HomeNotes on Amplified Fiddles

Part 4: Pickups Encode Bow Direction

Previously, I argued that a fiddle’s body must contribute less and less to the sound as live amplification needs increase. Landmarks on the road to louder sound are close mic placement, direct pickups (usually in-bridge piezo types), and solid-body electric violins. How can we neglect the fiddle’s body without making the sound unrecognizable? A likely answer is that the action of bow on string largely forms the fiddle’s essence. After all, bowing sets the violin family apart from all other instruments, and great players fully exploit the world of expression it affords.

In this article, I’ll encapsulate how bowing works and what a pickup “hears.” It’s not widely known, but a fiddle’s sound contains bow-direction information which is usually hidden from the human ear. You can think of it as analog metadata. This “directional coding” can be conserved very faithfully by pickups, and certain amplification conditions render it audible as a timbre difference between down- and up-bow strokes.

The physical process sustaining a bowed string’s vibration is cycles of stick-slip. In the “stick” phase, bow hairs drag the string in the direction and speed of bow movement. In the “slip” phase, the string disengages from the hairs, moves in the opposite direction, and carries a “pulse of force” to the bridge (more precisely a quick reversal of force direction). This cycle repeats with a period determined by string resonance—every 1/440th second for the first A above middle C, for example. I’ve simplified this description and recommend http://www.phys.unsw.edu.au/jw/Bows.html for greater depth and a helpful stick-slip animation.

During a slip phase, the “pulse of force” deflects the bridge’s top in a direction opposite that of bow motion. From a player’s perspective, this is toward the left for down-bows and right for up-bows. This translates respectively to downward or upward motion of the left (bass) foot of the bridge against the body’s top plate, since the right (treble) foot is braced by the soundpost. In turn, this implies that vibrations of all the instrument’s parts and associated air are also linked to bow direction. If a certain part is moving, say, “back” and nearby air is being rarefied when the bow is moving in one direction, then—at the same phase of the stick-slip cycle—this part is moving “forth” and the air is being compressed when the bow is moving in the other direction.

The picture below shows waveforms (see Sidebar near bottom of this page for definitions of some technical terms) of my fiddle (see Part 2) sustaining the open A. I recorded and initially displayed them using Digidesign’s Sound Designer II software. Time “0” is an arbitrary instant during the sustain, not the beginning of a bow-stroke. For a given bow direction, the pickup and mic signals are time-aligned (simultaneous) recordings—separate channels recorded at the same time. I later used Adobe Photoshop software to line up the pickup waveforms for down- and up-bows as mirror images, incidentally showing that the acoustic (microphone) waveforms are also mirror images.

Fiddle waveforms of up- versus down-bowed open A-string, using either piezo bridge pickup or microphone.

What justifies aligning the waveforms for different bow directions this way? In recordings not shown, I gently tapped damped strings near the bridge from the right and left. This simulated the slip-phase “force pulses” of down- and up-bows, respectively. Taps from the right caused the pickup’s signal to dip transiently, and from the left, to peak. Thus, as noted in the picture, I interpreted the major dips in the pickup’s down-bow waveform (which occur every 1/440th second) as slip phases; these correspond to major peaks for the up-bow. So this alignment of waveforms is not arbitrary; it places their stick-slip cycles in phase.

When two waveforms look as if a mirror is held parallel to the time axis such that one is a reflection, they have opposite polarity. It means that the signals’ oscillations have the same timing and magnitude, but a different sign (either positive or negative; there are only two possible polarities). If you touch the terminals of a nine-volt battery to those of a large loudspeaker, you may see the speaker cone push outward (sending out a pulse of compressed air); reverse the battery and the cone pulls inward (sending out a pulse of rarefied air). In the same way, the polarity of a fiddle’s sound depends on the direction of its input energy—the bow direction. Polarity is inverted by changing bow direction.

How is bowing-dependent polarity of a fiddle’s waveform significant? People normally can’t hear any difference between signals with opposing polarity, because the ear behaves more like a frequency analyzer than an oscilloscope (these devices depict harmonic content or waveform, respectively). If curious, test yourself: listen to a song on your stereo, then reverse the wires at each speaker and listen again (don’t reverse the left-right channels, but change how the two leads are connected to each speaker). Did you hear any difference? Most people cannot, most of the time. The human inability to hear polarity inversion is why I consider bow direction “encoded” in a fiddle’s sound; it is normally hidden information.

But polarity differences can be “decoded.” Notice in the picture that the pickup waveforms appear more asymmetrical (see definitions in Sidebar, below) than the mic waveforms. This is because large slip-phase “pulses” dominate the pickup’s signal, while the acoustic signal is more richly influenced by body resonances. When waveforms are asymmetrical, a polarity difference causes a timbral difference if played through a non-linear channel. Such a channel’s output is not consistently proportional to its input across its operating range. For example, a common type of non-linearity in vacuum tube amplifiers makes the gain progressively vary along a waveform’s vertical axis; one half of the waveform gets more gain than the other half. This causes harmonic distortion, and it is popular with electric guitar players because it can add body or warmth. Old recordings from the tube era can also be distorted this way, and it is still used in modern studios for effect.

But fiddle players, be warned: non-linearity makes the timbre of asymmetrical signals differ when changing bow direction inverts the polarity. In this two-minute sound file (Fiddle Polarity Demo MP3, 4.8 MB), I use my pickup-equipped fiddle and the distortion channel of my guitar amp to demonstrate. Granted, a pickup's signal is more prone to this kind of bow-direction decoding than the “less asymmetrical” acoustic sound.

Another way to detect sounds of opposite polarity is to mix them; this does not require waveform asymmetry. If sound waves are time-aligned (meaning in phase; see Sidebar, below) and identical except for polarity, they cancel each other out. Try inverting the hookup to just one of your stereo speakers; while you will hear a big difference, the exact results are hard to predict due to room reflections and differences in balance of recorded sounds between the two channels.

It’s tempting to wonder, visual effect aside, if synchronized bowing in orchestral string sections evolved to avoid mixing sounds of opposite polarity. However, many factors act to minimize polarity effects for acoustic ensembles: The fiddles (and their players) are each somewhat different, so their sounds are not identical. And no two of them have exactly the same pitch or distance to listener and walls. Most importantly, unlike stereo speakers, they are not time-aligned; their stick-slip cycles are completely phase-independent. Nevertheless, free bowing has been reported to sound more "glossy" than synchronized bowing (see http://www.stringsection.co.uk/blog/2010/03/20/up-and-down-bows). Perhaps directional coding helps explain this.

Mixing can be an important factor in pickup-equipped acoustic fiddles on loud stages.  As I said in Part 3, the body resonates with ambient sound and transfers some of its energy to the pickup (which can cause feedback). Some ambience is from instruments that sustain with consistent polarity (e.g., electric guitar or keyboard). Mixed in the pickup with the fiddle’s bowed-string polarity inversions, the ambient sound can cancel one bow direction and reinforce the other for certain notes. Solid-body fiddles avoid this hazard.

Does directional coding exist outside of the violin family? The plucked or strummed strings of guitars, mandolins, banjos, and the like can be excited from either direction, of course. But the directional information is present only during the attack, whereas bowing sustains directional bias through the entire note. Hammered or struck instruments such as pianos and percussion are usually excited from only one direction, and only for attacks. Virtually all wind instruments (and vocals) have just one directional mode: blowing (harmonicas use sucking, but I think this changes the note played; the reeds themselves are uni-directional). Accordions alternate direction of input energy but use different sets of reeds for each direction, according to my brief research. I’m sure there are exceptions out there (it's a big musical world), but polarity inversion between sustained notes seems pretty bow-specific.

I think the future of fiddle evolution will see the importance of polarity increase as more pickups are used and technology for processing, synthesizing, and “imaging” (in the Fishman sense; see Part 3) fiddle sounds slowly progresses. Probably engineers will remain the ones who are the most concerned, but I think amplified fiddle players should be aware of it. Consider it one of the trade-offs of amplification, albeit usually subtle. If nothing else, it helps us understand the uniqueness of the bowed instruments we love.

Acknowledgment: I thank John E. McLennan at the Music Acoustics Department, University New South Wales, Australia, for reading and giving me comments on an early version of this article in November 2011.

Sidebar for Part 4: Some Technical Terms

Waveforms and Linearity: Sound waveforms are basically graphs of sound waves. The horizontal axis is time, progressing left to right. The vertical axis represents instantaneous air pressure at a certain location such as a microphone or ear. This is not absolute air pressure, but the deviation from average (or ambient) pressure. Whether labeled or not, the average is at the center of the vertical axis (its zero point); positive values (upward) indicate compression and negative values (downward) rarefication. Most practical sound waveforms actually show the electrical output of a transducer, where the vertical axis can be voltage—which is ideally a linear function of pressure. A function is linear if a change in input (e.g., pressure) causes a proportional change in output (e.g., voltage) anywhere in the normal operating range of the device (e.g., mic). The output is an analog of the input (is interchangeable with it in principle). Indeed, an electrical analog of a sound wave can feed the input of an amplifier and loudspeaker which, if these are linear, faithfully reproduce the original sound wave.

Asymmetrical waveforms: Symmetrical waveforms have complementary information in their positive and negative halves—chopping off the top half and turning it up-side down makes it look exactly like the bottom half. Otherwise, the waveform is more or less asymmetrical. A waveform composed of pulses that last 1-millisecond separated by 100-millisecond intervals is “more asymmetrical” than, say, ocean swell (sharp crests and broad troughs), even though both waveforms are asymmetrical. The way I look at it, there is only one way to be symmetrical (complimentary halves), but many ways to be asymmetrical—some more significant than others.

Confusing Polarity with Phase: Commonly, signals of opposite polarity are wrongly called “out of phase” or "180 degrees out of phase" because they can cancel each other out (the irony is they cancel only when they are in phase). Some preamps have a polarity reversal switch (as a feedback countermeasure) miss-labeled as a “phase” switch. Phase properly refers only to time relationships of signals. For example, a mic mixes sounds coming directly from an instrument with sounds coming from the speakers or reflected from walls, floor and ceiling. These sounds are delayed by different time intervals depending on path length. At the mic, they may be “in phase” (reinforcing each other), “out of phase” (cancelling out), or anywhere in between (shifting the timing of phases). With the speed of sound as a constant, the exact result depends on frequency and path length. The point is: there are infinite possible phase relationships between signals, but only two polarities. Polarity only refers to the sign of a signal; two in-phase signals may have either the same or opposite polarity. Do not interchange the terms polarity and phase.

More Links to Explore

In addition to the external links cited within the text, here are some more that are relevant to this article:

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