Microtonal Experiments

A practical workflow for exploring microtonal tuning systems, discovering new sounds, and building your microtonal vocabulary.

Setting Up Your Microtonal Lab

The Basic Experiment Setup

Create a workspace for quick interval comparison:

// Reference note (Note 1)
frequency: module.baseNote.getVariable('frequency')
startTime: new Fraction(0)
duration: new Fraction(3)

// Experiment note (Note 2) - change this ratio to explore
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(1, 19)))  // 19-TET semitone
startTime: module.getNoteById(1).getVariable('startTime')
duration: module.getNoteById(1).getVariable('duration')

Both notes play together, making interval quality immediately audible.

Experiment 1: TET Comparison

Goal

Hear the difference between equal temperament systems on the same interval.

Setup

Create four notes, all playing simultaneously:

// Note 1: Reference (440 Hz)
frequency: module.baseNote.getVariable('frequency')

// Note 2: Pure major third (5/4)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(5, 4))

// Note 3: 12-TET major third (4 semitones)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(4, 12)))

// Note 4: 19-TET major third (6 steps)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(6, 19)))

// Note 5: 31-TET major third (10 steps)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(10, 31)))

What to Listen For

• Pure 5/4: Completely smooth, no beating
• 12-TET: Subtle but audible beating (~14 cents sharp)
• 19-TET: Different character, closer to pure
• 31-TET: Very close to pure, almost beatless

Record Your Observations

Note which approximation you prefer for different contexts.

Experiment 2: Neutral Intervals

Goal

Explore intervals that fall between major and minor.

Background

The "neutral third" lies between major (5/4 ≈ 386 cents) and minor (6/5 ≈ 316 cents), around 350 cents.

Setup

// Reference
frequency: module.baseNote.getVariable('frequency')

// Minor third (6/5)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(6, 5))

// Neutral third (11/9 ≈ 347 cents)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(11, 9))

// Major third (5/4)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(5, 4))

Try These Neutral Intervals

Interval	Ratio	Cents	Character
Neutral 2nd	12/11	151	Between major/minor 2nd
Neutral 3rd	11/9	347	Neither major nor minor
Neutral 6th	18/11	853	Between major/minor 6th
Neutral 7th	11/6	1049	Between major/minor 7th

Experiment 3: Septimal Intervals

Goal

Explore intervals based on the 7th harmonic.

Background

The 7th harmonic creates "bluesy" or "barbershop" quality intervals not found in standard Western music.

Setup

// Reference
frequency: module.baseNote.getVariable('frequency')

// Septimal minor third (7/6 ≈ 267 cents)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(7, 6))

// Septimal tritone (7/5 ≈ 583 cents)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(7, 5))

// Harmonic seventh (7/4 ≈ 969 cents)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(7, 4))

The Barbershop Seventh

The 7/4 "harmonic seventh" is distinctly different from the 12-TET minor seventh:

// Compare:
// 7/4 = 969 cents (pure, locked)
// 12-TET m7 = 1000 cents (31 cents sharper)

Experiment 4: Bohlen-Pierce Scale

Goal

Experience a completely non-octave-based tuning system.

Background

Bohlen-Pierce divides the tritave (3:1) into 13 equal parts, creating entirely new interval relationships.

Setup: BP Scale

// Note 1: Root
frequency: module.baseNote.getVariable('frequency')
startTime: new Fraction(0)
duration: new Fraction(1)

// Each subsequent note: one BP step higher
// BP step = 3^(1/13)

// Note 2: 1 BP step
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(3).pow(new Fraction(1, 13)))

// Note 3: 2 BP steps
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(3).pow(new Fraction(2, 13)))

// Continue through 13 steps to reach the tritave (3/1)

BP Consonances

BP emphasizes odd harmonics (3, 5, 7, 9...) instead of even ones:

// BP "major third" approximation (4 steps ≈ 435 cents)
.mul(new Fraction(3).pow(new Fraction(4, 13)))

// BP "tritave fifth" (6 steps)
.mul(new Fraction(3).pow(new Fraction(6, 13)))

// BP "major sixth" approximation (9 steps)
.mul(new Fraction(3).pow(new Fraction(9, 13)))

Experiment 5: Commas and Microtones

Goal

Hear the tiny intervals that differentiate tuning systems.

The Syntonic Comma

The difference between a Pythagorean major third (81/64) and a pure major third (5/4):

// Syntonic comma = 81/80 ≈ 22 cents

// Reference
frequency: module.baseNote.getVariable('frequency')

// Pythagorean major third
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(81, 64))

// Pure major third
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(5, 4))

// Play both together to hear the comma

Other Famous Commas

// Pythagorean comma (531441/524288 ≈ 23 cents)
// The gap after 12 pure fifths

// Diesis (128/125 ≈ 41 cents)
// Three pure major thirds vs one octave

// Septimal comma (64/63 ≈ 27 cents)
// Difference between 7/4 and 16/9

Experiment 6: Quarter Tones

Goal

Systematically explore 24-TET (quarter-tone) music.

Setup

// 24-TET divides the octave into 24 equal parts
// Each step = 2^(1/24) = 50 cents

// Reference
frequency: module.baseNote.getVariable('frequency')

// Quarter tone above (1 step)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(1, 24)))

// Semitone (2 steps, same as 12-TET)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(2, 24)))

// Three-quarter tone (3 steps)
frequency: module.getNoteById(1).getVariable('frequency')
  .mul(new Fraction(2).pow(new Fraction(3, 24)))

Quarter-Tone Melody

Create a melody using steps unavailable in 12-TET:

// Sequence: 0, 1, 3, 5, 7, 8, 10, 12 (in 24-TET steps)
// Creates a scale with quarter-tone inflections

Experiment 7: Custom Scales

Goal

Design your own microtonal scale.

Method 1: Just Intonation Scale

Pick ratios based on harmonic relationships:

// Custom 7-note scale using 7-limit intervals

// 1 (root): 1/1
// 2 (neutral 2nd): 12/11
// 3 (septimal minor 3rd): 7/6
// 4 (perfect 4th): 4/3
// 5 (septimal tritone): 7/5
// 6 (minor 6th): 8/5
// 7 (harmonic 7th): 7/4
// 8 (octave): 2/1

Method 2: Non-Standard TET

Try unusual divisions:

// 17-TET: Creates interesting interval approximations
// 22-TET: Good approximation of Indian shruti
// 41-TET: Excellent approximation of many just intervals

// 17-TET fifth (10 steps)
.mul(new Fraction(2).pow(new Fraction(10, 17)))

Recording Your Experiments

Save Successful Discoveries

When you find an interesting sound:

1. Save the module with a descriptive name
2. Note the ratios or TET steps used
3. Describe the sound quality

Build a Microtonal Catalog

Organize discoveries by:

Microtonal Library
├── TET Systems
│   ├── 17-TET Experiments
│   ├── 19-TET Experiments
│   ├── 22-TET Experiments
│   └── 31-TET Experiments
├── Just Intonation
│   ├── 5-Limit
│   ├── 7-Limit
│   └── 11-Limit
├── Non-Octave
│   ├── Bohlen-Pierce
│   └── Custom Tritave Scales
└── Favorites
    ├── Best Chords
    └── Best Melodies

Tips for Productive Experimentation

1. Use Long Durations

Short notes mask tuning differences. Use durations of 2+ seconds.

2. Try Different Timbres

Some instruments reveal beating better than others. Experiment with:

• Sine wave (pure, shows beating clearly)
• Organ (rich harmonics, emphasizes roughness)

3. Compare A/B

Always have a reference for comparison:

• Pure interval vs tempered
• One TET vs another
• Your custom scale vs familiar scale

4. Trust Your Ears

Theory guides you, but sound quality is subjective. Some "dissonant" intervals work beautifully in context.

5. Take Breaks

Ear fatigue affects perception. Rest between intense listening sessions.

Next Steps

After your experiments:

• Save as Modules - Build your library
• Build Compositions - Apply discoveries musically
• Study the Theory - Understand why intervals work