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Lesson 39

Harmonizing Major Scales with Triads & Seventh Chords

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Introduction

In our last lesson, we focused on the art of voice leading, mastering how to connect chords smoothly by inverting them and minimizing melodic leaps. This was about the "micro" level of musical construction—the elegant movement of individual notes from one moment to the next.

Now, we will zoom out to the "macro" level. Instead of just connecting pre-selected chords, we will ask a more fundamental question: in a given key, what is the complete family of chords at our disposal? This lesson introduces diatonic harmony, the system that governs which chords naturally belong to a scale. We will systematically build this "palette" of chords for the major scale, and in doing so, we will learn the essential language of Roman numeral analysis. This powerful notation allows us to understand and discuss chord progressions in a way that is independent of any specific key, a level of abstraction that should resonate with your background in physics and mathematics, where general principles are prized over specific examples.

By the end of this lesson, you will be able to harmonize a major scale with both triads and seventh chords and label them correctly with Roman numerals, giving you a foundational map of the tonal landscape.

The Logic of Diatonic Chords

Before we begin, let's briefly recall why the major scale is our starting point. As we touched on in our first module, the major scale is not an arbitrary collection of notes. Its structure can be derived from the fundamental physics of the harmonic series, making it a natural acoustic phenomenon. The intervals that form it are based on simple integer frequency ratios, which our brains perceive as consonant. You can find a rigorous derivation of this in the paper "A Scientific Theory of Music," which we've looked at before.

With the major scale as our framework (a set of seven notes), the process of harmonization is a systematic exploration of the possible chords we can build using only those seven notes. We call these diatonic chords. The process is straightforward: we pick a note from the scale to be our root, and then we stack thirds on top of it, again using only notes available within that same scale.

To label these chords in a universal way, we use Roman numerals. This system is brilliantly simple yet powerful.

How the Roman Numeral System Works - Music Theory

The video "How the Roman Numeral System Works" by Michael New provides an excellent, clear introduction to this concept. It highlights why this system is so useful for understanding and transposing music.

Watch from the beginning to the introduction. This establishes the core idea: a Roman numeral corresponds to the scale degree of the chord's root. Next, watch from this section. This is the crucial part that explains how the case of the numeral (uppercase vs. lowercase) and special symbols are used to denote the chord's quality (major, minor, or diminished). Finally, watch the segment from on the power of abstraction. The presenter explains how Roman numerals allow us to discuss chord progressions in a general way, untied to a specific key. This is the key reason the system is so fundamental to music theory.

Harmonizing the Major Scale with Triads

Let's apply this process to the C major scale: C, D, E, F, G, A, B.

We'll build a triad on each scale degree:

  1. Chord on C (scale degree 1): Stack thirds from C: C-E-G. This is a C Major triad. Since it's a major chord on the first degree, we label it I.
  2. Chord on D (scale degree 2): Stack thirds from D: D-F-A. This is a D minor triad. A minor chord on the second degree is labeled ii.
  3. Chord on E (scale degree 3): Stack thirds from E: E-G-B. This is an E minor triad. We label it iii.
  4. Chord on F (scale degree 4): Stack thirds from F: F-A-C. This is an F Major triad. We label it IV.
  5. Chord on G (scale degree 5): Stack thirds from G: G-B-D. This is a G Major triad. We label it V.
  6. Chord on A (scale degree 6): Stack thirds from A: A-C-E. This is an A minor triad. We label it vi.
  7. Chord on B (scale degree 7): Stack thirds from B: B-D-F. This is a B diminished triad. A diminished chord on the seventh degree is labeled vii°.

The result is a fixed pattern of chord qualities for any major key:
I (Major), ii (minor), iii (minor), IV (Major), V (Major), vi (minor), vii° (diminished)

This universality is a direct consequence of the major scale's unchanging pattern of whole and half steps. The distance between the notes is what determines the quality of the thirds we stack, and thus the quality of the resulting chord.

Roman Numerals – Open Music Theory

The "Open Music Theory" textbook provides a formal summary of these conventions. This will serve as a great reference.

First, read the introductory section up to the table in "Example 1". This recaps the basic mapping of scale degrees to numerals. Now, read the section "Roman Numerals and Quality". Pay close attention to the table summarizing the notation for major, minor, augmented, and diminished triads. The examples in G major and G minor will help solidify your understanding.

The chart below provides a fantastic lookup table for the diatonic triads in all twelve major keys. It's simply the pattern we just derived, transposed for you.

A table showing the diatonic triads for every major key. Notice the consistent pattern of major, minor, and diminished chords across each row (I, ii, iii, IV, V, vi, vii°).

Extending to Seventh Chords

Now, let's add another layer of complexity and color by stacking one more third on top of our triads to create diatonic seventh chords. The process is identical, but the resulting chord qualities are more varied.

Let's continue with the key of C Major:

  1. I Chord: C-E-G + B = C-E-G-B. This is a C Major 7th chord. We label it Imaj7 (or IM7).
  2. ii Chord: D-F-A + C = D-F-A-C. This is a D minor 7th chord. We label it ii7.
  3. iii Chord: E-G-B + D = E-G-B-D. This is an E minor 7th chord. We label it iii7.
  4. IV Chord: F-A-C + E = F-A-C-E. This is an F Major 7th chord. We label it IVmaj7 (or IVM7).
  5. V Chord: G-B-D + F = G-B-D-F. This is a G Dominant 7th chord. This is a crucial one, labeled simply V7. It contains a major triad but a minor seventh.
  6. vi Chord: A-C-E + G = A-C-E-G. This is an A minor 7th chord. We label it vi7.
  7. vii Chord: B-D-F + A = B-D-F-A. This is a B half-diminished 7th chord (a diminished triad with a minor seventh). We label it viiø7.

This process gives us a new universal pattern for diatonic seventh chords in a major key:
Imaj7, ii7, iii7, IVmaj7, V7, vi7, viiø7

Music Theory 1 - Video 15: Roman Numerals for Common Diatonic 7th Chords.

The video "Roman Numerals for Common Diatonic 7th Chords" by David E. Farrell is a concise and academic presentation that walks through this exact process.

Watch the first half of the video, from the beginning to the end of the major key section. The lecturer systematically builds each seventh chord, clearly explaining its quality and Roman numeral label. We will cover the minor key portion in our next lesson.

The image below shows these chords written on a musical staff for the key of C major.

The seven diatonic seventh chords of the C major scale, with their corresponding Roman numerals.

To formalize the notation for these more complex chords, let's return to our text resource.

Roman Numerals – Open Music Theory

This section of "Open Music Theory" details the specific conventions for seventh chords.

Read the section titled "Roman Numerals for Seventh Chords". The table here is key. It clarifies the symbols for major 7th (which often uses an explicit "M" or "maj"), dominant 7th, minor 7th, half-diminished (ø), and fully diminished (o) chords. Note the important convention: a capital Roman numeral with a 7 (e.g., V7) is assumed to be a dominant 7th chord by default.

Conclusion

In this lesson, we have moved from the practical mechanics of voice leading to the theoretical framework of diatonic harmony. By systematically stacking thirds using only the notes of the major scale, we have discovered the consistent "palette" of chords that defines the sound of a major key. Learning to label these chords with Roman numerals gives us a powerful, abstract language to describe harmonic function, regardless of the specific key.

Key Takeaways:

  • Diatonic chords are the set of chords built using only the notes of a given scale.
  • Harmonizing the major scale with triads yields a universal pattern of chord qualities: I, ii, iii, IV, V, vi, vii°.
  • Harmonizing with seventh chords also produces a universal pattern: Imaj7, ii7, iii7, IVmaj7, V7, vi7, viiø7.
  • Roman numerals are a key-independent system for labeling chords, indicating the root's scale degree (the number) and the chord's quality (uppercase for major, lowercase for minor, with additional symbols like ° for diminished and ø for half-diminished).
  • The V7 (dominant 7th) and viiø7 (half-diminished 7th) chords are unique and have special functions in creating harmonic tension, which we will explore soon.

You now have the map of the major key. In our next lesson, we will venture into the more complex and varied territory of the minor key. We will apply the exact same harmonization process to the natural, harmonic, and melodic minor scales, discovering new chord qualities and uncovering why minor key harmony is often richer and more ambiguous.