Filter Cutoff Calculator
Convert a MIDI note number and octave offset into its corresponding filter cutoff frequency in Hz. Useful for synth programming and sound design when you want to tune a filter precisely to a musical pitch or harmonic relationship.
About this calculator
Every MIDI note maps to a specific pitch frequency. The standard reference is MIDI note 69, which corresponds to A4 = 440 Hz. Moving one semitone up or down multiplies or divides the frequency by the twelfth root of 2 (2^(1/12) ≈ 1.05946). To find the frequency for any MIDI note, the formula is: f = 440 × 2^((noteNumber − 69 + octaveOffset × 12) / 12). The octave offset shifts the result by a whole number of octaves — each octave doubles or halves the frequency (2^1 = 2). This formula is used to set filter cutoff frequencies that are harmonically related to a played note, a common synthesis technique called keyboard tracking, which keeps the timbre consistent across the pitch range.
How to use
Suppose you want the cutoff frequency for MIDI note 60 (Middle C, C4) with an octave offset of +1. Step 1 — calculate the exponent: (60 − 69 + 1 × 12) / 12 = (60 − 69 + 12) / 12 = 3 / 12 = 0.25. Step 2 — compute the frequency: f = 440 × 2^0.25 = 440 × 1.18921 ≈ 523.25 Hz. This is exactly C5, one octave above Middle C, confirming that an offset of +1 raises the result by one octave as expected.
Frequently asked questions
How does MIDI note number relate to musical pitch and frequency?
MIDI assigns each semitone on a standard keyboard an integer from 0 to 127. The anchor point is note 69 = A4 = 440 Hz, established by international tuning standard ISO 16. Each step of 1 in the MIDI note number represents one semitone, which multiplies the frequency by 2^(1/12). Middle C is MIDI note 60, which equals approximately 261.63 Hz. This relationship allows precise, reproducible pitch calculations across all digital music software and hardware.
Why would you use a MIDI note number to set a filter cutoff frequency?
Setting a filter cutoff relative to a MIDI note creates a harmonically meaningful cutoff — for example, placing the cutoff exactly at the third harmonic of the played note. This technique, called keyboard tracking or key follow, ensures that the timbral color of a sound remains consistent as you play higher or lower notes. Without it, a filter tuned for a low bass note will sound too dark or too bright when the same patch is played in a different register. Synth designers use note-based cutoff values to achieve musically intentional filter responses.
What does the octave offset do in the filter cutoff frequency formula?
The octave offset shifts the calculated frequency up or down by whole octaves. Each unit of +1 adds 12 semitones to the exponent, which doubles the resulting frequency (one octave up). Each unit of −1 subtracts 12 semitones and halves the frequency (one octave down). This is useful when you want a cutoff that tracks the played note but is intentionally placed one or two octaves above it to emphasize harmonics, or below it to suppress them. It provides a fast, musically intuitive way to offset a keyboard-tracked filter.