Two Cardioids at the Sides of a Sphere

Introduction

I gather here my thoughts and data about a stereo configuration I proposed to rec.audio.pro. From the feedback I received by the Usenet, this didn't turn out to be a good idea, but it has been interesting and fun to do. If you have more comments please post them to the thread on rec.audio.pro.

I own two Rode NT5 cardioid microphones. After reading Günther Theile's paper On the Naturalness of Two-Channel Stereo Sound (J. Audio Eng. Soc. 39 (10) Oct. 1991), I was wondering how I can achieve some of the "naturalness" of a sphere microphone with what I have, i.e. using my cardioids instead of omnis.

In this setup, two cardio mikes are horizontal and parallel, pointing forward to the source, with their capsules almost touching two opposite points on the equator of a sphere. The mikes stick outside the sphere much like the figure-of-eights in the Schoeps KFM360. Here is a couple of pictures of this setup:

 

The sphere I'm using is a white lamp made in polycarbonate, you may find such things in gardens or on exterior walls. It's essentially a plastic shell, few millimeters thick and hollow, 20cm diameter. Mike Rivers points out that I may get resonances in the plastic and in the air inside the cavity.

Some abstract considerations

Before my first recording I was trying to figure out what I was going to get. Intuitively, the timing of the stereo image should be "natural" in Theile's sense. The amplitude, however is difficult to predict. I thought I could just take the equation for the sound field and calculate the gradient in polar coordinates. Once I have the gradient (modulo and direction) I know the response of the mike: the modulo is an overall factor, the direction relative to the main axis of the mike is the angular coordinate in the mike's polar pattern. It turns out that the gradient of the sound around the sphere has a radial component and a tangent (direction of theta) component, but no component in the direction of phi as the wave function has no dependency on phi; and both radial and tangent components depend on the frequency. I'd need some computer programming to evaluate the actual magnitude and direction of the gradient, but it may be strongly dependent on the frequency. If the direction depends strongly on the frequency, so does the mikes' response, resulting in coloration.

Soundhaspriority points out that a cardioid doesn't behave as a cardioid if put against a boundary. I could argue on that, but he made me think twice on what I was doing: although Crown and other manufacturers have marketed directional microphones against some boundary surface, it is true that the surface has always been chosen to be flat (with one notable exception I know of, i.e. Schoeps KFM360). Directional microphones are arguably designed to have a uniform response in frequency when in the far field, i.e. when hit by plane waves. In the near field, sound from a point source is made of spherical waves and not plane waves, so the well-known proximity effect can be put in relation with the curvature of the sound wavefront. Now, plane waves hitting a reflecting spherical surface will bounce with a curved wavefront, so I can expect some proximity effect. If I'll ever work out the math, I think I'll try to derive an "effective distance" of the sound source from the Laplacian of the sound wave.

Summarizing:

Based on formulas in a paper by Steve Turley, I made some plots of sound intensity around the sphere (the plots are generated with SciLab 4.1):

Click here to download an animation from 80Hz to 8000Hz in 1/3 octave steps (1.47 MB).

Actual recording

The biggest problems can be evaluated by ear, so here are some recordings for anyone to judge. The recording took place on Dec. 7, 2006 in Genova (Italy), Chiesa di S. Maria di Castello, right in front of the altar. The choir (9 singers) is distributed around a hemicycle centered in the sphere at a distance of about 160cm, so that the sphere receives sound from 180° in front and beside it. The conductor is behind the sphere facing the choir and the altar.

The equipment: a Rode NT5 matched pair, a Rolls portable phantom power, an M-Audio MicroTrack 24/96 as a recorder. Apologies for my amateurial recording: I have very little experience in audio engineering.

  1. rehearsal excerpt: wav (12.45 MB) and mp3 at 224kbps (1.98 MB)
  2. concert excerpt: wav (28.98 MB) and mp3 at 224kbps (4.61 MB)

The first take is from a rehearsal session before the concert. For the sake of comparison I put also the very same piece as performed an hour later in concert with a similar arrangement but without the sphere and with the mikes in a near coincident configuration 11.5cm apart at an angle (mic-to-mic) of 50°. According to Wittek's Image Assistant, this configuration has a recording angle of 180° with a fairly smooth dependency of the "phantom" (direction of the stereo image of the source) on the azimuth of the sound source.

If you download and listen to the samples, please post a comment on rec.audio.pro.

Further experimentations

As time permits, I'd like to try again after covering the sphere with some furry coating: without reflections some of the coloration could go away. Also I can try filling the sphere with heavy material (sand or rice?) or absorbing material (rockwool?) to kill resonances inside the hollow.

Another try would be with a furry disc (Jecklin disc): one could expect results comparable to a furry sphere, but it is not hollow and it is more convenient to carry around.


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