About concepts of chromatic arpeggios over a chord (and chord-scale).
1) The chord 7-scale is split to 5-string + 4-string parts.
2) 2nd concept of CA: We substitute the voice melody M of the song with a simplicial submelody SM of it. Each note of the simplicial submelody is a note of the underlying chord. Then we extend the simplicial submelody SM, with small oscillations (within the 7-note chord-scale) 4 times faster, (e.g. if the SM has notes that are of duration 1/4, then the oscilaltion is with 4 notes of duration 1/16) around each note of the simplicial submelody. The result is the chromatic arpeggio CA-SM, which on the island of Crete is also called "condilies." The pattern of the oscillation determines the style-signature of the condilia.
3) 3rd concept of CA: We create a random sequence over the 5-string or 4-string of the underlying chord, so that it randomly sequences a uniform distribution of notes of it. This is also a chromatic arpeggio fitting harmonically to the underlying chord.
4) 4th concept of a CA: We design a melodic pattern over the 7-notes mode of the underlying chord , which is of the type: a) stationary waving, or b) Spike or c) straight vector.
If the sequenced notes are a uniform distribution of the 7-notes mode of the underlying hord then, we have an harmonically fitting to the underlying chord, chromatic arpeggio.
5) Then assume that , we are given a melodic theme M to make an improvisation with it. We identify the M , as a chromatic arpeggio CA , of a chord C. Then we compose a chord progression, C1, C2, ...Ci , with the chord C in it, and we create chromatic arpeggios CA(i) for each chord Ci. The result is a composition-improvisation based on the melodic theme M=CA.
