How to Find the Actual Cutoff Range of a Bipolar Filter LFO

A bipolar modulation signal moves in both positive and negative directions around zero. For example, the Surge XT 1.3 manual specifies an LFO range of −1 to +1 when Unipolar is disabled. Ableton’s LFO documentation describes bipolar modulation as moving in both directions around the parameter’s base value. Surge XT User Manual, Max for Live Devices — Ableton Reference Manual

Those definitions establish direction, but they do not establish a frequency span. A depth setting might represent hertz, semitones, octaves, or a fraction of a parameter’s internal range. Consequently, “cutoff 1 kHz, depth 50%” does not provide enough information to calculate universal endpoints.

The essential distinction is between symmetry in the modulation’s control domain and symmetry in hertz. Equal upward and downward octave movements produce different numerical changes in frequency. From 1 kHz, one octave downward reaches 500 Hz, while one octave upward reaches 2 kHz.

Create a temporary copy of the patch so you can simplify its modulation without losing the original sound. Use this diagnostic setup:

1. Keep one LFO routed to one filter’s cutoff.
2. Temporarily remove cutoff envelopes, key tracking, velocity assignments, automation, and macro movement.
3. Set any LFO offset to zero and remove modulation of the LFO’s depth.
4. Choose a full-height sine or triangle waveform with a slow cycle, such as four seconds.
5. Hold one note long enough to observe several complete cycles.
6. Start with identical modulation on the left and right channels.

These are practical isolation steps, not settings every instrument names identically. Check both dedicated filter controls and the modulation matrix. Surge XT, for example, provides separate filter-envelope amounts and filter key tracking; its LFO also has an envelope generator that multiplies the waveform. A rising LFO envelope can therefore make an early cycle narrower than later cycles. Surge XT User Manual

Write down the unmodulated cutoff as your base frequency. If the patch must retain other modulation, define the test conditions instead: the held note, velocity, envelope stage, and macro positions. Your result then describes that particular patch state.

First read the destination’s depth units and confirm whether the displayed amount means a one-sided excursion or the entire sweep width. The following equations assume a full-amplitude bipolar waveform reaching −1 and +1, constant depth, and no limiting at the filter’s boundaries.

Depth expressed in hertz

If the destination explicitly adds and subtracts a frequency amount Δf, use:

Minimum cutoff = f₀ − Δf

Maximum cutoff = f₀ + Δf

Here, f₀ is the base cutoff. With an illustrative base of 1,000 Hz and a depth of ±300 Hz, the endpoints are 700 Hz and 1,300 Hz. Apply this calculation only when the modulation is documented as linear in hertz.

Depth expressed in octaves or semitones

For exponential frequency control, an octave represents a frequency ratio of two. With one-sided depth D in octaves:

Minimum cutoff = f₀ × 2^(−D)

Maximum cutoff = f₀ × 2^D

If depth S is given in semitones, substitute S/12 for D. These illustrative results show why subtracting an arbitrary hertz amount would give the wrong answer:

Base cutoff	One-sided depth	Minimum	Maximum
1,000 Hz	12 semitones / 1 octave	500 Hz	2,000 Hz
1,000 Hz	24 semitones / 2 octaves	250 Hz	4,000 Hz

A documented hardware example is the Doepfer A-120’s CV1 input, which follows a 1 V/octave relationship. Under that relationship, an illustrative ±1 V signal gives a ±1-octave excursion, provided the filter remains within its operating range. Measure the voltage reaching the input after any attenuation or offset; the LFO’s nominal output alone is insufficient. Doepfer A-120 VCF 1 Manual

Depth expressed as a percentage

Check what the percentage describes before calculating. Ableton’s LFO distinguishes modulation relative to a base value from Remote Control mode, which sets the parameter through Min and Max mapping limits. Its global Depth control and Offset control also affect the output. These controls should not be interpreted as percentages of the displayed cutoff frequency. Max for Live Devices — Ableton Reference Manual

For a destination documented as logarithmic across its frequency range, a useful mathematical model is f(p) = Fmin × (Fmax/Fmin)^p, where p is normalized position from 0 to 1. If modulation adds ±d to that position, evaluate f(p−d) and f(p+d). This is a conditional model, not a description of every synth.

For illustration, suppose the documented range is 20–20,000 Hz, the base position is 0.5, and modulation adds ±0.1 normalized units. The calculated endpoints are approximately 317 Hz and 1,262 Hz. A depth label reading “10%” justifies this calculation only if the maker defines it that way.

Use the most direct evidence your device provides: a documented effective-value readout or a display that explicitly follows modulation. First verify what you are watching. A stationary knob or tooltip may describe the base setting rather than the changing destination value.

Ableton’s Auto Filter documentation explicitly says its display shows modulated filter curves for the left and right channels. That makes those curves useful for observing the sweep separately from its base control. Numerical readings from a graph still have the precision allowed by its scale. Live Audio Effect Reference — Ableton Reference Manual

Follow this measurement sequence:

1. Run the isolated LFO slowly through several full cycles.
2. Observe the lowest and highest positions of the effective cutoff or modulated response curve.
3. Freeze the modulation near each extreme if the device supports it. Ableton’s LFO offers a Hold toggle for this purpose.
4. Read or estimate each endpoint and record the method used.
5. Repeat at a slower rate if the display moves too quickly to resolve the extrema. Max for Live Devices — Ableton Reference Manual

If there is no useful modulation display, compare the audio response at frozen endpoints. Feed broadband noise through the filter, analyze the output, and compare it with static cutoff settings using the same filter type, resonance, drive, and routing. Adjust a static reference until its response matches each frozen endpoint. This is a practical estimation method derived from comparing like-for-like filter responses.

Keep analyzer settings consistent. Ableton’s Spectrum documentation explains that block size affects frequency-analysis accuracy, averaging smooths the display over time, and Channel selects left, right, or both. Use settled endpoint captures rather than a heavily averaged trace of the entire moving sweep. Live Audio Effect Reference — Ableton Reference Manual

Treat an analyzer match as an estimate. A resonance peak is a response feature, and changing resonance changes that response. Doepfer’s manual describes resonance as emphasizing frequencies around cutoff; it does not establish a universal rule that the tallest spectral peak equals the exact cutoff value. Doepfer A-120 VCF 1 Manual

Check the assumptions behind your calculation before changing the depth. The following diagnostic sequence separates several common causes:

Observation	What to check next
One endpoint stops moving as depth increases	Test for a destination limit or mapping boundary by moving the base cutoff inward.
The sweep is shifted upward or downward	Inspect LFO offset and other cutoff modulation.
Early cycles have a smaller range	Check LFO fade-in, envelope scaling, or depth automation.
Short notes never reach both endpoints	Hold a longer note and inspect retrigger behavior.
Left and right appear to disagree	Inspect stereo phase, rate differences, and analyzer channel selection.
A random waveform gives changing extrema	Separate the range observed during the test from the source’s possible range.

The stereo case deserves particular care. Auto Filter can run independent left and right modulation: a 180° phase difference places one channel at its peak when the other is at its minimum. Inspecting both channels together can obscure that relationship. Live Audio Effect Reference — Ableton Reference Manual

Also inspect the waveform itself. The endpoint formulas assume the source actually reaches both full-scale values. A custom shape, shortened playback window, or scaled source may use less of the available span. Record the range reached during your intended note or phrase as well as the full-cycle range if both matter to the sound.

Once you know the scaling, work backward from your desired endpoints. For an unclipped exponential sweep with equal positive and negative depth, the required base is the geometric mean:

Base cutoff = √(minimum × maximum)

One-sided depth in octaves = ½ × log₂(maximum/minimum)

Suppose you want a sweep from 250 Hz to 4,000 Hz. The base is √(250 × 4,000) = 1,000 Hz. The endpoint ratio is 16, equivalent to four octaves across the whole sweep, so the required one-sided depth is two octaves, or 24 semitones.

For a destination explicitly linear in hertz, use the arithmetic mean for the base and half the endpoint difference for depth. The same 250–4,000 Hz target would require a 2,125 Hz base and ±1,875 Hz depth. Choose the equations that match the destination’s documented behavior.

When depth units are unspecified, use the measured endpoints as a calibration aid. Adjust the base to position the sweep, adjust depth to widen or narrow it, and recheck both ends after each change. Once it fits, restore the musical waveform, rate, and other modulation, then measure again under the conditions of the actual phrase.

Keep a compact record with the patch: base cutoff, depth units, polarity, offset, waveform, test note, and measured minimum and maximum. Those details turn a vague depth setting into a reproducible filter range and make later adjustments much easier.

• Max for Live Devices — Ableton Reference Manual Version 12
• Live Audio Effect Reference — Ableton Reference Manual Version 12
• User Manual — Surge XT 1.3
• System A-100: VCF 1 A-120 Manual — Doepfer