Thank you sir D. Safe travels.
Ungleyug: Not magic when you know how it works, but can still be awe inspiring. I use a similar ambisonic decoder and it's pretty amazing even knowing what's going on under the hood!
Still doesn't make any sense to me.
The way i understand the double MS, there are two cardioid elements one at 0 degrees and one at 180. By summing and phase, one can arrive at a single, mono microphone pattern- in largely the same way dual diaphragm LD microphones can have a continuously variable pattern (let's not debate weather or not the "omni" pattern created is "real").
In the schoeps DMS decoder, that rear facing cardioid microphone can also give rear channel information.
But, if there is no rear facing element, how can the pattern be varied at all?
You have it right. I'll work though it..
Here’s the deal: A cardioid pattern is equivalent to the sum of and omni and a figure-8 mixed at equal signal levels.
If you have forward and backward facing cardioids, then a straight sum of the two adds their omni components. The figure-8 components of the two cancel out, since they face opposite directions and have opposite polarity. So you end up with just the omni part X 2.
If you change the polarity of one of the microphones first (say the backward facing one) then the omni components have opposite polarity so they cancel out and the figure-8 components add together so you end up with just the figure-8 part X 2 (forward facing).
By mixing the two in different amounts (changing the ratio) you get different patterns between omni and figure-8. And by changing the polarity of one or the other you point that pattern forward or backwards. Cool so far?
What the Dual M/S plugin probably does is apply capsule equalization to the files first, then sums the forward and back facing cardioids and divides the result by 2 to get an omni. It also takes the same forward and back facing cardioids and inverts the polarity of the back one before summing them and dividing by 2 to get a forward facing figure 8.
The plugin then has 3 basic patterns to work with: an omni, a forward facing figure-8 and the side facing figure-8. That’s horizontal only ambisonic B-format. It’s then straight forward to mathematically derive first order patterns pointing in any horizontal direction, with patterns and angles independent of each other.
If the rear facing cardioid isn’t there, the program does the same math. It sums the forward facing cardioid with zero (the missing back mic) and gets a forward facing cardioid instead of an omni. It also sums the forward facing cardioid with the inverted polarity the missing back mic (negative zero) and gets a forward facing cardioid instead of a forward facing figure-8.
It then does the same B-format processing, but the omni (W component) and the forward facing figure-8 (Y component) are actually forward facing cardioids instead of the expected omni and 8. So if you set the program to give you just a mono omni, it thinks it is doing that and displays an omni on screen, but the audio output is a forward cardioid.
Without the extra back facing cardioid, the output of the plugin becomes standard two channel M/S decoder, but the graphics and controls don’t realize the back cardioid is missing and still act like it’s working with all three signals.
The reason I suggested dialing in a mono mid and changing the pattern from omni through figure-8 and back and listening for timbre vs level changes is because if what I outline above is correct, the actual audio output will be a forward cardioid for all of those settings, but the output should increase in level as you adjust things toward the cardioid position in the middle of the adjustment range and decrease in level towards the omni or figure-8 settings. That’s because the plugin is expecting the rear facing cardioid and is still dividing the sums involving it by 2. If you specify a forward facing cardioid, it doesn’t do that and the resulting output level should be higher.
If you did include the backward facing cardioid input, then doing the same would change the pattern from omni through cardioid to figure-8 as expected (and as displayed) and the timbre of the sound would likey change, but the level should not.
Hope it makes sense and I hope I got it all straight.