Physicists think of time and space as aspects of the same thing. Gerald Fischbach applies the same theory to bow division


It was about a hundred years ago that a Swiss patent-office clerk turned our perception of reality inside-out by proving that space and time were not distinct forms of measurement, but two ways of looking at the same thing: the space-time continuum, as it has come to be called. It takes some doing to wrap our minds around Einstein's revolutionary insight, but string players have an easier time than most, because we constantly live with our own double-perspective phenomenon: the bow-distribution-speed continuum.

The analogy isn't perfect, but it is useful. When managing the bow, time is space and vice versa. It's risky to keep track of only one and ignore the other. Continuous awareness of bow placement, distribution, stroke duration and speed are hallmarks of the highest levels of bow control.

Bow division and bow speed should be part of even the first year of study. Consider the simple folk song Long, Long Ago. With bow speed as a constant, if we use a whole bow on the crotchets the quavers take up half a bow. Or, if the amount of bow is the constant and the speed of the crotchet whole bow is, say, 20mph, the quavers will be twice as fast: 40mph.


Which plan is musically better? The bow-division plan seems better suited than the bow-speed plan to the flowing nature of the music. Its constant bow speed facilitates smooth connection of bow strokes; that also enables a constant bow pressure and contact point, ensuring continuity of dynamics and tone colour.

Our standard terms for discussing bow division are rather limited: upper/ lower, middle, frog, tip. They've served our needs so far, but in several of the ensuing examples, it will be useful to talk about eighths of a bow, as indicated below. In the music examples where these are used, the symbol indicates where the bow is at the beginning of a stroke.


Manipulation of bow speed and distribution is an endless skill. Early on the player swishes back and forth like a windscreen wiper, until trouble raises its inelegant head. More thoughtful approaches involve either symmetry or asymmetry. Symmetrical bow distribution plans are the easiest, spending the same time on down and up bows, requiring little planning to get right, often using hooked bowings. A passage from Bach's A minor Concerto features hooked bowings in almost all editions, as indicated above the stave.


Asymmetric bow distribution plans, where successive bow strokes last uneven lengths of time, require more attention from the performer but can be more eloquent. I prefer to play the Bach passage with the composer's original markings, as indicated under the stave. With these, the passage dances lightly on its feet in a way that the more militaristic, hooked bowing can't emulate.

The opening of the Mendelssohn Violin Concerto is usually performed with hooked bowings, as indicated above the stave. But the original markings, shown below the stave, help to shape an undulating phrase of considerable beauty and interest:


This approach calls on more complicated bow-stroke arithmetic, subtracting a down bow from the previous up bow, adding the subsequent up bow; being in control of where the bow is at any moment. During the planning stage, this maths is combined with a kind of bow-stroke time travel. One skips mentally to a future moment when the bow needs to be at a particular point, and then works backwards to the present, calculating the bow-stroke arithmetic to get there. In the Mendelssohn example we look ahead to the soaring five-note down bow, where it's clear we want a whole bow and therefore must start at the frog. Working backwards yields the bow-division plan indicated. The first bow stroke, minus the second, plus the third, minus the fourth, plus the fifth equals a whole bow.

Asymmetric bow-distribution plans can lead to interesting musical shapes and conversations. Asymmetric accidents, however, can cause unmusical lumps in a phrase. The opening of the Bach Chaconne contains a classic example of this. The tendency is to use almost a whole bow on the dotted crotchet chords, followed by a quaver bow 'belch' as it comes all the way back to the frog, creating an inadvertent accent on the lightest metric moment of the bar. We'll return to the Chaconne later to propose a couple of solutions.

Alternatively, when a long bow stroke, inadequately planned for, causes a player to run out of bow the result may be to play the next stroke early. The technical term for this is 'rushing'. From the teacher, the advice 'slow bow' is usually more useful than 'don't rush'.

String players go to considerable lengths to organise longer note values on down bows. My theory is that we are less embarrassed about running out of bow on a down than an up bow: few things are worse than running out of bow when moving towards the frog! This has led to some of the more serious sins of past editions and some unmusical traditions. Consider the opening phrase of the solo violin in Mozar's G major Concerto:


If we sing the melody, we naturally put an energetic emphasis on the down-beat note and sing the second note lightly. However, most standard editions suggest either two down bows or up-down. Both of these de-emphasise the downbeat and inspire an ungainly stress on the second beat. Bowing these down-up puts our power stroke on the down beat - the chord (evidence that Mozart intended a stronger down-beat than second beat), and works beautifully with Mozart's slurring of the following six semi-quavers. Many editors 'correct' this to three slurred couplets, in spite of the fact that Mozart slurs them two plus four in every solo appearance.

Bow strokes have musical 'temperatures' and sound density, depending on these variables. It can be useful to think in the following terms:

Bow stroke temperature:

slow bow = warm; fast bow = cool

Bow stroke density:

slow = opaque; fast = transparent

It's a little more complicated than that. For a warm sound, the slow bow stroke is also relatively close to the bridge and deep into the string, while a cool sound finds the fast bow stroke further from the bridge and more on the surface of the string. The same goes for opaque (close, deep) and transparent (further, lighter).

Bow speed when considered alone seems to have a linear relationship to dynamics: faster = louder; slower = softer. But dynamic changes often imply colour changes and therefore unexpected solutions can yield the most effective results. For instance, pianissimo is not piano with something subtracted; it is an intensification of the piano gesture. I usually think of piano as a warm dynamic and pianissimo as cool. Therefore, I usually play pianissimo with a faster (and lighter and further-from-bridge) bow stroke than piano.

At the higher levels of artistic control, bow speed is a 'variable variable': for expressive or tactical reasons, even within a single bow stroke, one might start at one speed and change speeds en route. In the demonic opening theme of the Franck Sonata's second movement, each of the first three bow strokes might have three distinct speeds: a fast beginning, a slower middle and a re-energised end, bringing to life the pickups to the next bow stroke:


The dark side to this capability is demonstrated by the unskilled player who starts a long bow stroke too fast, and runs out of bow towards the end of the stroke. Bow changes are smoothest when the speed of the beginning of a new stroke matches that of the end of the previous one. The player should organise a bow speed for the end of a stroke that best serves the expressive needs of the moment and must take care to start the next stroke with the same speed. An unskilled player may compound the lumpiness of a phrase with a stroke that starts too fast and slows down at the end followed by one that shoots in the other direction with a burst of speed.

A retake can sometimes be like a space-time warp, the bow magically relocating almost instantaneously to another place, or in effect making the bow longer or shorter than it actually is. The eminent 20th-century pedagogue Paul Rolland used to recommend a retake solution for the quaver in the opening bars of the Bach Chaconne, as indicated above the stave. This is an example of using a retake to effectively shorten the bow. My preference has come to be an asymmetric plan, as shown below the stave:


Bow speed has a relationship to string thickness and length. The thicker, lower-pitched strings prefer a relatively slow bow; the thinner, higher-pitched strings, faster. As you climb up any given string with the left hand, thus shortening the vibrating string length, the shorter string cries out for a faster bow stroke. You can literally hear the string calling for a change of bow speed! Its call will be a pressed groan when too slow on the higher strings in higher positions, or a kind of whistly pitch-deficient sound when the bow is too fast on the lower strings in lower positions. For happiest tonal results, the sounding point is relatively farther from the bridge for lower strings and pitches, closer for higher. Likewise, long, thick strings prefer more pressure than short, thin ones.

Chords are classic examples of this relationship between bow speed and string thickness. In an arpeggiated chord, the lower note or notes in most cases should be played with a slower bow speed, the upper notes faster.

Harmonics require special attention regarding bow speed, as well as sound point and pressure. The image we have of harmonics tends to be that of something requiring lightness of touch. In fact, only one factor is appropriately described as light - the fourth-finger pressure (or sometimes that of the third finger). When the harmonic is a strong gesture, then even that should be strong. The bow stroke should be authoritative rather than light, with a markedly faster bow speed and correspondingly more bow than for a stopped note. The bow's sounding point should be four times as close to the bridge as that of a firmly stopped finger.

Once you open the floodgates of awareness of bow speed and division, the endless expressive possibilities wash over you and your universe of artistry is changed forever.

This article was first published in The Strad's September 2004 issue.