Tuning Systems: Equal Temperament vs Just Intonation
Here's a simple tool that makes it easy to compare the equal temperament
tuning system (aka 12-TET or 12 equal temperament) with the Just Intonation
tuning system.
Just Intonation is not a fixed system, and there are several
different interpretations. Here, we'll use the
five-limit tuning. Another option would be
Pythagorean tuning.
Read more about these two tuning systems below.
Select a root note and then click on the piano keyboard keys below to hear
notes in equal temperament (12-TET) or in just intonation. You'll see the
frequency in hertz appear at the bottom of the screen.
Notice how in Just Intonation the note frequencies change depending on the
selected root note, while in equal temperament the note frequencies stay
consistent between each octave.
Equal Temperament (12-TET)
- C3
-
C♯
D♭ - D
-
D♯
E♭ - E
- F
-
F♯
G♭ - G
-
G♯
A♭ - A
-
A♯
B♭ - B
- C4
-
C♯
D♭ - D
-
D♯
E♭ - E
- F
-
F♯
G♭ - G
-
G♯
A♭ - A
-
A♯
B♭ - B
Just Intonation
Fundamental:
- C3
-
C♯
D♭ - D
-
D♯
E♭ - E
- F
-
F♯
G♭ - G
-
G♯
A♭ - A
-
A♯
B♭ - B
- C4
-
C♯
D♭ - D
-
D♯
E♭ - E
- F
-
F♯
G♭ - G
-
G♯
A♭ - A
-
A♯
B♭ - B
Just Intonation Ratios
The Just Intonation ratios used for this tool are the following:
| Name | Ratio |
|---|---|
| Unison | 1/1 |
| minor 2nd | 16/15 |
| Major 2nd | 9/8 |
| minor 3rd | 6/5 |
| Major 3rd | 5/4 |
| Perfect 4th | 4/3 |
| Tritone | 45/32 |
| Perfect 5th | 3/2 |
| minor 6th | 8/5 |
| Major 6th | 5/3 |
| minor 7th | 9/5 |
| Major 7th | 15/8 |
| Octave | 2/1 |
Equal Temperament (12-TET) and Just Intonation
Equal temperament is the tuning system used in modern Western music and is the tuning system in use for almost all musical instruments today. It approximates the just intonation tuning system and allows for intervals between the notes that are the same across different keys.
The just intonation tuning system is a method of tuning musical instruments based on simple whole number ratios between the frequencies of musical notes. This system emphasizes the purity and consonance of intervals, minimizing the dissonance that arises from complex frequency ratios.
Equal temperament (aka 12 tone equal temperament) divides each octave into 12 equal steps, making slight modifications to just intonation. Equal temperament allows us to play in any key and transpose music easily. It maintains a consistent sound across different keys, simplifies harmony and chord progressions, and is more practical for fixed-pitch instruments.
