ChordSpace is based on Jazz harmonic theory.
Jazz i a predominantly homophonic music, meaning that it has a single melody line working over a chord progression. This describes the overwhelming bulk of modern popular music, but jazz has the most developed and best understood theoretical base.
Typically, in such music, when a chord is struck it defines the, "key of the moment." Harmonic Theory attempts to explain what notes can be used to extend that chord, what notes sound good when played over it and what chord sounds good coming after it.
In jazz harmonic theory that basic chord will invariably be a four note tetrachord. Since jass, like most western music, deals (mainly*) in seven note scales this leaves three notes with which to extend the chord. These three notes are known as tensions.
Together the four chord notes and the three tensions also define the scale which will be used** for the melody while while the key of the moment still sounds. Once the next chord is struck a new key of the moment is set in place and a new scale will be used.
* Diminished and other 8 note scales are currently beyond the scope of ChordSpace.
** This ignores accidentals (out of key notes) which are used, typically as passing or approach notes, at the descretion of the soloist.