Topic: Stereophonic recording angle - a nerd approach

[matsa]

What bugs me is the lack of detail in the Williams diagrams. The iso-SRAs are just not detailed enough, in particular the frustrating gaps between 30°, 40°, and 50°!
From the page http://www.sengpielaudio.com/Visualization-ORTF-E.htm (some discrepancy from Williams, but a more recent and strict approach) I extracted data for SRA as a function of Micdistance and Micangle. I fitted the data to the least inaccurate function (out of ~275) and came up with the following (R^2=0.996):
SRA=20,1900424+3943,5811374038926*(((0,0328265208*Micdistance+5,11867762)^(-7,70454293))*((0,000002187212904*Micangle+0,0000323917522)^(-1,032215267)))

Now, I realise that this is NOT helpful in any way, but plugged into a smartphone (using e.g. the PowerOne free app on my iPhone) I can find more accurate values for mic distances or angles for any given a required SRA. The accuracy of the fit is within +/-3°, which is pretty much better than what you can attain with your protractor or interpolating from Williams charts on the fly anyway. (I have uploaded the equation to some kind of PowerOne library four your convenience - you should be able to find it if you look for SRA in there.)
Note: The fit is only valid within the ranges given by Williams. The values were extracted in the ranges of 0<Micdistance<50cm and 0<Micangle<120°. Outside the given range, and at some edge regions the fit breaks down and gives erroneous output, so always check your Williams charts.

Thoughts? 

[page]

well done.

I've always been lazy and just pulled up the sengpiel site on my smart phone when I forget to do the estimates at home before hand, but I understand that's not an option for everyone.

[Gutbucket]

Strong mathwork! The nerd region of my brain congratulates you and is always thrilled to find comraderie in recording geekdom.

Yet the practical 'applied use' side of my brain asks why anyone would need a more accurate answer to begin with.. compounded with the ability to quite easily estimate a more accurate approximation by simply looking at the values which are listed on the diagrams and choosing one that lies between them.

I've yet to find a good answer or come to a firm conclusion on when choosing a slightly larger or smaller SRA than the Orchestra Angle is appropriate and by how much.  If that more basic issue is in question, how important is it to have a more accurate answer?

I think all this SRA stuff is helpful, but best used as a general guideline in combination with a number of other variables, all of which are important in choosing the most appropriate setup for any particular recording situation.

[MIQ]

Hi matsa,

Thanks for posting your findings.  It looks like the equation you created is for cardiods.  I plugged it into Excel and tried a few configs.  It matches the Sengpeil SRA results pretty well within the limits you call out.  Nice!  The SRA results at mic dist = 0 are quite different between Sengpeil and Williams.  Sengpeil has choosen 18dB as the difference in mic level that describes the SRA while Williams has used 15dB.  To be really geeky you can add Wittek/Theile into the mix  .  They are the creators of the Image Assistant http://www.hauptmikrofon.de/ima2-folder/ImageAssistant2.html.  They use a mic level difference of 15.8dB for coincident SRA calculations (closer to Williams). 

As Gut mentioned. the accuracy is nice to have when doing the calculations but setting the SRA exactly to the "orchestra angle" is not always the only solution worth considering. 

-MIQ

[matsa]

Thanks!
I agree with you all. The actual usefulness of this whole thing is - as you all politely pointed out - questionable at best.
I was trying to get a feeling for the SRA and the Williams charts were too low resolution. As I was looking for an app, the only one I found wasn't really usable.
Not sure if I will use the results myself, but in principle I like the idea of not having rough estimates early (because of error propagation).

Anyhow, since the process is rather quick, I also extracted the data from Williams charts for cardoids and made a good (+/-3° error) fit for up to 40cm and 140° micangle: SRA=24,9135+(((-0,493607Micdistance+53,1948)^(4,81333))*((9,14511Micangle+584,9)^(-2,06015)))

/Matsa

[stevetoney]

^ You're only taking this out to 4 (or 5) significant digits.  Are you sure that's enough?!?   

He he...joking.

[matsa]

Well... the 584.9 was actually 584.9001, so I'm still on 6 significant digits. Sorry, mate...

On a serious note - can this be good for anything? Ever? Really?
I circled back to my original frustration, fitted the low SRA angles (which gave the largest errors) separately and carefully. Used the function to fill in the gaps in Williams plot (for cardoids).

Enjoy