Topic: Stereophonic Zoom Formulas

[mosquito]

Anyone happen to have figured out what the mathematical formulas for the curves in the SZ charts are?  I want to extend the charts.  I've done a guesstimate for Cards, but I'm probably going to be way off for Hypers and others.

[DSatz]

Prof. Williams has published a little book with curves plotted for all the well-known (and some less-well-known) microphone pickup patterns, as well as a great deal of explanation and useful commentary: Microphone Arrays for Stereo and Multichannel Sound Recording. I believe it is available in the U.S. from Posthorn Recordings (i.e. Jerry Bruck) in New York. However, it doesn't have the actual equations that he uses.

Alternatively, you could go to www.hauptmikrofon.de, a site run by Dr. Helmut Wittek, and click on "Image Assistant," which will let you vary the parameters of a microphone setup in real time and see the resulting effects. But that site doesn't list the equations, either. (Sorry, if it was the equations that you actually wanted!)

--best regards

[Gutbucket]

He also had a simple but informative website with extensively linked charts (far more extensive and extended than the one's in the paper, not sure of his book) outlining inumerable combinations of stereo, 4, 5 and 6 channel arrays along with 'multiple output channel format' combination arrays.   I was quite sorry to see the site disapear a year or so ago but I haven't checked to see if it's back up or not.  I'll look for the link.

Playing around with the Image Assistant tool mentioned above will probably get you the information you want, and is pretty fun to mess around with.

[Gutbucket]

His website is back up: http://www.mmad.info/

Also has all of his AES preprints availabe there as free PDF downloads- a great resource!

[mosquito]

Whoops.  My post didn't post.  (Prolly an error on my part.)

Thanks for all of those.  I did find references to Microphone Arrays for Stereo and Multichannel Sound Recording, but I can't afford a copy and have studied what's available at mmad.info and downloaded the free PDFs.  Really nice stuff.  I hadn't seen the Image Assistant though and that will be useful.  (I did look at the Java class for it, but can't figure out anything from it without a lot of work.)  It will be great for plotting some points to estimate the curves.

Here's a version of the cardioid chart that I've put together.  It's an OK estimate, but the narrower the SRA, the more off I think I am.  Note, this is really ugly and wasn't intended to be distributed.  The vertical red bars correspond to where the curves should intersect the x-axis and match the red bars in the "Mics Omni AB Spacing" chart for SRAs ±40°, ±30°, ±20° and ±15°.



Mic-SRA-03-Cardio-Extended-Estimate02.sm.jpg
Mics-Omni-AB-Spacing-02.jpg

Figuring out what the equasions are will make it much easier and more accurate to produce more and better extended charts.

I've also been looking at the polar patterns of pairs of mics to better envision their combined characteristics.  These are generic plots for XY-90° Cardioid and XY-90° Hyper.  For the cardioid chart:

- The center black curve is a cardioid pattern.

- The large black curve is the pattern for XY-90° Cardioid if the two mic outputs were summed.

- The blue curve is the summed pattern shrunk to the size of the cardioid pattern for shape comparison.

- The circle is simply a unit circle with angles measured in radians.

The chart for Hypers is similar.



Dual-Cardiod-Comparison.jpg
Dual-Hyper-Comparison.jpg

I also want to do some 3D modelling of the combined patterns because the side views aren't the same as the above view.


(And bah.  How do I manage inline attachments?  It's not working for me.)

[Gutbucket]

Unfortunatley I don't read German, but if you do I noticed a paper on Dr. Wittek's site mentioned above, which might be what you're looking for- (Theoretic basis of the Image Assistant- background information about the psychoacoustical and mathematical fundamentals of the localization curves).

I've also been looking at the polar patterns of pairs of mics to better envision their combined characteristics.

..I also want to do some 3D modelling of the combined patterns because the side views aren't the same as the above view.

In looking for a couple links for you that relate to this ^^^^^, I just dug out the post below, made in the team classial thread here about year ago.  Shamelessly self-quoting for context, this is picking up after the portion about how to use the Stereo Zoom concept-

..Williams charts are set-up to let you choose between angles and spacings for a certain SRA using a particular pickup pattern.  They also tell you a little bit about how even the distribution of instrument sources across the playback stage will be within that pickup and playback angle.  But other than that they don't tell you anything about why you might choose one combination over another.  One perhaps obvious, or at least fairly often discussed choice is a preference for either the sharper imaging of mic setups that rely primarily on level differences generated by mic pattern or the less sharp imaging but deeper and spacious sound of setups that primarily use the spacing between mics to record time of arrival differences.  Rarely discussed and I'd argue more important, especially for less than ideal situations such as this one, is the effect on the reverberant pickup of everything outside of the SRA.  I feel the sound of the room and the correct balance of that contribution with the direct sound is the most critical aspect when choosing a setup.  For me, the real value of the Stereo Zoom concept is providing the ability to hold the pickup angle variables constant and change how the reflections and reverberation in the room are recorded.

As far as the Stereo Zoom is concerned, two cardioids spaced 44cm apart and pointing straight ahead with no angle between them and two omnis spaced 44cm act identically.  They produce the same SRA and distribution of sound sources between the speakers.  But we all know they'll sound very different. One reason for that is the cardioid pair is angled so that the mics reject all sound arriving from directly behind them as a pair, whereas the omni pair doesn't favor any particular direction.

What I'm suggesting is to 'read between the lines' of the Stereo Zoom info and using it to consider ways of setting up your mics to reduce the negative aspects of the recording environment.  You could use your cardioid pair like spaced omnis and cut down significantly on the contribution of the sound bouncing off that back wall.  The more angle between the mics, the less the stereo pair acting together will limit pickup of sound bouncing off the back wall.

I find the Stereo Zoom relationship between mic pickup pattern, distance and angle between the mics very interesting and relatively easy to get an feel for.  Most recordists develop an instinctive understanding of the concept even if they may not have a clear intellectual idea of what is going on or if they've never heard of the Stereo Zoom stuff. The part that fascinates me is the huge contribution of everything outside of the Stereo Zoom SRA.  The idea of choosing a setup to cut down on the sound bouncing off the back wall is part of that.  Other important factors that I'm trying to understand more completely are the nature of the the reverberant and reflective contribution from 'that other 240º'.  Questions like: how much of the reverberance from the rest of the room is recorded as mono vs stereo information?  Were does that reverberance and room reflections appear in the stereo soundstage illusion on playback?  How differently does the stereo pair capture reverberance and reflections from above and below as opposed to the side or back. If this sounds interesting you might take a look at a thread I posted last fall which gets into that: Why Blumlein sounds more spacious than other coincident or near-so arrays The link there to Stan Linkwitz's page on Mapping from recording to playback is pretty easy to understand and explains why 48% of the total reverberation of the room is captured as mono reverberation using an ORTF pair. 

Everything I've mentioned so far considers only sound on the horizontal plane. Lnkwitz only looks at the horizontal plane as I recall, yet reverberant sound comes from all directions.  When considering the entire 3-D pickup of a stereo pair in a real room, that 48% mono reverberation figure for ORTF would be much higher still.  Michael Williams' 1991 AES paper91st AES Convention in New York - Preprint 3155« Early Reflections and Reverberant Field Distribution in Dual Microphone Stereophonic Sound Recording Systems » does a good job of explaining what happens above and below the horizontal plane.  This one was enlightening for me with 3-D analysis of both individual mics and of stereo pairs.  In most cases, the farther the source of sound is above or below the horizontal plane of the mics, the more it is recorded as mono instead of stereo information, and that happens surprisingly rapidly.

This spring I ran across another excellent paper by Geoff Martin that he's made available on his website which goes further in depth: General Response Characteristics of Microphone Configurations.  If the Linkwitz page and the Williams papers make sense, then take a look at this one. It is quite technical and through. Even if reading the whole paper is not your thing, you may get something out of checking out the colored globe images that illustrate the 3-D pickup of stereo pairs and analyzes what I'm getting at.

[mosquito]

Thanks Gutbucket.  That discussion does go directly to what I'm trying to do:  make tools that help people envision the behaviors better. 

I'm still surprised at the number of people that think of microphones like cameras and sorta consider different patterns as very similar to the differences between wide angle and telephoto lenses.  And too I'm surprised that many people don't know how to distinguish what they're hearing from what they're listening to.  (I know I shouldn't be surprised though, it is one of those things that nearly everyone does so few actually analyze it to understand how it really works.)  FWIW, I was surprised at the shapes of the combined patterns.  Somehow I convinced myself that the nulls in the separate patterns would still outweigh the pattern of the other mic, but generally they don't.

And thanks for the link to the PDF.  Some of the equations in it I've seen before, but not all of them.  My German is pretty darn rough, but I can send it through Google Translate too.