Intervals in 12-ET
| Step | Name | Cents | Hz | JI ≈ | Comma |
|---|
Cross-ET Comparison (12-ET Reference)
| Interval | 12-ET | 24-ET | Δ (cents) | Nearest |
|---|
Octave Visualization — 12 Steps
C4
C5
| Step | Name | Cents | Hz | JI ≈ | Comma |
|---|
| Interval | 12-ET | 24-ET | Δ (cents) | Nearest |
|---|
Equal temperament is the tuning system that makes the piano work — divide the octave into equal steps, and you can modulate to any key. But 12-ET is just one point on a vast landscape of possibilities. Musicians in India use 22-ET, some microtonal composers use 19-ET or 31-ET, and experimental tunings go all the way to thousands of steps per octave. Each system names intervals differently, approximates just intonation ratios differently, and creates unique musical possibilities. No single reference tool shows how interval naming, cent values, and just intonation equivalents change across all these systems — until now.
Interval Notation Forge is an interactive reference tool for exploring equal temperament systems. Select any ET (from 1 to 5760 steps), and the tool computes:
Cent calculation: In an N-ET system, each step is 1200/N cents. The frequency of step k is f₀ × 2^(k/N).
Interval naming: The tool uses a generalized naming convention. For 12-ET, the standard names apply (unison, minor 2nd, major 2nd, etc.). For other ETs, intervals are named by their nearest 12-ET equivalent with a modifier indicating the step number.
Just intonation matching: The tool searches a database of common JI ratios (from 1/1 up to 64/1) and finds the one whose cent value is closest to each ET step. The comma is the difference in cents.
Cross-ET comparison: For each diatonic interval (the 7 white-key intervals in 12-ET), the tool finds the nearest step in the selected ET and shows the cent deviation from the 12-ET value.