I'm an electroacoustic musician using a single microphone input into a laptop Logic Pro audio mixing environment with 6 auxiliary channels. Each auxiliary has unique fx/eq and I can send its audio to any of the other 5 auxiliary channels via their respective input busses:
Auxiliary 1 -> Buss 2 3 4 5 6
Auxiliary 2 -> Buss 1 3 4 5 6
Auxiliary 3 -> Buss 1 2 4 5 6
Auxiliary 4 -> Buss 1 2 3 5 6
Auxiliary 5 -> Buss 1 2 3 4 6
Auxiliary 6 -> Buss 1 2 3 4 5
I'd like to calculate the number of possible bussing combinations based on whether a buss is either on or off. Not sure if this is a basic or advanced calculation as my 2nd year university calculus and stats days are far too long ago to remember the details.
Each of the 6 'switches' (aux channels) has 5 switches (busses) any one of which can be on or off (2 positions).
For instance aux 1 can have all of its 5 busses to the other 5 auxiliaries (2-6) open (sending audio) or closed, or any combination between. Likewise for aux 2 and so on.
So... does that mean aux 1 has or 32 possible switching positions and thus all six auxiliaries together would have or about a billion possible combinations?
So now, if I understand you rightly, you have an array of 5 x 6 = 30 on/off switches, each of which can be toggled independently of all the others. If this is the case, then there are possible configurations.
[Edit] Beaten to the punch by Plato!
Cool, now aux bussing possibilities is a nice bit of complexity in compositional structure. These auxiliary channels are software analogues of the channel strips on an audio mixer, they have volume faders, pan, EQ and so on:
I use them along with a single audio channel strip in live performance to create different FX loops on the fly within the 6 auxiliary channels. Their aux busses are the audio connections between them and the Audio Channel is the originating audio source.
I'd like to complicate things a bit now by introducing another concept - aux channel output can be either on (its buss is receiving audio) or off (no audio bussed to that channel). The original audio input comes from the Audio Channel with 6 busses, each of which can send audio to its respective aux channel 1-6. This audio channel strip then has = 64 possible bussing combinations sending audio out to the auxiliaries.
Two simplest case examples would be audio channel busses all off thus sending no audio to any aux (aux outputs 1-6 = off)... or all busses on to each aux (aux outputs 1-6 = on) ... and 62 other possible variations in between.
Audio chnl -> busses 1-6 -> aux 1-6 -> output 1-6
- Firstly, how many total bussing combinations would there be if I add the 6 buss audio channel to the aux bussing array?
- And of this total how many are useful (aux output = on)?