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Sequences-Part 2

by Matt Raum

In the last issue I introduced sequences. Before moving on, I thought I'd give you some more sequences to study. They're just so useful. What is music (or any art) but mathematics? Shapes, patterns, intervals, sequences. Last issue I wrote some example sequences in notation, tab, and also as numbers.

Ex: 1-2-3-4-2-3-4-5-3-4-5-6-4-5-6-7...

Play that on your instrument and you will hear that mathematical thought expressed musically. Look at the numbers above and you can see it expressed numerically. Below I've tried to express that thought geometrically.

                   5-6-7-8
               4-5-6-7
           3-4-5-6
       2-3-4-5
   1-2-3-4

In all the examples I provided last month, I had you play the sequence ascending, then descend in the mirror image of the sequence. Let's do that, also, to the geometrical expression of the musical thought above.

               5-6-7-8-8-7-6-5
            4-5-6-7        7-6-5-4
         3-4-5-6              6-5-4-3
      2-3-4-5                    5-4-3-2
   1-2-3-4                          4-3-2-1

Now, musically, again.

It may seem a little abstract. You're unlikely to think of geometry while you're playing Soldier's Joy. I think it is useful, though, to think in new ways about music, and the examples above, I hope, show the beauty of sequences and the relationship of music and mathematics. Music is magic, but a magic based on logic.

Enough philosophy, here are some more sequences.

This one is a descending pattern, ascending through the scale. Kind of like walking down backwards on an escalator going up. When you get to the second floor, you'll get on the down escalator and try to walk up backwards.

This one ascends two thirds, descends one third, then does the same on the next scale degree. Two steps forward and one step back. That's life, my friend. This also leads nicely into my topic for the next issue, arpeggios.

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Matt started playing guitar at age eleven and was first interested in old time blues. The blues led to the Allman Brothers which led to the Grateful Dead which led to the David Grisman Quintet which led to Matt switching from guitar to mandolin. In June of 2000 he moved from North Dakota to Nashville. He has since won the Tennessee state mandolin championship in Clarksville and twice placed third at Winfield. He has played with the Nashville Mandolin Ensemble, the Hot Club of Nashville, Roni Stoneman, and various local bluegrass and country bands. His first book for MelBay, Mandolin Technique Studies, was released in September of 2004 and a follow up book is in the works.