I believe that Nando may have been thinking about reproduction with
loudspeaker arrays. He has a system with eight loudspeakers on the
horizontal plane, as do I. So good up to third order. But I actually have
24 full-range loudspeakers available. Would it be advantageous to expand
our systems to higher order? I've been asking this question for a very long
time. With higher order program material slowly becoming available, perhaps
we can find out.

Eric Benjamin

On Thu, Dec 2, 2021 at 5:57 AM Jens Ahrens <jens.ahr...@chalmers.se> wrote:

> Hi Fons, hi Nando,
>
> Please excuse that I’m responding to both of you in the same mail. There
> is sufficient overlap in the matters to keep the thread from diverging.
>
> @Fons: Thanks for the clarification! We will look into this.
>
> @Nando: (The question was what the high orders contribute.)
>
> It’s hard to tell how exactly the high orders contribute. One aspect is
> the interaural coherence that needs to be appropriate. The other main
> aspect is what I typically term the equalization: Below the aliasing
> frequency, things are fine anyway. Above the aliasing frequency, the
> spectral balance of the binaural signals tends to be more even the higher
> the orders are that are present. The deviations from the ideal spectral
> balance also tend to be less strongly dependent on the incidence angle of
> the sound if higher orders are present.
>
> Much of the angle dependent deviations of the spectral balance can be
> mitigated, for example, by MagLS so that the perceptual difference between,
> say, 7th order and infinite order is small. I can’t tell if it gets any
> smaller with higher orders. My (informal) feeling is that somewhere between
> 5th and 10th order is where the perceptual difference to the ground truth
> saturates, both in terms of equalization and the coherence.
>
> Best regards,
> Jens
>
>
>
> > On 2 Dec 2021, at 11:20, Fons Adriaensen <f...@linuxaudio.org> wrote:
> >
> > Hi Jens,
> >
> >> I’m attaching Fig. 1 from the JASA article.
> >
> > Nothing was attached (or it got lost...)
> >
> >> If I’m not misreading, then the 7th order is available somewhere between
> >> 2 kHz and 3 kHz and higher. Aliasing kicks in at around 4 kHz-ish.
> >
> > So the question is if this small range (less than one octave) actually
> > contributes anything useful.
> >
> >> My guess is that it is not more or less sensitive than SMAs.
> >
> > I'd agree.
> >
> >> I’m as close as a few centimetres to the surface of the array. This
> >> triggers a lot of the high orders at low frequencies, and if there
> >> is something that is not ideal, then the low frequencies tend to go
> >> through the ceiling.
> >
> > If they don't that could just be because their contribution at LF
> > is filtered out anyway, e.g. if your A/B process includes high pass
> > filters of an order at least one higher than the order of the
> > component they act on.
> >
> >> How would I be noticing if the microphone mismatch is above
> >> the tolerance level?
> >
> > One way uncalibrated capsule gains will show up is that after
> > binaural rendering you get significant ILD at LF, which should
> > never happen except for very close sources.
> >
> > This actually happened recently with a binaural rendering system
> > I was working on. When the room sound (early reflections and
> > reverb tail) was added, this resulted in excessive ILD at LF,
> > and a perception of the room sound that was clearly biased to
> > one side.
> >
> > The room sound in this case was from a real room, measured using
> > an SMA. Analysing these measurements revealed capsule gain errors
> > up to +/-3 dB. When these were compensated for, the problem
> > disappeared.
> >
> >
> > You could just measure the B-format polars at LF, but that would
> > require an anechoic room.
> >
> > You could instead compute the theoretical capsule signals for a
> > set of directions, apply some gain errors, send the result through
> > your A/B process, and plot the result.
> >
> > The only thing that mitigates this problem is statistics: with
> > a high number of capsules contributing to each harmonic, errors
> > tend to average out to some extent.
> >
> > Ciao,
> >
> > --
> > FA
> >
> > _______________________________________________
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