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In the final episode of Battlestar Galactica, Starbuck enters 1123 6536 5321 as co-ordinates to jump to our Earth, from the episode it had something to do with the music. I'm wondering exactly what it is to do with the music? And also if there was some out of universe significance to these numbers?

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The correspond directly to "the song" and its notes composition. There is a breakdown of it here.

1123 6536 5321 = (C#) C# D E A G# E A G# E D C#

A full description of the intent of the scoring and how it all corresponds is in this blog

I was going to quote the section of the blog that details this specific part, but it is far too long, detailed, and contains too many pictures. Go read it, it is interesting :)

However he notes that its final representation is:

This generated the coordinates: 112 carom 365 dist 365321.

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