## Stereo microphone systems [^1] ### A-B (delay-based) A-B microphone system uses two parallel [[Directivity of Microphones#omnidirectional|omnidirectional]] microphones with a clear distance. ### X-Y Blumlein pair (intensity-based, coincident) Blumlein pair uses the setup of two identical $90^\circ$ *crossed* figure-of-eights microphones, and arranged in complete symmetry with respect to the recording axis. According to Michael Gerzon, the Blumlein pair system has a most remarkable *stereo stability*. A classic Blumleinian coincident microphone pair uses two figure-of-eight microphones pointing to $\pm 45 ^\circ$, in other words, two microphones are positioned $90^\circ$ from each other. [[blumlein.png:pic]] The pickup pattern of a classic Blumleinian microphone pair can be defined as: $$ \label{blumlein} g_{XY}(\varphi) = \left[ \begin{array}{l} \cos(\varphi + 45^\circ) \\ \cos(\varphi - 45^\circ) \end{array} \right] $$ where $\varphi$ is the angle of the sound source relative to the microphone pair, $g(\varphi)$ is the response of the Blumlein microphone pair to sound signals at different angles of incidence $\varphi$, and $X$ represents the front-right signal, while $Y$ represents the front-left one. Assuming a signal $s$ originates from an angle of $\varphi$, the pickup signals's gain can be expressed as: $$ g(\varphi) s = \left[ \begin{array}{c} X \\ Y \end{array} \right]. $$ As the sound source moves from the right channel $X$ at an angle of $-45^\circ$ to the left channel $Y$ at an angle of $+45^\circ$, the captured signal would be panned from the channel $X$ to the channel $Y$, the transition can be represented as follows: $$ g_{XY}(-45^\circ) = \left[ \begin{array}{l} 1 \\ 0 \end{array} \right] \, , \quad g_{XY}(45^\circ) = \left[ \begin{array}{l} 0 \\ 1 \end{array} \right]. $$ Sound comes from the sides that have angles $\varphi$ ranged from $-135^\circ$ to $-45^\circ$ and certainly also $45^\circ$ to $135^\circ$ will make a Blumleinian microphone pair producing out-of-phase signals between $X$ and $Y$ channels. Compared to a A-B microphone system, the sonic characteristic of a Blumleinian microphone pair has weaker sense of space and depth. ### ORTF: (near-coincident) ORTF (Office de Radiodiffusion Télévision Française) is a variation on the basic X-Y coincident technique, which uses two cardioid microphones spaced 7 inches (17 cm) apart and facing outward with an angle of $110^\circ$ between them. <svg xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://web.resource.org/cc/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:svg="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" width="1100" height="600" id="svg2" sodipodi:version="0.32" inkscape:version="0.45.1" version="1.0" sodipodi:docbase="C:\Documents and Settings\Iain\Desktop" sodipodi:docname="ORTF.svg" inkscape:output_extension="org.inkscape.output.svg.inkscape"> <defs 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style="font-size:40px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-indent:0;text-align:start;text-decoration:none;line-height:100%;letter-spacing:normal;word-spacing:normal;text-transform:none;direction:ltr;block-progression:tb;writing-mode:lr-tb;text-anchor:start;opacity:1;color:#000000;fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;marker:none;marker-start:none;marker-mid:none;marker-end:none;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;visibility:visible;display:inline;overflow:visible;enable-background:accumulate;font-family:Tahoma" x="155.47887" y="682.46857" id="text4466-es" sodipodi:linespacing="100%" systemLanguage="es"><tspan sodipodi:role="line" id="tspan4468-es" x="155.47887" y="682.46857">110º</tspan></text><text xml:space="preserve" 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</g> </svg> ### M-S: (intensity-based) The M/S technique employs a mid ([[Directivity of Microphones#omnidirectional|omnidirectional]], sometimes [[Directivity of Microphones#cardioid|cardioid]]-directional to front) cartridge that directly picks up the mono sum signal, and a side (figure-of-eight) cartridge that directly picks up the stereo *difference* signal. A native MS recording pair uses a pair of omnidirectional microphone (mid, $W$) and figure-of-eight microphone (side, $Y$). [[native_ms.png:pic]] The pickup pattern of this MS microphone pair can be defined as: $$ \label{ms} g_{WY}(\varphi) = \left[ \begin{array}{c} 1 \\ \sin(\varphi) \end{array} \right] $$ where $\varphi$ is the angle of the sound source relative to the microphone pair, $g(\varphi)$ is the response of the MS microphone pair to sound signals at different angles of incidence $\varphi$, with $W$ denoting the mid signal $M$ and $Y$ representing the side signal $S$. Assuming a signal $s$ originates from an angle of $\varphi$, the pickup signals' gain can be expressed as: $$ g(\varphi) s = \left[ \begin{array}{c} W \\ Y \end{array} \right]. $$ The mid $W$ cartridge signal’s relation to the mono sum signal, and the side $Y$ ­cartridge signal’s relation to the stereo difference signal, can be expressed as follows: $$ M = \frac{1}{2(L+R)} $$ $$ S = \frac{1}{2(L-R)} $$ In other words, the left $L$ and right $R$ stereo signals are derived from the sum and difference of the mid $W$ and side $Y$ signals $$ L = M + S $$ $$ R = M - S $$ ## External resource - [https://www.michaelgerzonphotos.org.uk/](https://www.michaelgerzonphotos.org.uk/) - SCHOEPS Double MS Plugin (Plug in for dematrixing double MS recordings): [https://tonsturm.com/product/schoeps-double-ms](https://tonsturm.com/product/schoeps-double-ms) ## References [1] Zotter, Franz & Frank, Matthias. (2019). Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality. 10.1007/978-3-030-17207-7. Download: [https://link.springer.com/content/pdf/10.1007/978-3-030-17207-7.pdf](https://link.springer.com/content/pdf/10.1007/978-3-030-17207-7.pdf) [2] Ballou, G. (Ed.). (2009). Electroacoustic Devices: Microphones and Loudspeakers (1st ed.). Routledge. https://doi.org/10.4324/9780240812687 [^1]: This entry mainly developed its content by re-structuring Zotter & Frank comprehensive Springer handbook of Ambisonics. Also figures come from this book.