# B&O Tech: Combinatorics

#26 in a series of articles about the technology behind Bang & Olufsen loudspeakers

I occasionally drop in to read and comment on the fora at www.beoworld.org. This is a group of Bang & Olufsen enthusiasts who, for the most part, are a great bunch of people, are very supportive of the brand (and yet, like any good family member, are not afraid to offer constructive criticism when it’s warranted…) Anyways, during one discussion about Speaker Groups in the BeoVision Avant, BeoVision 11, BeoPLay V1 and BeoSystem 4, the following question came up:

## Speaker Groups

Would be interesting to know how many different ‘Speaker Group constellations’ you actually could make with the new engine. Of course you are limited to 10, if you want to save them. But I guess that should be enough for most of us.

This got me thinking about exactly how many possible combinations of parameters there are in a single Speaker Group in our video products. As a result, I answered with the response copied-and-pasted below:

Multiply the number of audio channels you have (internal + external) by 17 (the total number of possible speaker roles not including subwoofers, but including NONE as an option in in case you want to use a subset of your loudspeakers) or 22 (the total number of possible speaker roles including subwoofers)  to get the total number of Loudspeaker Constellations.

If you want to include Speaker Level and Speaker Distance, then you will have to multiply the previous result by 301 (possible distances for each loudspeaker) and multiply again by 61 (the total number of Speaker Levels) to get the total number of possible Configurations.

This means:

If you have a BeoPlay V1 (with 2 internal + 6 external outputs) the answers are

• 136 constellations without a subwoofer, or
• 176 constellations with subwoofers, and
• a maximum of 3,231,536 possible Speaker Groups Configurations (including Levels and Distances)

If you have a BeoVision 11 without Wireless (2+10 channels), then the totals are

• 204 constellations without a subwoofer, or
• 264 constellations with subwoofers, and
• 4,847,304 possible Speaker Groups Configurations (including Levels and Distances)

If you have a BeoVision 11 with Wireless (2+10+8 channels), then the totals are

• 340 constellations without a subwoofer, or
• 440 constellations with subwoofers, and
• 8,078,840 possible Speaker Groups Configurations (including Levels and Distances)

If you have a BeoVision Avant (3+10+8 channels), then the totals are

• 357 constellations without a subwoofer, or
• 462 constellations with subwoofers, and
• 8,482,782 possible Speaker Groups Configurations (including Levels and Distances)

Note that these numbers are FOR EACH SPEAKER GROUP. So you can multiply each of those by 10 (for the number of Speaker Groups you have available in your TV). The reader is left to do this math on his/her own.

Note as well that I have not included the Speaker Roles MIX LEFT, MIX RIGHT – for those of you who are using your Speaker Groups to make headphone outputs – you know who you are… ;-)

Note as well that I have not included the possibilities for the Bass Management control.

## Sound Modes

This also got me thinking about the total number of possible combinations of settings there are for the Sound Modes in the same products. In order to calculate this, you start with the  list of the parameters and their possible values which is listed below:

• Frequency Tilt: 21
• Sound Enhance: 21
• Speech Enhance: 11
• Loudness On/Off: 2
• Bass Mgt On/Off: 2
• Balance: 21
• Dynamics (off, med, max): 3
• Listening Style: 2
• LFE Input on/off: 2
• Loudness Bass: 13
• Loudness Treble: 13
• Spatial Processing: 3
• Spatial Surround: 11
• Spatial Height: 11
• Spatial Stage Width: 11
• Spatial Envelopment: 11
• Clip Protection On/Off: 2

Multiply all those together and you get 1,524,473,211,092,832 different possible combinations for the parameters in a Sound Mode.

Note that this does not include the global Bass and Treble controls which are not part of the Sound Mode parameters.

However, it’s slightly misleading, since some parameters don’t work in some settings of other parameters. For example:

All four Spatial Controls are disabled when the Spatial Processing is set to either “1:1” or “downmix” – so that takes away 29282 combinations.

If Loudness is set to Off, then the Loudness Bass and Loudness Treble are irrelevant – so that takes away 169 combinations.

So, that reduces the total to only 1,524,473,211,063,381 total possible parameter configurations for a single Sound Mode.

Finally, this calculation assumes that you have all output Speaker Roles in use. For example, if you don’t have any height loudspeakers, then the Spatial Height control won’t do anything useful.

If you’d like more information on what these mean, please check out the Technical Sound Guide for Bang & Olufsen video products downloadable from this page.