19-TET

19-TET (19-Tone Equal Temperament) divides the octave into 19 equal steps. It offers better approximations of pure thirds than 12-TET while remaining relatively accessible.

Overview

Property	Value
Steps per octave	19
Step ratio	2^(1/19) ≈ 1.03716
Octave ratio	2:1 (exact)

Why 19-TET?

19-TET was explored by Renaissance theorists and has these advantages:

1. Better major thirds: 6 steps = 2^(6/19) ≈ 1.2447 (vs just 5/4 = 1.25)
2. Better minor thirds: 5 steps = 2^(5/19) ≈ 1.2002 (vs just 6/5 = 1.20)
3. Good fifths: 11 steps = 2^(11/19) ≈ 1.4946 (vs just 3/2 = 1.50)
4. More notes: Microtonal possibilities

Expression Syntax

Single Step

// One 19-TET step
new Fraction(2).pow(new Fraction(1, 19))

Multiple Steps

// Major third (6 steps in 19-TET)
new Fraction(2).pow(new Fraction(6, 19))

// Perfect fifth (11 steps in 19-TET)
new Fraction(2).pow(new Fraction(11, 19))

Applying to BaseNote

// Note at 6 steps above BaseNote (major third)
module.baseNote.getVariable('frequency').mul(
  new Fraction(2).pow(new Fraction(6, 19))
)

Intervals in 19-TET

Interval	19-TET Steps	12-TET equivalent	Quality
Minor second	2	~1	Smaller
Major second	3	~2	Similar
Minor third	5	~3	Very good
Major third	6	~4	Very good
Perfect fourth	8	~5	Good
Tritone	9-10	~6	Two options
Perfect fifth	11	~7	Good
Minor sixth	13	~8	Very good
Major sixth	14	~9	Very good
Minor seventh	16	~10	Good
Major seventh	17	~11	Good
Octave	19	12	Perfect

Comparison with Just Intonation

Interval	Just	19-TET	Cents off
Perfect fifth	3/2	2^(11/19)	-7.2
Major third	5/4	2^(6/19)	-7.4
Minor third	6/5	2^(5/19)	+0.1
Major sixth	5/3	2^(14/19)	+7.3

The thirds are significantly better than 12-TET!

Using the TET-19 Module

1. Open the Module Bar
2. Find Melodies category
3. Drag TET-19 onto the workspace

Building a 19-TET Scale

// Each note references the previous
note2.frequency = note1.frequency.mul(
  new Fraction(2).pow(new Fraction(1, 19))
)
note3.frequency = note2.frequency.mul(
  new Fraction(2).pow(new Fraction(1, 19))
)
// ... continue for all 19 notes

Musical Applications

Better Harmony

19-TET's thirds sound closer to pure intervals:

• Major triads have a warmer, more consonant sound
• Minor triads are closer to the natural minor third

Microtonal Exploration

The extra 7 notes per octave enable:

• Finer pitch distinctions
• New melodic possibilities
• Unique scales not available in 12-TET

Split Accidentals

In 19-TET, sharps and flats are distinct:

• C# ≠ Db (they're different pitches!)
• This enables enharmonic distinctions

Challenges

Different Intervals

Musicians familiar with 12-TET need to relearn interval fingerings.

Limited Instruments

Few acoustic instruments are built for 19-TET. RMT Compose is ideal for exploring it.

Notation

Standard notation doesn't represent 19 pitches well. New notation systems exist but aren't standardized.

Tips

1. Start with triads - Hear how much better the thirds sound
2. Use the module - Load TET-19 to hear the scale
3. Compare with 12-TET - Play the same melody in both systems
4. Explore new scales - 19-TET enables scales impossible in 12-TET

Next Steps

• Try 31-TET for even higher resolution
• Explore Bohlen-Pierce for a completely different approach
• Create your own system with Custom TET