The gamut; a traditional way to sing the octave. "Do" refers to C, "re" to D, etc.

The syllables are derived from a Latin hymn:

Ut queant laxis resonare fibris
Mira gestorum famuli tuorum,
Solve polluti labii reatum,
Sancte Iohannes.

Translated by dann:

"Ut queant laxis" = "just as your servants"
"Resonare fibris" = "may sing freely"
"Mira gestorum"   = "of the miracles"
"Famuli tuorum"   = "of your works,"
"Solve poluti"    = "release the stains (of sin)"
"Labii reatum"    = "from their lips"
"Sancte Johannes" = "Saint John"

"Ut" has been "do" for a long time, but it's still the gamut and not the gammado. "Sol" is still common, but I don't know what happened to si.

A more famous appearance of the gamut is in The Sound of Music, with a song that goes something like:

Doe, a deer, a female deer
Ray, a drop of golden sun
Me, a name I call myself
Far, a long long way to run
Sew, a needle pulling thread
La, a note to follow So
Tea, a drink with jam and bread
That will take us back to... (repeat)

Beside the traditional song, this new ditty is a trendier way to help children learn the scale, and to sing each note correctly:

Do, the stuff that buys me pop

Re, the man who sell the pop

Me, the guy who drinks the pop

Fa, a long way to buy pop

So, let's have another pop

La, the French word before pop

Ti, no thanks I'm having pop

That will bring us back to do, do, do, do.

I'm not sure exactly where this version comes from, but I'm sure it was some clever person who changed the words around and it passed as oral tradition.