The Natural


Steve Wallace is awesome – string bass virtuoso, blogger extraordinaire, humble humanist, wit galore. Today we examine his left hand. It wanders, and in a good way.

It strays from the bass fingerboard the way Roberto Luongo strays from the net. Or the way Jacoby Ellsbury strays from first base. I have no idea who these people are, but Steve enjoys baseball and I thought that including a sports analogy here would be appropriate. Steve’s left hand likes to stray from the fingerboard to turn tuning pegs.

Depending on the piece, Steve will retune his strings 5 or 6 times per minute, deftly moving his hand from fingerboard to pegs in milliseconds. It is exciting to watch because his timing and taste are impeccable, and you almost want him to make a mistake, but he doesn’t. He never misses an entry – perfect notes, perfect rhythm, flawless performance.

So, why does he do it? My theory lies in physics. Not the conscious kind of physics requiring analysis and thought, but the kind of physics that thousands of hours and mountains of talent have transformed into something as natural as breathing.

Instruments tuned to equal temperament, such as the piano, can never be in tune with the natural harmonic series. By design, the intervals (5ths, 4ths, 3rds and 2nds) that lay between the tonics are arrived at mathematically to provide an equal distance between each semitone in the chromatic scale.


The above staff illustrates a natural harmonic series from low C (1st harmonic) through high C (16th harmonic). The plus/minus figures above each harmonic represent the pitch deviation between equal temperament and the natural harmonic series. For example, harmonic number 5, representing the interval of a major 3rd above the tonic, resonates 14 cents below the equal temperament major 3rd. That is, if a piano is tuned to A=440 Hz, the major third above A in equal temperament would be C#=554 Hz. However, that same major 3rd in the natural harmonic series would be C#~550 Hz representing an almost ~1% deviation in pitch.

Why does this matter? Let’s say that Steve is playing a jazz standard in the key of Bb (such as One Note Samba or My Foolish Heart or 12 Bar Blues) and he chooses to play his open D string. If the piano is playing a root Bb chord, Steve’s D (the major 3rd) is 14 cents sharper than it should be. If the piano is playing a three chord (a D minor or D major), the note is exactly in tune. If the piano is playing a six chord (a G minor or a G major), the note is 2 cents flatter. When appropriate and more so in ballads than bebop, Steve will twist the tuning peg to make the open-string pitch work within the chord.

The open strings on an upright bass are the notes E, A, D and G. It is a monstrously cerebral exercise to calculate how the pitch of each open string can be represented in every chord in any given key signature. As a tune moves forward through its chord progression, finding a pitch compromise on the fly and making each note fit in the context of its root and inversion is almost impossible. Yet the best of the best do this for us, albeit sometimes unconsciously, and it is these micro-adjustments and attention to detail that elevate our appreciation of music.

Art isn’t easy.

I know that if I was to ask Steve to confirm this roaming, flying-fingerboard, pitch-theory he would say “What?” and with a confident smile shift the subject to the Toronto Blue Jays. Thank you, Steve Wallace, for doing what you do so very well.

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