Note to Hz: The Physics of Music Frequencies
Everything is Math
Music feels emotional, but it is built on rigid physics. Every note you play on a guitar or synthesizer corresponds to a specific number of vibrations per second, measured in **Hertz (Hz)**.
Understanding this relationship is secret weapon for mixing. Instead of guessing where to boost an EQ, you can calculate the exact frequency of the song's key. This guide bridges the gap between Music Theory and Audio Engineering.
The Formula: 12-Tone Equal Temperament
Modern Western music uses a tuning system called 12-Tone Equal Temperament (12-TET). This system divides the octave into 12 mathematically equal steps.
The standard reference pitch is A4 = 440 Hz. To find the frequency of any other note ($f_n$), we use this formula:
Where n is the number of semitones away from A4.
- A#4 is 1 semitone up ($n=1$).
- A3 is 12 semitones down ($n=-12$).
Since an octave is a doubling of frequency, A5 is exactly 880 Hz ($440 \times 2$).
Full Frequency Chart (C0 - C8)
Here is the reference chart for standard tuning ($A=440$).
| Note | Frequency (Hz) | Wavelength (cm) | Use Case |
|---|---|---|---|
| C0 | 16.35 Hz | 2100 cm | Felt, not heard (Sub-bass rumble) |
| A0 | 27.50 Hz | 1254 cm | Lowest note on standard piano |
| E1 | 41.20 Hz | 837 cm | Lowest string on 4-string Bass |
| A2 | 110.00 Hz | 313 cm | Punchy Kick / Snare fundamental |
| C4 (Middle C) | 261.63 Hz | 131 cm | Center of vocal range |
| A4 | 440.00 Hz | 78 cm | Standard Tuning Reference |
| C8 | 4186.01 Hz | 8 cm | Highest note on standard piano |
Practical Applications in Production
1. Musical EQ
If your song is in the key of G Major, the root note is G. Looking at the chart, G2 is roughly 98 Hz.
When mixing the Bass or Kick, setting your EQ boost exactly at 98 Hz (or its octave 49 Hz) will make the low-end feel "in tune" with the song. Boosting random frequencies creates dissonance.
2. Synthesizer Tuning
In Modular Synthesis, oscillators often track 1 Volt per Octave. Understanding that 1V adds exactly double the frequency helps you design complex FM (Frequency Modulation) patches where ratios must be precise integers (1:1, 2:1) to avoid harsh metallic noise.