One of the most common and easiest ways to improvise is by using chord tones. You can arppegiate chords and other chords found in their extensions to have lots of notes at your disposal.
Example 1: An F Dominant Chord
F7 --> [extensions] F13 --> F A C Eb G Bb D
From those notes you can spell put four seventh chords:
F7 Ami7b5 Cmi7 Ebmaj7
And Five Triads:
Fmaj Adim Cmin Ebmaj Gmin
These chords can be played over An F7 chord and will sound great. You can use different patterns too. Another concept that is important is Sequences. Seqences are melodic or harmonic patterns that immediately repeat at a different pitch. And are commonly used by most if not all jazz musicians. They are great tools to use while improvising.
Example:
F G A C G - B C D F C - A B C E B
This can also be applied to the above mentioned chords.
F A C Eb -A C Eb G - C Eb G Bb - Eb G Bb D
or like this
A F - C A - Eb C - G Eb - Bb G - D Bb Ect,
Side-Steppin' [A Half step Approach]
You can spice up an arppegiated phrase by approaching each chord tone by a semi-tone, this device was employed by many jazz musicians adds a bop-ish flavour to your line.
Example:
E F - G# A - B C - D Eb
You could also put another note before the first note of each grouping to make a chromatic sequence.
Eb E F - G G# A - Bb B C - Db D Eb
There are some notes that sound better than others on a given chord. For example, The "fourth" over a major chord is generally considered to be an "avoid" note and is usually replaced by a #4. Where as a "fourth" over a major chord is very pretty. Ultimately you have to experiment and use your ears.
Common Tones
A good way to make soloing easier is to look for common tones between chords. For example,
Fmi7 Bb7 Ebmaj7
The chord tones Ab and F are found in both the Fmi7 and Bb7 chords, and Bb and D are both found in Bb7 and Eb maj7.
Also, you can use extensions for more options.
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