γ²(f) = |Gxy(f)|² / (Gxx(f) × Gyy(f)). Computed via Welch method with multiple averaged blocks.

Why is coherence low?

Reflections (most common), background noise, non-linearity (clipping), or time variance during measurement.

How to improve coherence?

Increase signal level, move mic closer, add averages (helps noise not reflections), add acoustic treatment.

Coherence threshold for EQ?

Only EQ where γ² > 0.6. Above 0.7 ideal. Below 0.5 = unreliable data. AI diagnostic weights by coherence.

Does more averaging help coherence?

For noise: yes. For reflections: no (deterministic, present in every average). Distinction matters for choosing the fix.

Coherence: The Most Underused Measurement in Live Sound

What Coherence Actually Measures

Coherence is the frequency-domain equivalent of the correlation coefficient. At each frequency bin, it answers the question: "How much of the microphone signal at this frequency was caused by the measurement signal, versus other sources?"

The formula: γ²(f) = |G_xy(f)|² / (G_xx(f) × G_yy(f))

Where G_xy is the cross-spectral density (input × output), G_xx is the input auto-spectral density, and G_yy is the output auto-spectral density. All computed via Welch's method with multiple averaged blocks.

Interpreting Coherence Values

γ² > 0.9: Excellent

The measurement dominates. The transfer function magnitude and phase at this frequency are highly reliable. EQ decisions based on this data will be effective.

γ² = 0.6 - 0.9: Moderate

The measurement is still useful, but some contamination exists. For system EQ, corrections based on this data will be partially effective. The actual problem might be larger or smaller than the magnitude trace suggests.

γ² = 0.3 - 0.6: Poor

More of the output energy at this frequency comes from noise, reflections, or non-linearity than from the measurement signal. The magnitude trace is unreliable. EQ applied here will be largely ineffective or counterproductive.

γ² < 0.3: Unreliable

The output at this frequency is essentially unrelated to the input. The magnitude data is noise. Do not make any adjustment decisions based on it.

The Four Causes of Low Coherence

1. Room Reflections

The most common cause in live sound. At frequencies where strong reflections arrive from different directions with different delays, the combined response varies from one measurement block to the next (because the exact interference pattern depends on sub-wavelength position and timing). This variance reduces coherence.

Low coherence due to reflections is especially common below the Schroeder frequency where discrete room modes dominate, and at frequencies where the path difference between direct and reflected sound creates a comb filter null.

2. Background Noise

Ambient noise (HVAC, traffic, audience) is uncorrelated with the measurement signal. At frequencies where the noise level approaches the measurement signal level, coherence drops. The fix: increase measurement signal level, or measure during quiet periods.

Rule of thumb: coherence drops below 0.9 when the signal-to-noise ratio falls below 10 dB at a given frequency.

3. Non-Linearity (Distortion)

When the system clips, compresses, or limits, the output contains harmonics not present in the input. These harmonics are uncorrelated with the input at the fundamental frequency. Severe non-linearity (clipping, limiter pumping) shows as broadband coherence reduction.

The problem detector identifies clipping and THD+N to distinguish non-linearity from other coherence-reducing factors.

4. Time Variance

Any change in the system during measurement — a person walking through the measurement path, a door opening, HVAC cycling — changes the transfer function between blocks. This variance reduces coherence. Longer measurement durations are more susceptible; more averages help if the variance is intermittent.

Improving Coherence

Increase measurement level: Higher pink noise level improves SNR at all frequencies. Target at least 10 dB above the ambient noise floor.
Move the mic closer to the speaker: Reduces the reverberant-to-direct ratio, improving coherence. Useful for initial system characterization before measuring at listening positions.
Add more averaging: Doubling the number of averages improves coherence for noise-related degradation but not for reflection-related degradation.
Reduce reflections: Acoustic treatment at first reflection points improves coherence across a wide frequency range.
Use a better window: The Blackman-Harris window (used by SonaVyx) has excellent side-lobe suppression, reducing spectral leakage that can degrade coherence.

Coherence and EQ: The Golden Rule

The magnitude response of the transfer function only tells you what the frequency response looks like. Coherence tells you whether you should trust it. Without coherence, a 10 dB dip at 315 Hz is ambiguous — it could be a comb filter (unfixable with EQ) or a speaker rolloff (fixable with EQ). With coherence, the answer is clear:

10 dB dip + high coherence (>0.7) → system response issue → EQ correction will work
10 dB dip + low coherence (<0.5) → reflection/noise artifact → EQ will be ineffective; address the physical cause

This is why the AI diagnostic engine weights its EQ recommendations by coherence — higher-coherence frequency ranges get stronger corrections; low-coherence ranges get advisory notes instead of EQ bands.