Fairly straightforward question, really!
Is there an equivalent (I don't think it's a particularly controversial point) and what do you call it?
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I personally have done 16 mise en scenes and the perfect translation of mise en scene for in soud is Bresson. Bresson is a play of foleys and minor play of ambiences. However here the foleys are most important. A foley as unimportant as clothes rustle is given more importance and is dynamically larger. If you need I can send you references of my own mise en scene which you can refer to understand and get a better idea of it.
In Bresson the use of BGM is very minimal and its as good as not being present in your sound track. Bresson is very difficult to achieve as you try to define the narrative through diagetic and non - diagetic sound. Because there is no BGM to support your narrative, there is a huge strain on the sound design. You have to foreshadow your emotion through sound. It is very difficult and pretty difficult to achieve. Its Even more difficult to bridge gaps between scenes through sound.
The sound equivalent of mise en scène would be soundscape / soundtrack. Mise en scène is a term used to describe a number of different visual design elements such as set design, space, lighting, costume etc. The term soundtrack (or soundscape in theatre) is used in a similar way and can be equally broken down into categories such as dialogue, ambiance, sfx, music etc.
I think mise en scene relates to all aspects of film production, including sound.
Because it means "putting on stage" or something like that, i think it can be interpreted as pertaining to anything that has been put into the world of the film. Things like the blocking of the actors, or the way a set is dressed; but also the inclusion of a loud highway outside, or neighbours having loud sex on the other side of the wall.
It's kind of an ambiguous term for me, but that's my basic take on it.