About two thousand years ago a perfectly respectable lady called Elizabeth became pregnant and her husband lost his voice. He stayed silent as a silo until the child was born. The child was called John and when John grew up he began telling people that they were naughty and chucking them in a river. Now, if you or I tried a stunt like that we'd be brought up by the police pretty sharpish. But John got away with it and, if you can believe it, was considered rather holy for all his attempted drownings. Chaps at the time called him John the Baptist.
Seven hundred years later somebody else lost his voice, or at least had a terribly sore throat. He was an Italian chap who went by the cumbersome moniker of Paul the Deacon so he wrote a verse prayer to John the Baptist that went thuslyly:
Ut queant laxis
[O let your sevants sing your wonders on,
With loosened voice and sinless lips, St John.]
Four hundred years later, somebody set this little poem to music. He wrote a pretty, climbing melody, in which each line started a note higher than the last, until with the words Sancte Iohannes it dropped again to the bottom.
So the first note was on the syllable Ut, the one above was on the Re in Resonare, then Mi in Mira, Fa, So, La...
The problem with Ut, though, is that it's a rather short syllable and difficult for a singer to hold. Try it. So it got changed to Do (perhaps for Dominus, but nobody's sure), and that gave do, re, mi, fa, so, la and, by extension, Si for Sancte Iohannes. Then somebody pointed out that there was already a So beginning with S and you couldn't rightly have two of them beginning with the same letter. So Si was changed it to Ti.
Do re mi fa so la ti do
Which is just a shortening of a hymn to John the Baptist. The shortening technique was invented by a fellow called Guido of Arezzo.
So poor Ut was consigned to history, or nearly. It sort of survives. You see the lowest note was also known as gamma, after the Greek letter. So the lowest note of the scale was once known as gamma or ut. Then a whole scale came to be known as gamma-ut. And that is why when you go through the whole scale, you still run through the gamut.
Which means that this explanatory video is a damned lie.
Julie Andrews singing the praise of John the Baptist