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Christianity gets its seven day period from Judaism, and it may well hearken back to Babylonian astronomy (seven planets, including the sun (Sunday) and moon (Monday)). The Romans, on the other hand, had an eight-day week with market days every eighth day (ninth counting inclusively, hence their name nundinae). In the middle ages, market towns had market days on fixed days of the week, every week, providing a commercial rhythm that had to give some rise to weekly consciousness before the twentieth century.
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while the seven day week is arbitrary, it is also worth noting that the French Revolution had experimented with a metric ten day week, which ended up being a total bust because laborers only got one week in ten of rest rather than one in seven.
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That seems like an implementation issue rather than a systemic one.

There's no reason you couldn't do off 2 on 8 or off 3 on 7 or off 2 on 2 off on 2 off on 2 or off on 3 off on 2 off on 2 or off on 4 X2 or...just about anything...

We see this today where people's schedule's aren't really in sync with the week where they'll do 4 on 3 off or split days off or 21 on 7 off (regardless of days in the month).

There are also a few people who do 6 28 hour days in a week claiming that it boost productivity because their days are longer.

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The Soviets had a 5 day week between the two world wars https://en.wikipedia.org/wiki/Soviet_calendar
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