In Memoriam: Siegfried Linkwitz, 1935–2018

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In Memoriam: Siegfried Linkwitz, 1935–2018

Siegfried Linkwitz, who died in September, 2018, is famous for the Linkwitz-Riley crossover alignment. But his work in audio went far beyond that. He was a profound thinker about the foundations of audio, and in particular about the all-important question of establishing some reciprocity between the recording of sound and its playback. At first sight, this might seem a simple thing: Recording with a flat microphone and playing back on a flat speaker might seem to suffice. And anechoically, this is essentially true. Do this out of doors, far off the ground, and the playback will match the original sound extremely well. But in reality, where music is recorded in its natural indoors environment and played back in a listening room, things are more complicated. In this article, I want to look at just one of the many observations that Linkwitz made on this subject, but one that is to my ears particularly important. There are many more, and we would all do well to study carefully his website (http://www.linkwitzlab.com/frontiers.htm). Information abounds here, the fruit of a lifetime of serious thought about audio matters. We owe him a great debt.

Diffuse Field and Direct Arrival: Why Speakers Need to Be Not Exactly Flat

When you listen to a singer or player in an auditorium, a lot of what you hear has bounced off the walls of the auditorium many times before it gets to you. Because the ear/brain locates a sound source using the first arrival of the sound, it seems to the listener as though the sound comes straight from the source. But the physical reality is that much of the sound has been highly reflected. And this highly reflected sound is coming at you from many different directions and with a variety of time delays. It is what acoustics people call “a diffuse sound field.”

The mathematical model of this is somewhat complicated. But the direct experience of it is easy to arrange. Walk out of the hall and turn a corner, but leave the door open. You are not hearing direct arrival any longer, but you can still hear the music. The diffuse field, as its name suggests, diffuses out to where you are. It is everywhere and nowhere but you can still hear the music and it is still quite loud, almost as loud as if you were in the hall at a moderately distant audience location.

The diffuse field has a lower high-frequency content than the sound really close to the source, because the reflections have reduced high-frequency content, and the air in the hall soaks up the highs, too. But there is an additional effect that has to do not with what the hall is doing to the sound but with how your ears hear it. Namely, the ear is comparatively less sensitive in the 3–4kHz region. This has to do with ear canal resonance. The basic resonance boosts the 3–4kHz region, but it boosts it more for frontal arrival than for diffuse field.

What this means is that if you move farther back in the hall and thus hear more diffuse field compared to direct arrival, the extreme top will be reduced—that part is physical—but because of the way your hearing works the 3-4kHz region will sound reduced, too, compared to the sound really close to the source, where the direct arrival predominates. No doubt you have noticed this. People talk about “back of the hall” sound. And a lot of what they are referring to has to do with comparatively less energy in the 3–4kHz region.

How This Affects the Balance of Recordings

Let us hear what Linkwitz himself had to say on this (quoted from the website listed earlier):

“Around 3kHz our hearing is less sensitive to diffuse fields. Recording microphones, though, are usually flat in frequency response even under diffuse field conditions. When such recordings are played back over loudspeakers, there is more energy in the 3kHz region than we would have perceived if present at the recording venue, and a degree of unnaturalness is introduced. This applies primarily to recordings of large orchestral pieces in concert halls where the microphones are much closer to the instruments than any listener [would be]. At most listening positions in the hall the sound field has strong diffuse components.”

This effect combines with the roll-off of response in the diffuse field itself. This roll-off typically starts somewhere between 2 and 4kHz. But even if you had a hall where the reverberant field was flat to say 6kHz, then the prominence of the diffuse field in the picture and the relative dip in the ear’s response to diffuse field would make the sound have less perceived 3–4kHz energy at audience locations than at close-up microphone locations.

What to Do to Make Recordings Sound Right

Linkwitz again: “I use a dip of 4dB to equalize for this. The circuit consists of R, C, and L in series, forming a frequency-dependent ladder attenuator in conjunction with the 5.11k ohm source resistor. You may choose to make the notch filter selectable with a switch for different types of recordings.”

How Big Is This Effect?

Maybe this seems like something too theoretical to worry about, like the kind of thing that theorists like me (and Linkwitz) worry about, and that are perhaps interesting to consider but do not really matter. But look at that number: 4dB. Take an EQ device and shove up the 3–4kHz region by 4dB. I promise you the effect is not small! But this shoving up is what is happening if you do not use the dip Linkwitz recommends. Of course, speakers produce a diffuse field in listening rooms, but typically they are directional enough above 1kHz or so that the effect still applies, because the direct arrival is relatively larger versus the diffuse field than in concert halls. 

This is something important. My personal view is that it accounts for a large percentage of why musicians and other people who listen hard to live music but not so much to audio think that audio does not sound right compared to live music. I recall Lincoln Mayorga telling me that his goal in co-founding Sheffield Lab was to try to make recordings that sounded as much like a real piano as the recordings Artur Schnabel made in the 1930s, compared to which, and to reality, modern recordings were too “bangy.” This simple EQ change would do a lot to rectify the difference between recorded and live in many cases.

A second point to note is that Linkwitz suggests the idea of making the matter adjustable. The idea that one particular non-adjustable speaker could be ideal for playback of all recordings is not on the table here.

Linkwitz’s Thoughts in General

I did not know Linkwitz well personally, though we did have a number of interesting conversations over the years. But I miss his presence on the audio scene. He was a man who thought long and deeply about the foundations of audio and connected science to audio in a most helpful and informative way—the diffuse field issue is typical: The difference between diffuse field response and frontal arrival response had been studied for a long time. But Linkwitz played a very valuable role in taking this theoretical scientific matter and bringing it to everyone’s attention by considering how it actually influences audio in practice and what you can do to fix it. He combined here, and on many other topics, vast knowledge of acoustical and electrical theory with a wealth of practical experience of how audio actually works. In addition to his own direct contributions (that crossover, in particular), he bridged the canyon that too often separates psychoacoustics and engineering theory from practical audio. Fortunately, he left behind that website, where you can almost feel as if he were telling you all the things he knew that you would want to know, too. He is gone, may he rest in peace, but his presence lives on to the benefit of us all.

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