EXAMPLE 1
Standard tuning
12-TET
100.00 cents / step
The familiar piano grid uses a step ratio of approximately 1.059463.
Temperament calculator
N-TET Temperament Calculator
Explore equal divisions of the octave from 1-TET to 53-TET, hear each step and compare microtonal pitches with the familiar 12-tone grid.
FreeNo loginWorks offlineWeb and desktop
Core formula
step size (cents) = 1,200 / N
step ratio = 2^(1 / N)
frequency at step k = reference × 2^(k / N)
cents at step k = k × 1,200 / N
The final step k = N always reaches exactly one octave above the reference frequency.
How equal temperament divides an octave
N-TET means that the 2:1 octave is divided into N equal logarithmic steps. Each step has the same frequency ratio, while its size in cents is 1,200 divided by N.
Twelve-tone equal temperament is only one possibility. Nineteen divisions offer finer thirds, 24-TET provides quarter tones, and 31-TET closely approximates several just intervals. Amanita maps every step to its nearest 12-TET note and displays the cents difference.
Worked examples
Concrete values you can verify in the calculator and transfer directly to a production session.
EXAMPLE 2
Quarter-tone system
24-TET
50.00 cents / step
Each conventional semitone is divided in half, creating 24 equal pitches per octave.
EXAMPLE 3
Nineteen divisions
19-TET · step 7 · 440 Hz
568.01 Hz
The seventh step is 442.11 cents above the reference and sits between familiar 12-TET notes.
| System | Step size | Frequency ratio | Typical interest |
|---|---|---|---|
| 9-TET | 133.33 cents | 1.080060 | Wide, unfamiliar scale steps |
| 12-TET | 100.00 cents | 1.059463 | Standard Western tuning |
| 19-TET | 63.16 cents | 1.037155 | Alternative thirds and diatonic scales |
| 24-TET | 50.00 cents | 1.029302 | Quarter tones |
| 31-TET | 38.71 cents | 1.022611 | Fine interval approximations |
| 53-TET | 22.64 cents | 1.013164 | High-resolution pitch lattice |
Use it in a session
The calculator is deliberately direct: set the musical context, inspect the result and copy it where you need it.
- Choose the number of divisionsSelect a preset or set any N from 1 to 53.
- Set the reference pitchUse 440 Hz or another frequency as step zero.
- Explore the scaleClick rows to hear frequencies and compare their drift from the nearest 12-TET pitch.
Where it helps
Microtonal composition
Create scales that move outside the conventional twelve-note octave.
Synth tuning
Calculate exact frequency ratios for oscillator or tuning-table programming.
Interval study
Compare how different equal temperaments approximate familiar intervals.
Sound design
Build evenly spaced resonator banks and spectral pitch structures.
Studio note: When comparing temperaments, listen to intervals as well as individual steps. The character of an N-TET system becomes clearer in chords and repeated melodic shapes.
Calculate it in Amanita
Open the exact tool with your saved tempo and tuning values intact. Nothing to install, no account and no ads.