Whence 556?

[Chuck Guzis]

List:

This is one that's bothered me for most of my adult life.  As you may or
may not know, there were three industry standard densities for 7 track
1/2" tape:  200, 556 and finally 800 cpi/bpi.

So 200 and 800 are nice decimal multiples of 10.   But 556 doesn't fit
that pattern--it's not a "nice' number, being the product of 4 and 139
and doesn't correspond to any computer-related characteristics that I
know of. It's not metric.  So why 556 and not 400, 512 or 600?

There's got to be a story there, somewhere.   I think the 556 density
came in around the 1401/7090 time with the 729 II.

Anyone know the story?

--Chuck