Fons, have you heard any music recordings with EigenMike?  No one seems to 
have tried.

Elko has a standing invitation to bring EM to any venue that Aaron & Eric 
are recording world class orchestras in good halls ... I mean obscure Mid 
West bands in non-descript halls :)  They can reliably record a zillion 
channels.

I've been trying to follow Angelo and his Merry Mens' efforts with EM but 
IIRC ... the best result so far, shows 1st order Ambi with an absolute 
(nearly brick wall) top limit of 10kHz which sorta ties in with your 
observations.

This was with Angelo's beloved funky Kirkeby FIRs :D

It's so nearly there but not quite.

Date: Thu, 14 May 2015 09:52:59 +0000
From: Fons Adriaensen <f...@linuxaudio.org>
To: sursound@music.vt.edu
Subject: Re: [Sursound] Converting 16 mic array recording to B format
 .......
The limits pointed out above are something that Gary Elko has clearly
understood very well (and some others apparently have not).
The beamforming sofware that comes with the Eigenmike will in general
not let you do things that depend on unrealistic accuracy of the mic
gain calibration.

On the upper end the limit for the EM is around 8 kHz. Above that,
the SW will just give you the signal of the single capsule that
is closest to the intended direction of the beam. The polar pattern
above the upper limit will be the one resulting from diffraction
caused by the solid spherical body (this becomes quite directional
in the frequency range considered). This at least produces a clean
signal in the upper octave which is better than the chaotic pattern
a beamformer would produce.

On the lower end, the limits that can be achieved assuming +/- 0.5 dB
gain errors are roughly

  1st order: 50 Hz
  2nd order: 630 Hz
  3rd order: 1.6 kHz
  4th order  2.5 kHz

The latter has such a limited frequency range that it's probably
better to forget about it. The EM software wisely doesn't claim
anything above third order.

The result of this, in particular of the lower frequency limits,
is that any higher order directional pattern will have to be a
compromise between on-axis and diffuse-field frequency response.
The requirements for this will depend on the application: a spot
mic or a set of beams intended for surround reproduction. The
tradeoff can be made partly by EQ.

So when using the EM for e.g. orchestral recording using a number
of beams pointed at the various sections of the orchestra, you will
need some rather unconventional EQ for the best results. This will
probably surprise most sound engineers used to the more traditional
way of using a set of normal mics to cover the sections. It may
also put them off. But it is certainly possible to make very good
recordings with the EM.

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