Any links to readily accessible definitive literature that explains what the resulting recording pattern and angle approximations would result from decoding a coincident mid-side pair using different polar patterns as the mid (e.g., omni, subcardioid, cardioid)? Let’s just assume here that the mid and side are recorded at the same dB, all else equal.
For example, running omni as the mid what relative decode combination of mid and side would result in a subcard pattern @ 90 degrees, etc.? Is there a chart?
The Dooley & Streicher paper, is a good start. If your trig is not too rusty, you can build a a simple spreadsheet to give you all these answers and more.
Thus an 1:1 M:S mix would give the following virtual XY outcomes:
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Starting M mic => virtual XY
[polar pattern] included angle polar pattern
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1. Omni => 180.0 0.500 + 0.500.cos (cardioid)
[“V = 1 + 0.cos(theta)”]
2. Subcardioid => 146.6 0.401 + 0.599.cos
[“V = 0.7 + 0.3cos(theta)”]
3. Cardioid => 126.9 0.309 + 0.691.cos (~ supercardioid)
[“V = 0.5 + 0.5cos(theta)”]
3. Supercardioid => 113.2 0.221 + 0.779.cos
[“V = 0.34 + 0.66cos(theta)”]
5 Hypercardioid => 106.3 0 167+ 0.833.cos
[“V = 0.25 + 0.75cos(theta)”]
6 Fig-8 => 90.0 0.000 + 1.000cos (Fig-8)
[“V = 0 + 1.cos(theta)”]
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(all above pertains only to non-existent perfect mics)
To generate a subcardioid virtual mic, the starting M mic has to be fatter than subcard. An omni will – logically, from symmetry considerations alone! – always generate back to back (180 deg.) virtual XY mics. And to get a subcardioid of nominal “0.7 + 0.3.cos” pattern, you would need an extra 7.36dB omni gain (M:S ratio 2.33:1).
If you doggedly want subcardioid XY at 90 deg., then you would need to start with an “even fatter subcardioid” as mid M – and apply a large dosage of M gain .For example, 11.87dB gain on a mid M of pattern “V = 0.745 + 0.255.cos(theta)” would yield a 90deg mic splay, with a subcardioid pattern of 0.674 + 0.326.cos(theta). Such an M mic is unlikely to exist.
But what you want is always theoretically posssible with a 3-mic array: (a) two Fig-8's plus an omni, or (b) double M/S, with back to back cardioids plus one Fig-8. Such arrays allow you to get any first order virtual mic pattern, at any mic angling.