Click here to purchase the entire book in PDF format. Virtual Blumlein We'll begin with a fairly simple case - two bidirectional microphones, one facing forward towards the middle of the stage (the ``mid'' microphone) and the other facing to the right (the ``side'' microphone). If we plot these two individual polar patterns on a cartesian plot the result will look like Figure 10.140. Figure 10.140: Two bidirectional microphones with an included angle of $90^\circ$, with one facing forward (blue line) and the other facing to the right (red line). The same can be shown as the more familiar polar plot, displayed in Figure 10.141. Figure 10.141: A polar plot showing the same information as is shown in Figure 10.140 Now, let's take those two microphone outputs and, instead of sending them to the left and right outputs as we normally do with stereo microphone configurations, we'll send them both to the right output by panning both channels to the right. We'll also drop their two levels by 3 dB while we're at it (we'll see why later...) What will be the result? We can figure this out mathematically as is shown in the equation below. $$S_{total} = 0.707 S_{mid} + 0.707 S_{side}$$ (11.22) $$= 0.707 \left ( \cos(\vartheta) + cos(\vartheta + \frac{\pi}{2}) \right )$$ (11.23) $$= \cos \left ( \vartheta + \frac{\pi}{4} \right )$$ (11.24) If we were to plot this, it would look like Figure 10.142. Figure 10.142: The resulting sensitivity pattern of the sum of the two bidirectional microphones shown in Figure 10.140 with levels dropped by 3 dB. You will notice that the result is a bidirectional microphone aimed $45^\circ$ to the right. This shouldn't really come as a big surprise, based on the assumption that you've read Section 1.5 way back at the beginning of this book. In fact, using the two bidirectional microphones arranged as shown in Figure 10.140, you can create a ``virtual'' bidirectional microphone facing in any direction, simply by adding the outputs of the two microphones with carefully-chosen gains calculated using Equations 10.25 and 10.26. $$M = \cos \sigma$$ (11.25) $$S = \sin \sigma$$ (11.26) where $M$ is the gain applied to the mid bidirectional, $S$ is the gain applied to the side bidirectional and $\sigma$ is the desired on-axis angle of the virtual bidirectional. One important thing to notice here is that, for some desired angles of the virtual bidirectional microphone, you're going to have a negative gain on at least one of your microphones - possibly both of them. This, however, is easy to accomplish on your average mixing console. You just have to hit the polarity flip switch. So, now we've seen that, using only two bidirectional microphones and a little math, you can create a bidirectional microphone aimed in any direction. This might be particularly useful if you don't have time to do a sound check before you have to do a recording (yes... it does happen occasionally). If you set up a pair of bidirectionals, one mid and one side and record their outputs straight to a two-track, you can do the appropriate summing later with different gains for your two stereo outputs to create a virtual pair of bidirectional microphones with an included angle that is completely adjustable in post-production. The other beautiful thing about this technique is that, if you are using bidirectional microphones whose front and back lobes are matched to each other on each microphone, your resulting matrixed (summed) outputs will be a perfectly matched pair of bidirectionals - even if your two original microphones are not matched... they don't even have to be the same brand name or model... Let's say that you really like a Beyer M130 ribbon microphone for its timbre, but the SNR is too low to use to pick up the sidewall reflections, you can use it for the mid, and something like a Sennheiser MKH30 for the side bidirectional. Once they're matrixed, your resulting virtual pair of microphones (assuming that you have symmetrical gains on your two outputs) will be perfectly matched. Cool huh?