord (A-C#-E-G), the 3rd harmonic of the root A (3 x 110Hz = 330Hz) clashes with the 2nd harmonic of the fifth E (which is tuned to ~164.81Hz in ET, so its 2nd harmonic is ~329.62Hz). This small difference creates a beat frequency of 0.38 Hz, a slow, churning dissonance that contributes significantly to the chord's drive to resolve. This beating is absent in the Just and Overtone tuned versions where the harmonics align perfectly.
This is a profound insight: the primary engine of tension and release in Western functional harmony—the V7 chord's drive to resolve to the I chord—is underpinned by a physical phenomenon of wave interference that you can calculate. This dissonance is not a flaw of equal temperament but a feature that composers have exploited for centuries. In contrast, the major 7th chord's constituent intervals (Major 3rd, Perfect 5th, Major 7th) have more consonant ratios, resulting in less intense beating and a more stable, relaxed sound.
Practical Construction Exercise
To internalize these structures, let's practice building them. Determine the notes for the following seventh chords using the "stack of thirds" method.
| Chord to Construct | Root | Third | Fifth | Seventh | Stacked Thirds Recipe |
|---|---|---|---|---|---|
| A Major 7th | A | ? | ? | ? | M3 + m3 + M3 |
| E Dominant 7th | E | ? | ? | ? | M3 + m3 + m3 |
| C Minor 7th | C | ? | ? | ? | m3 + M3 + m3 |
| B Half-Diminished 7th | B | ? | ? | ? | m3 + m3 + M3 |
Click to reveal the answers
| Chord to Construct | Root | Third | Fifth | Seventh | Stacked Thirds Recipe |
|---|---|---|---|---|---|
| A Major 7th | A | C# | E | G# | A ->(+4)-> C# ->(+3)-> E ->(+4)-> G# |
| E Dominant 7th | E | G# | B | D | E ->(+4)-> G# ->(+3)-> B ->(+3)-> D |
| C Minor 7th | C | Eb | G | Bb | C ->(+3)-> Eb ->(+4)-> G ->(+3)-> Bb |
| B Half-Diminished 7th | B | D | F | A | B ->(+3)-> D ->(+3)-> F ->(+4)-> A |
Conclusion
In this lesson, we have expanded our harmonic vocabulary from three-note triads to four-note seventh chords. By simply extending the principle of stacking thirds, you can now construct the five most important seventh chords that underpin countless musical styles.
More significantly, you've seen how the unique sonic identity of each chord is not arbitrary. It is deeply rooted in the physical interactions of its composite frequencies. The relaxed quality of a major 7th and the tense, driving nature of a dominant 7th can be explained by the degree of dissonance arising from interfering harmonics—a phenomenon quantifiable with the tools of physics.
Key Takeaways:
- Seventh chords are four-note chords built by stacking three third intervals on a root note.
- The five primary types are Major 7th, Dominant 7th, Minor 7th, Half-Diminished 7th, and Fully-Diminished 7th.
- Each type can be defined by its underlying triad and the quality of the seventh interval above the root.
- The characteristic tension of the dominant 7th chord in equal temperament is physically caused by beating between the upper harmonics of its notes.
- These chords are the essential next step in building richer harmonies, adding color, depth, and tension that triads alone cannot provide.
Having progressed from three to four-note chords, the next logical step is to continue this process. In our following lesson, we will explore extended chords, stacking even more thirds to create 9ths, 11ths, and 13ths, which are responsible for the lush, complex harmonies found in jazz, house, and funk.