12-Tone Equal Temperament Pitch Frequency
Calculates the exact acoustic frequency in Hertz of any note on the standard 12-tone equal temperament (12-TET) musical scale relative to concert pitch A4 (440 Hz).
\[ f_n = f_0 \cdot 2^{n/12} = 440 \cdot (\sqrt[12]{2})^n = 440 \cdot (1.059463094)^n \]
Plain Text Formula:
f_n = f_0 * (2^(n / 12)) = 440 * (1.059463094)^n
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ f_n \] | Target Note Frequency | Hertz (Hz) | Pitch frequency of the evaluated musical note |
| \[ f_0 \] | Concert Pitch Standard | 440.0 Hz | International tuning reference frequency for note A4 |
| \[ n \] | Semitone Offset | semitones | Integer distance from A4 (e.g. C5 is +3, Middle C4 is -9) |
| \[ \sqrt[12]{2} \] | Semitone Ratio | 1.059463094... | Exact twelfth root of two frequency multiplier |
💡 Worked Engineering Example
Problem Statement:
Calculate the frequency of Middle C (C4), located 9 semitones below concert A4 (n = -9).
Step-by-Step Solution:
- Multiplier = 2^(-9/12) = 2^(-0.75) = 0.5946035575
- f = 440 * 0.5946035575 = 261.6255 Hz
🎯 Result: Middle C (C4) frequency in standard 12-TET tuning is 261.63 Hz.