Create a Major Triad

In this tutorial, you'll build a major chord (triad) using just intonation ratios.

Objective

Create a three-note major chord where all notes play simultaneously.

Prerequisites

• Completed Build a Major Scale or equivalent experience
• Understanding of ratios for thirds and fifths

The Major Triad

A major triad consists of:

Note	Interval	Ratio	Decimal
Root	Unison	1/1	1.000
Third	Major third	5/4	1.250
Fifth	Perfect fifth	3/2	1.500

Step 1: Start Fresh

1. Load the "octave" interval module from the Module Bar
2. Or reset to default and clear existing notes

Step 2: Create the Root

1. Click the BaseNote
2. Click "Add Note" > "Add at Same Time"
3. Select the new note
4. Set frequency:

module.baseNote.getVariable('frequency')

5. Set duration to a whole note:

new Fraction(60).div(module.findTempo(module.baseNote)).mul(new Fraction(4))

6. Click Save

Step 3: Create the Third

1. With the root selected, click "Add Note" > "Add at Same Time"
2. Select the new note
3. Set frequency (major third = 5/4):

module.baseNote.getVariable('frequency').mul(new Fraction(5, 4))

4. Keep the same duration and start time
5. Click Save

Step 4: Create the Fifth

1. Select the root note again
2. Click "Add Note" > "Add at Same Time"
3. Select the new note
4. Set frequency (perfect fifth = 3/2):

module.baseNote.getVariable('frequency').mul(new Fraction(3, 2))

5. Click Save

Verification

1. Click Play
2. You should hear all three notes at once - a major chord!
3. The chord should sound bright and happy

Visual Check

In the workspace, all three notes should:

• Start at the same time (aligned vertically)
• Have different vertical positions (different frequencies)
• Be stacked: Root → Third → Fifth (bottom to top)

Understanding the Sound

The major triad sounds consonant because:

• 5/4 and 3/2 are simple ratios
• They align with the natural harmonic series
• The frequencies have many common overtones

Compare with 12-TET:

• TET major third = 2^(4/12) ≈ 1.26 (slightly sharp)
• Just major third = 5/4 = 1.25 (pure)

Exercises

Exercise 1: Minor Triad

Change the third from major (5/4) to minor (6/5):

module.baseNote.getVariable('frequency').mul(new Fraction(6, 5))

The chord now sounds sad/dark!

Exercise 2: Add the Octave

1. Add a fourth note at the same time
2. Set frequency to 2/1:

module.baseNote.getVariable('frequency').mul(new Fraction(2))

This creates a fuller sound.

Exercise 3: Chord Inversion

Create a first inversion (third in the bass):

Note	Expression
Third (bass)	baseNote × 5/4
Fifth	baseNote × 3/2
Root (high)	baseNote × 2

Exercise 4: Chord Progression

Create a second chord that plays after the first:

1. Create a new root at startTime = firstChord.startTime + firstChord.duration
2. Build a chord on that root
3. You now have a two-chord progression!

Save Your Module

1. Menu > Save Module
2. Name it major-triad-just.json

Chord Reference

Other common chords in just intonation:

Chord	Ratios
Major	1/1, 5/4, 3/2
Minor	1/1, 6/5, 3/2
Diminished	1/1, 6/5, 36/25
Augmented	1/1, 5/4, 25/16
Major 7th	1/1, 5/4, 3/2, 15/8
Dominant 7th	1/1, 5/4, 3/2, 7/4
Minor 7th	1/1, 6/5, 3/2, 9/5

What You Learned

• Creating simultaneous notes using "Add at Same Time"
• The ratios that make a major chord
• How to verify chord structure visually and aurally
• The difference between major and minor thirds

Next Steps

• Add Rhythm - Create rhythmic patterns
• Note Dependencies - Link chords together
• Explore the Chords category in the Module Bar