Building Triads From Any Root

Welcome to the third lesson in our music theory module. In our previous session, we established a systematic way to construct major and minor scales—the palettes of notes that define a musical key. We saw that any scale can be generated algorithmically from a starting note (the tonic) and a specific sequence of intervals.

Today, we take the next logical step: combining notes from these scales to build harmony. We will focus on the most fundamental building block of harmony in Western music: the triad. The goal of this lesson is for you to be able to construct the three most common types of triads—major, minor, and diminished—starting from any root note. Mastering this is essential, as these triads form the basis of the chord progressions that drive the energy in progressive house music.

From Scales to Chords: Stacking Thirds

A chord is simply a group of three or more notes played simultaneously. A triad, as the name implies, is a specific type of three-note chord. In the last lesson, we built scales by moving from one note to the next (e.g., C, then D, then E...). To build a basic chord, we instead skip notes, stacking them in intervals of a third.

Think of the C major scale: C - D - E - F - G - A - B.
If we take the 1st note (C), skip the 2nd (D), take the 3rd (E), skip the 4th (F), and take the 5th (G), we get the notes C, E, G. This is a C major triad. The three notes are called the Root (the note the chord is built on), the Third, and the Fifth.

The following video provides an excellent introduction to this concept and the different types of triads, or "qualities," that exist.

A More Precise Formula: Intervals and Semitones

While deriving triads from a scale is intuitive, a more rigorous and universally applicable method is to define them by their internal interval structure. This allows you to build any triad from any root note, even without first thinking of its corresponding scale.

From our first lesson, we know a semitone is the smallest interval, the distance from one key to the very next on a piano. We can define every triad using semitone counts from the root note. There are two key intervals we need to build triads:

• Minor Third (m3): An interval of 3 semitones.
• Major Third (M3): An interval of 4 semitones.

A triad is simply a stack of two of these "third" intervals. The combination of major and minor thirds determines the chord's quality—its characteristic sound or mood.

Here are the formulas for the three triad types we're focusing on:

1. Major Triad (Bright, Stable):

   • Structure: Root + Major Third + Minor Third
   • Semitone Formula: Root, R+4, R+7
   • Example (C Major): C, C+4st (E), E+3st (G)

2. Minor Triad (Dark, Pensive):

   • Structure: Root + Minor Third + Major Third
   • Semitone Formula: Root, R+3, R+7
   • Example (C Minor): C, C+3st (E♭), E♭+4st (G)

3. Diminished Triad (Tense, Unstable):

   • Structure: Root + Minor Third + Minor Third
   • Semitone Formula: Root, R+3, R+6
   • Example (C Diminished): C, C+3st (E♭), E♭+3st (G♭)

Notice that for major and minor triads, the fifth is "perfect"—it's 7 semitones above the root. The only difference between them is the third (4 semitones vs. 3 semitones). The diminished triad has both a minor third and a "diminished fifth" (6 semitones).

The next segment of the video explains these interval combinations clearly.

An Algorithm for Building Triads

The process shown in the video—starting with a major triad and then modifying it—is an excellent practical algorithm for building any triad you need.

Let's formalize it:

1. Start with the Root Note. Let's use D.
2. Build the Major Triad. You can do this in two ways:
   • Scale Method: Think of the D Major scale (D, E, F♯, G, A, B, C♯). Take the 1st, 3rd, and 5th notes: D, F♯, A.
   • Interval Method: Apply the formula R+4, R+7. Starting from D: D+4st is F♯, D+7st is A. Result: D, F♯, A.
3. Modify to Create Other Qualities:
   • To get D Minor: Lower the third of the major triad by one semitone. F♯ becomes F. Result: D, F, A.
   • To get D Diminished: Lower the fifth of the minor triad by one semitone. A becomes A♭. Result: D, F, A♭.

This method is systematic and removes guesswork, especially when dealing with keys that have many sharps or flats. Let's see it in action one more time.

(Note: The video also mentions the "augmented" triad (R, R+4, R+8), which has a tense, sci-fi feel. While less common than the other three in progressive house, it's good to know it exists. It's created by raising the fifth of a major triad.)

Practical Application: Building and Hearing Triads

It's time to put this theory into practice. Hearing the different emotional qualities of these chords is just as important as knowing how to build them.

1. Open Ableton Live and place a simple instrument like a piano or a basic synth patch on a MIDI track.
2. Create a new, empty MIDI clip and open the piano roll.
3. Using the semitone formulas (R, R+4, R+7, etc.), program the following triads. Play each one and listen carefully to its character.
   • C Major: C3, E3, G3
   • C Minor: C3, E♭3, G3
   • C Diminished: C3, E♭3, G♭3
   • F Major: F3, A3, C4
   • A♭ Major: A♭3, C4, E♭4
   • G Minor: G3, B♭3, D4
   • B Diminished: B3, D4, F4

As you play them, try to associate the sound with the description: Does C Major sound "bright"? Does C Minor sound "pensive"? Can you feel the instability and tension in the C Diminished chord, making you feel like it needs to resolve to another chord? This ear training is a crucial part of internalizing music theory.

Conclusion

In this lesson, we moved from single notes to the world of harmony by learning to construct triads. These three-note chords are the atoms from which complex molecules of chord progressions are built.

Here are the key takeaways:

• A triad is a three-note chord built from a Root, a Third, and a Fifth.
• The quality of a triad is determined by its interval structure, which can be expressed as a simple semitone formula:
  • Major: Root, Root + 4 semitones, Root + 7 semitones
  • Minor: Root, Root + 3 semitones, Root + 7 semitones
  • Diminished: Root, Root + 3 semitones, Root + 6 semitones
• A reliable method for construction is to first build the major triad and then lower the third and/or fifth to create the other qualities.

You now have the tools to build a major, minor, or diminished chord on any of the twelve notes. In our next lesson, we will see how these triads naturally arise when we stay within a single key. We'll learn how to identify the diatonic chords of a scale, which will set the stage for constructing the powerful chord progressions central to the deadmau5 sound.