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"Good improvisation communicates harmonic progression melodically. Effective melodies manipulate harmonic content through the use of guide tones and preparatory gravity notes, masterfully woven in systematic tension, release, and transparent harmonic definition."
Many students come to their jazz mandolin lesson wanting to learn about advanced chord substitutions and leave with an assignment that challenges the student to develop better timing. This seems to be an area of study that most aspiring musicians tend to skim over. Maybe this happens because talking about altered notes, arpeggios, tri-tone subs, and modes can be really fun and somewhat sexy, where a discussion on eighth notes seems downright dull or boring.
Please allow me to introduce you to the most important musical idea in jazz. The Mighty Eighth Note! The eighth note is the standard unit of measure in jazz and many other musical forms. A quarter note is merely a note that lasts for the duration of two eighth notes. A half note lasts for the duration of 4 eighth notes. Most jazz melodies are built primarily out of eighth notes because eighth notes used in a syncopated style is a fundamental part of what we call "swing". If we are playing a quarter note based melody, and it just won't swing, we can displace some of the melody notes by an eighth note to create some syncopation, resulting in a better swing feel.
The best advice I ever received about improving my jazz feel was to practice playing a steady stream of eighth notes while the metronome clicked on beats 2 and 4. This is not anywhere near as easy as it sounds. Most people struggle with this at first, but those who stick with it will eventually get it. The end result will be a much smoother delivery of eighth note passages whether they are written or improvised. This ability to relax and stay in sync with the metronome should also make it possible to play much faster.
As mandolin players, we need to take a close look at pick direction and decide how pick-strokes can relate to timing. I believe at slow to medium tempos, playing notes with all down-strokes provides a rich, full-bodied sound. At higher tempos we will need to use alternate picking but remember that alternate picking is not just down-up-down-up. Alternate picking is a technique where all strong beats or numbered beats are played with a down-stroke and all weak beats (ands) are played with up-strokes. This makes many jazz lines tricky due to the fact that many melodies are syncopated and begin with the up-beat (and). The general rule of alternate picking is "numbered beats" are down, "ands" are up.
I have put together this short video demonstrating this practice technique. You may want to do yourself (and your band mates) a favor and spend a little more time on the Prince of all notes, The Mighty Eighth Note. You will be glad you did.