The MusicXML tutorial is not clear enough as to how the number in the <divisions> element is initialized in MusicXML. Is it related to MIDI files? Because I have cross checked with different samples having the same time signatures and the number keeps changing.
Divisions is an arbitrary number to allow you to specify the durations of notes independently from from the "type" of note.
You specify the <divisions> as part of the measure attributes, where it means "number of divisions per quarter note".
Then for each note within the measure you specify <duration> which determine the note's length as a fraction of one quarter note.
So in the following example, within the attributes group we are stating that there are 4 divisions per quarter note. Then, in the first note, which is a quarter note, we are stating that the note lasts for 4 divisions. The next note is an eighth note so we state that it lasts for 2 divisions, and so on...
<measure number="1">
<attributes>
<divisions>4</divisions>
<time>
<beats>2</beats>
<beat-type>4</beat-type>
</time>
</attributes>
<note>
<pitch>
<step>C</step>
<alter>0</alter>
<octave>4</octave>
</pitch>
<duration>4</duration>
<type>quarter</type>
</note>
<note>
<pitch>
<step>C</step>
<alter>0</alter>
<octave>4</octave>
</pitch>
<duration>2</duration>
<type>eighth</type>
</note>
<note>
<pitch>
<step>C</step>
<alter>0</alter>
<octave>4</octave>
</pitch>
<duration>1</duration>
<type>16th</type>
</note>
<note>
<pitch>
<step>C</step>
<alter>0</alter>
<octave>4</octave>
</pitch>
<duration>1</duration>
<type>16th</type>
</note>
</measure>