This article, describes techniques to improvise over chord transitions X1->X2 based on a choice of a chord scale S(X) of each the chord X (e.g. chord scale or scale of a chord of the C major chord may be the Ionian mode of the C major scale)
Arpeggiating in such a scale is considered as an improvisation fitting to the chord, under the rule that more than 50% of the time (that because of the uniform arpeggiation it means more than 50% notes of the scale of a chord ) the notes have more than 50% of intervals relative to the notes of the chord that are melodic (3rds) or harmonic (4th or 5ths) rather than chromatic (2nds).
Arpeggiating the scale means that more or less in the average we have a uniform distribution of the duration of the notes of the scale , which is a statistical concept.
Then the chord transition X1->X2 can be improvised by
1) Common notes of the 2 chord scales S(X1), S(X2)
2) Vector-chord arpeggios (=chord-closure arpeggios e.g. chord closure of the chord c-e-g is the c-d-e-f-g) of X1 , X2 inside S(X1) S(X2) that are the closest possible
3) Same pattern simple arpeggios over S(X1) , and S(X2) and although we change scale we do not change the arpeggio pattern.Here the common featute of the improvisation betweenn the 2 chords is not common notes but common rhythmic arpeggiating pattern.
ETC.
Here are 4 videos that explain it with piano.
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