When the iconic Notre Dame cathedral in Paris caught fire last month, people found some hope in the news that scientist Andrew Tallon had used laser scanning to create precisely detailed maps of the interior and exterior of the cathedral—an invaluable aid as Paris rebuilds this landmark structure.

The acoustics of the cathedral—how it sounds—are also part of its cultural heritage, and given the ephemeral nature of sound, acoustical characteristics can be far trickier to preserve or reproduce. Fortunately, a group of French acousticians made detailed measurements of Notre Dame's "soundscape" over the last few years, along with two other cathedrals. That data will now be instrumental in helping architects factor acoustics into their reconstruction plans.

Dialing in the reverb

"We have a snapshot of the acoustics from two years ago and a computer model that can reproduce that," said Brian FG Katz, research director of the National Center for Scientific Research (CNRS) at Sorbonne University in Paris, who worked in tandem with Tallon's laser scanning project. "The idea is if they want to, for example, change the materials, we can tell them what the impact of those changes will be on the acoustics. We're not trying to force anybody to restore it one way versus another, but they should be able to make an informed decision about the acoustic impact."

Katz became interested in documenting and digitally reconstructing the soundscapes of historic spaces over a decade ago, after a colleague told him about doing so for Harvard University's Fogg Lecture Hall. That colleague in turn was inspired by physics professor (and father of modern architectural acoustics) Wallace Clement Sabine, who was tasked with figuring out why the acoustics in the hall were so dreadful back in 1895.

Ultimately, Sabine was able to determine that there was a definitive relationship between the quality of a room's acoustics, the size of the chamber, and the amount of absorption surfaces that were present. And he came up with the formula for calculating reverberation time, still the critical factor for gauging a space's acoustical quality. Point of note: reverberation is not the same as an echo, which is what happens when a sound repeats. Reverb is what happens indoors when sound can't travel sufficient distance to produce those echoing delays. Instead, you get a continuous ring that gradually "decays" (fades).

"Cathedral acoustics are different from other spaces, just in terms of the high level of reverberation, the mixing, and the very complex geometry," said Katz. Notre Dame has a six-second reverberation time for mid-frequencies. The long reverberation and mixing means that compositions requiring precise clarity on any specific note or instrument (including the human voice) quickly becomes muddied—a Mozart concerto or symphony, for instance, quickly descends into cacophony. "You basically hear three notes, and noise, and then the last note a long time later," he said. Gregorian chants and organ music, however, work very well in that setting. But the reverberations and quirks of the space posed a challenge for getting precise measurements of the cathedral's acoustical profile.

Add a bit of bits

Computer modeling has become one of the modern acoustician's most important tools. Sound diffusing through a performance space can be modeled as particles of light bouncing around that space, much like a billiard ball bounces around a table in response to being hit by the cue. Acousticians can use those models to calculate the impulse response of the sound. What's an impulse response? Clap your hands inside an empty concert hall or church. That's the impulse. The sound reflections you hear are the building's response.

Record both impulse and response, then compare the acoustic profile with a recording of just the impulse for reference, and you can extract a model of the room's reverberations. Once the sound field of a modeled space has been determined, it's possible to simulate the sound as it would appear within the real space—a technique called auralization, the acoustic equivalent of visualization techniques. Auralization software can help acoustical consultants predict and perfect how a proposed performance space design will sound, based on a wide range of parameters: room size and shape, surfaces, materials, and other design features.

That's pretty much what Katz and his colleagues have done for Notre Dame—capturing the fine details of the cathedral's unique soundscape before the fire. They set up a collection of omnidirectional 3D microphones, along with a dummy head microphone and strategically placed loudspeakers as the sound sources. That allowed them to create an aural map of the cathedral's acoustics using numerical simulation software.

Some might be surprised to learn that Katz's team made their measurements using commercial equipment, rather than laboratory grade hardware. Granted, the latter are designed to be hardy, to stand up to the rigors of field work. But Katz found the commercial microphones and amplifiers were more stable and had a better signal-to-noise ratio. "They worry about listening to it, as opposed to it just being data," he said. "In the end, we're interested in being able to listen to these models."

"We have a snapshot of the acoustics from two years ago and a computer model that can reproduce that."

The resulting model enabled Katz and company to create a virtual reality version of Notre Dame with all the acoustical parameters in place. He used it to create his Ghost Orchestra project, using a special close-mic recording of a performance of "La Vierge" in honor of the cathedral's 850th anniversary in 2012.

"By feeding the recordings to the appropriate source positions in the model, we were able to recreate the acoustic performance of this concert, allowing the listener to move within the cathedral to explore and experience the complex acoustics of this large and historic space," said Katz. "That way you can listen to how the acoustics change as you move around the space." (You can watch 360 video extracts on YouTube here and here. It's best enjoyed with good headphones.)

And since Notre Dame will be closed for the next five years or so as the city rebuilds its prized cathedral, Ghost Orchestra's virtual concert platform is one way the general public can continue to enjoy "live" concerts there. The same conservatory that recorded "La Vierge" recorded a dozen other concerts performed at Notre Dame, according to Katz, and it's possible to feed recordings of other live concerts played elsewhere into the virtual model to hear how they would sound in Notre Dame.