Actually a week has 8 nights, but most people forget that we start the week half way through one night and finish it half way through another.
Hmm... Surely though you have half a night at the start of a week, and half a night at the end, plus six nights between the week days.
half + half + six = seven
It's probably the same reason we say "octave," because we count the first and the last notes as complete.
Which is a double-misnomer because really there 12 notes in an octave: A, A#, B, C, C#, D, D#, E, F, F#, G, and G# (since the B-C and E-F tone differences are the same as between a natural and a sharp)
A liturgical "Octave" is also eight days, say from this Sunday through to and including next Sunday.
Final f in Literary Welsh is dropped in Colloquial Welsh. You also get adref and adre, and pentref and pentre. It doesn't mean anything in particular!