The specification called for a transfer function measurement of the installed PA system. The measurement engineer ran pink noise through the system at a moderate level — 'We don't want to disturb the office workers,' he explained — and placed the measurement microphone at the far end of the open-plan office, forty meters from the nearest speaker.

The result showed coherence of 0.11. The magnitude response was essentially flat. Perfectly flat. Suspiciously flat. Not the kind of flat that means 'well-designed speaker system' but the kind of flat that means 'you're measuring something with a flat spectrum.' Like, for instance, the HVAC system.

The pink noise level at the measurement position was approximately 52 dBA. The HVAC noise at the same position was 58 dBA. The measurement microphone was receiving 6 dB more HVAC noise than test signal. The transfer function was showing the frequency response of the air conditioning, not the PA. The coherence of 0.11 was the transfer function's way of screaming 'I am not measuring what you think I am measuring.'

When the engineer increased the test signal by 15 dB and moved to a position twenty meters away — where the signal-to-noise ratio was positive — the coherence jumped to 0.87 and the transfer function revealed the PA's actual response, which was not flat at all.

The Moral: The test signal must be louder than the ambient noise at the measurement position. SonaVyx's coherence indicator turns red below 0.5 for exactly this reason — low coherence means you need more signal, less noise, or a closer microphone position.