The Hand of Guido (also known as the Guidonian Hand) is based on the solmization which Guido is credited with having developed c.1025. The syllable names are based on the hymn:

ut queant laxis

resonare fibris

mira storum

famuli tuorum

solve polluti

labii reatum

Sancte Joannes!

Since the hymn ascends from one note of the scale to another at the beginning of each line as the music proceeds, the association between each scale tone and the syllable at the beginning of the line.

In a response to Romain Ferrari on the usenet news group rec.music.early, John Howell tells the history of the development of solmization in this manner:

Dear Romain: There is nothing legendary about Guido. We have his
writings, in which he describes his innovations. I suspect that the
situation was one that has been repeated many times in the development of
human culture. The time was right, there was a background of developments
that had not yet been codified, and one person, in one place, with
professional responsibilities that led him to seek new solutions turned out
to be the one person who did the work and gets the credit.

The "thousand years old tradition system" was simply to learn new music by
ear, listening to a teacher sing it and memorizing it. There was no system
of musical notation in general use. This held true until the middle of the
9th century, when the "Musica enchiriadis" and its companion treatise
appeared and explained how the new art of improvising a 2nd part to an
existing chant melody was done. The musical illustrations of this
"organum" were notated in a very strange but absolutely accurate pitch
notation, derived somewhat from ancient Greek music theory and based on
disjunct tetrachords with a half step between the two middle notes. It
used lines drawn across the page--one line for each note--with the
syllables of the text placed in the space over the line representing the
pitch for that syllable.

Theorists apparently used this notation over the next century, but working
musicians never did. Instead, beginning in the early 10th century, they
began experimenting with the mnenomic devices called neumes, sketched in
over the lines of text as reminders of the melodies that had already been
memorized. Hightened neumes were more exact, and one or two dry lines
scored across the page to represent fixed pitches even more so.

That is the state of musical notation when Guido was born. At about the
age of 20, he was assigned to teach the choirboys their chants, a task that
he said took about 10 years. He wanted to make the process more efficient.
Taking elements of the various experimental notations that he was
obviously aware of, he codified a notational system that used staff lines
like the enchiriadis notation but also used the spaces between the lines.
He also expanded the system of disjunct tetrachords from the enchiriadis
notation into a system of overlapping hexachords, retaining the key feature
of the tetrachords--the half step between the two middle notes. And yes,
he composed the melody to that hymn and invented the ut, re, mi, fa, sol,
la system of syllables that was still being taught in almost its original
form well into the 18th century, 800 years later!

Guido has been called a music theorist. I disagree. To me he is one of
the most inventive and effective music educators who has ever lived. His
system made it possible to teach the choirboys all the chants of the mass
and offices in two years rather than 10. It also made it possible, for the
first time in the Christian era, for a singer to read a new piece of music
accurately without ever having heard it sung.

Yes, one person can make that big a difference. But don't think that his
innovations were universally known, appreciated, or adopted. There are
books of Spanish chant from as late as the 14th century that are unreadable
today because they use the neumatic system and there are no parallel
sources in a more readable notation.

While this presents (in marvelously colorful style!) the history of the solmization, it doesn't really illustrate what it was, nor how it works. The folowing table goes some distance to fill this void (note that one of the many original versions of this table is here, at Thesaurus Musicarum Latinorum):

The table is read from left-to-right, bottom-up. The first note is Gam, the lowest note that was acknowledged in theoretical works for centuries. This note got the singular name of "ut". Properly named, it is Gam-ut, and it would be written in text as G ut. The next two notes are named similarly: A re and B mi. These notes begin the 'hard' (durum) hexachord on G. At the next note, c fa ut, a new hexachord starts, and ut is the name of the first note in this hexachord. This is a "natural" hexachord, and proper naming of the notes require naming the note letter, and each syllable from each hexachord of which it is a member. Thus, c fa ut.

The next set of notes through f fa ut follow this pattern, with two syllable names after the letter name. The next note, g, starts another Hexachordum Molle, an octave above the first, but with the b flatted. The first three scales are called "Musica Vera", ie, true, or real music. The scales formed by octave shifts, with the B changed, are known as "Musica Ficta". Note that only six notes are considered part of the hexachord, which bear the names, in order, ut, re, mi, fa, sol., la, and stand in one column of the table above. Thus, the shifted hexachordum molle that starts on f' has the notes f' fa ut, g' sol re ut, a' la mi re, b(flat)' fa mi(flat'), c'' sol fa, and d'' la sol. The e'' la at the top of the second-to-last column where the hexachord syllables are found is not part of this hexachord.

In this way, each note of the 20 in the Gam-ut is fairly individually named. Since there are only 20 notes to deal with, memorizing the full proper names of each note wasn't hard, and in fact, compared to the previous system, it was considerably easier.

Guido not only codified this system, producing the four-lined staff with the neumes which fell on lines and spaces, but he also codified a mnemonic, referred to variously as the Hand of Guido (or Guidonian Hand), Guido's Harmonic Hand, and variations in languages across Europe. There are many representations of the Hand in music tretises, beginning in the 13th century and carrying on for as long as the hexachord system was used, deep into the 16th century. Two such illustrations are in the tretises of Amerus (example CSM25-24) and Elias Salomo (example GSIII-22). The former is less schematic, better showing where the notes lie on the hand, the latter is far more legible.

Thus we have Guido d'Arezzo to thank for the basis of the staff notation that we use to this day, and the names of the notes (letter names as well as solemization), and can credit him with an idea that found life again seven centuries later in the mind of Carl Orf. In fact, many systems of mnemonic using the hand have been attempted over the centuries, as shown on the Images of Memory; Hands page at the University of Brighton School of Design.

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