How to Tune a Static Comb Filter’s Resonances to a Note

A comb filter has a repeating pattern of peaks and valleys in its frequency response. Two basic structures matter here: a feedforward comb combines an input with a delayed copy, while a feedback comb recirculates the delayed output. The feedback structure produces a decaying series of repetitions and is the relevant starting point when you want a ringing resonator. Julius O. Smith’s “Comb Filters” explains both structures.

In this article, tuning means placing the lowest nonzero resonance at the target frequency. That definition removes an ambiguity: placing any higher peak on a note does not necessarily make that note the base of the resonance pattern.

“Static” means keeping the tuning fixed during the sound. For the initial setup, disable modulation of delay or pitch, including envelopes, LFOs, automation, and keyboard tracking. A fixed-note mode is useful when available. For example, Massive X’s Fix mode sets the comb tuning independently of incoming MIDI pitch. Massive X manual: Filter

Choose a note, octave, and tuning reference first. Under twelve-tone equal temperament with A4 set to 440 Hz, the frequency is:

[ f_0=440\times2^{(n-69)/12} ]

Here, (n) is the MIDI note number: A4 is 69 and middle C is 60. Inspired Acoustics’ note-frequency reference provides this formula and the corresponding table.

For a basic positive-feedback comb, calculate:

[ T_{\text{ms}}=\frac{1000}{f_0} ]

The resulting resonances occur at (f_0,2f_0,3f_0,\ldots), within the available frequency range. Cycling ’74 illustrates the relationship with a 2 ms delay, which gives 500 Hz spacing. MSP Delay Tutorial 6: Comb Filter

The following values are calculated from those equations, using A4 = 440 Hz. The negative-feedback column places its lowest resonance at the same target note; the reason for its shorter delay is explained next.

Target note	Frequency	Positive-feedback delay	Negative-feedback delay
A2	110.000 Hz	9.091 ms	4.545 ms
C3	130.813 Hz	7.645 ms	3.822 ms
A3	220.000 Hz	4.545 ms	2.273 ms
C4	261.626 Hz	3.822 ms	1.911 ms
A4	440.000 Hz	2.273 ms	1.136 ms
C5	523.251 Hz	1.911 ms	0.956 ms

Use the frequency appropriate to your actual reference tuning. Also check the unit beside the control: 2.273 milliseconds is 0.002273 seconds. If the device accepts a note or frequency directly, use that control and verify the resulting spectrum instead of translating it into milliseconds unnecessarily.

For the basic model used here, feedback is defined by (y[n]=x[n]+g,y[n-M]). With positive (g), resonances occur at integer multiples of the inverse delay. With negative (g), they move halfway between those positions. This polarity-dependent placement is derived in Smith’s comb-filter analysis.

Expressed in seconds, the two patterns are:

• Positive feedback: (f_k=k/T), with the first nonzero peak at (1/T).
• Negative feedback: (f_k=(2k+1)/(2T)), with the first peak at (1/(2T)).

Consequently, negative feedback needs:

[ T_{\text{ms}}=\frac{500}{f_0} ]

For an illustrative A4 setup, positive feedback at 2.273 ms gives peaks near 440, 880, and 1,320 Hz. Switching to negative feedback without changing that delay gives peaks near 220, 660, and 1,100 Hz. Shortening the negative-feedback delay to 1.136 ms places the peaks near 440, 1,320, and 2,200 Hz.

This gives you a practical choice: positive feedback for a complete integer harmonic series, or negative feedback for odd multiples of the chosen fundamental. Massive X documents the same all-harmonic versus odd-harmonic distinction for its feedback polarity control. Massive X manual: Comb

Check the manual’s sign convention before interpreting a knob’s plus or minus label. Also identify which signal a polarity switch inverts: changing an external wet signal’s polarity is a different operation from changing the feedback-loop polarity.

Use this sequence to separate tuning from the character of the source sound. You need a comb or short-delay processor, a test source, and a spectrum analyzer that can show individual peaks near your target.

1. Establish a simple configuration. Disable delay modulation, tempo synchronization, and pitch tracking. Bypass optional dispersion or all-pass processing where possible.
2. Choose the feedback polarity. Use the appropriate delay equation above.
3. Enter the calculated delay. Start with moderate feedback, then increase it enough to make the resonance pattern readable.
4. Test with broadband material. Use noise or a short broadband burst. Inspect the processed output on its own before adding parallel dry routing.
5. Locate the lowest intended peak. Check its frequency and at least two neighboring peaks against the expected series.
6. Fine-tune the delay. Repeat the test after each adjustment, keeping the other controls fixed.

Cycling ’74 uses white noise and a harmonically rich pulse as test sources, explaining that filtering is easier to observe when the input contains many frequencies. That makes broadband material a useful diagnostic before testing your musical source. Cycling ’74: Trying out the comb filter

For A4 with positive feedback, look for peaks near 440, 880, and 1,320 Hz. Do not accept a single peak near 440 Hz as sufficient confirmation: it could be a higher resonance in a lower-tuned series. Checking the neighboring peaks tests both the tuning and your interpretation of the polarity.

If you measure the ringing tail after a burst, use enough feedback for the tail to remain visible. For the ideal feedback model, a decaying response requires feedback magnitude below one; the exact relationship between a device’s displayed percentage and its internal coefficient depends on its implementation. Smith: Feedback Comb Filters

First check the delay control’s resolution. At a sample rate (f_s), the ideal positive-feedback delay length is:

[ M=\frac{f_s}{f_0} ]

For the illustrative case of A4 at 48 kHz, this is 109.0909 samples. An integer-only delay cannot represent that exact value.

Calculated from (f=f_s/M), 109 samples gives approximately 440.367 Hz, about 1.44 cents sharp. A 110-sample delay gives approximately 436.364 Hz, about 14.37 cents flat. A finely displayed millisecond value therefore does not, by itself, establish the processor’s effective tuning resolution.

Fractional-delay processing represents delays between integer sample positions. Different interpolation methods have different amplitude and phase behavior; Smith specifically discusses interpolation choices inside feedback loops. “Delay-Line and Signal Interpolation”

For a processor that approximately follows the inverse-delay relationship, use this measurement-based correction:

[ T_{\text{new}}\approx T_{\text{old}}\times\frac{f_{\text{measured}}}{f_{\text{target}}} ]

For example, suppose a hypothetical measurement shows a 435 Hz peak at 2.30 ms, and your target is 440 Hz. The corrected starting point is (2.30\times435/440\approx2.274) ms. This is a calculated illustration, not a measured product result. Retest after applying it. If the controls use note offsets, adjust their fine-tuning control against the measured peak instead.

A processor may include more than a delay and feedback gain. Nonlinear Labs’ C15 documentation describes both an all-pass filter and a low-pass filter inside its comb feedback branch. The all-pass changes frequency-dependent phase, which acts like additional frequency-dependent delay. C15 User Manual: Comb Filter

That is why the reciprocal-delay equation is a starting point for a more elaborate resonator. Establish the simple tuning first, add the desired dispersion, and then measure again. If the peaks no longer follow an integer series, identify which resonance you want anchored to the note rather than trying to align every peak.

Damping also changes the balance of the tail. In the low-pass feedback model documented by Smith, higher frequencies decay faster than lower frequencies. “Lowpass-Feedback Comb Filter”

Set the final damping and feedback before your last tuning check. With deliberately uneven partial spacing, describe the setting as a selected resonance anchored to the note; the full spectrum may no longer constitute that note’s harmonic series.

Once the test signal shows the expected peaks, restore the intended source and diagnose the remaining issue by what you observe.

Observation	Next check
The apparent pitch is an octave lower	Recheck feedback polarity and the lowest resonance.
The resonance pattern moves during playback	Inspect delay modulation, pitch envelopes, automation, and keyboard tracking.
Noise reveals the tuning, but the source barely rings	Inspect whether the source supplies energy near the intended resonances.
The tuning changes after timbre adjustments	Recheck feedback-path filters and dispersion.
Nearby delay settings jump past the target	Check parameter resolution and fractional-delay support.

The source-energy check follows from ordinary filtering: a linear comb shapes the frequencies presented to it. A sparse input may reveal only part of its response. Cycling ’74’s recommendation to use sources with many partials is particularly useful here. MSP Delay Tutorial 6: Comb Filter

Finish by checking the final routing and saving the note, reference frequency, feedback polarity, delay, and relevant tone settings together. A verified static tuning consists of a fixed control state and a resonance pattern that matches your chosen target. Calculate the delay, inspect several peaks, and make the final adjustment with the actual sound and feedback-path settings in place.

• “Comb Filters” — Julius O. Smith, Physical Audio Signal Processing
• “MSP Delay Tutorial 6: Comb Filter” — Cycling ’74 Documentation
• “Filter” — Native Instruments, Massive X Manual
• “MIDI note numbers and center frequencies” — Inspired Acoustics
• “Delay-Line and Signal Interpolation” — Julius O. Smith, Physical Audio Signal Processing
• “Comb Filter” — Nonlinear Labs, C15 User Manual
• “Lowpass-Feedback Comb Filter” — Julius O. Smith, Physical Audio Signal Processing