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Left-Arm Positional Sense: Shifts, Placements, Intermediate Notes and Distance Measuring

In this article, we will look at different aspects of our left-arm positional sense. In other words, we will try to answer the question “how do we know where our left hand is on the cello fingerboard” ?

Obviously, after sounding any one note, our ears tell us where our hand is on the fingerboard. We could call this our “aural positional sense” (see below). The term “left-arm positional sense” however refers to something quite different. It refers to our ability to know (sense) where our hand is on the fingerboard (on which note we have our finger) before sounding any note. This is one of the most fundamental skills of playing a string instrument, and is also one of the most difficult to acquire.

Every different note, on each of the four strings, played with each of the five fingers (including the thumb) has its own unique coordinates of angles and postures, of the fingers, hand, wrist, arm and shoulder. Even if we just consider the most commonly used notes, this still gives us several hundred minutely different sets of spatial coordinates that our body and brain need to learn, memorise and automate. But this is just the simplified version: the reality is in fact even more complicated! The hand postures necessary for those notes that precede and follow the playing finger greatly affect the hand position of the playing finger, which means that the same note, played with the same finger, can have quite different postures (coordinates) according to what comes before and after it. Consider, for example, the difference in hand posture between the first finger on any note in extended as compared to non-extended position.

A computer (or SatNav/GPS) would remember and learn these coordinates as numbers, but we remember them as spatial, kinesthetic “feelings”: each finger on each different note has its own unique “feel” that we get used to. The memorising, classifying and automation of this positional information is what requires string players to practice so much. If we don’t practice enough, our fingers soon start landing in the wrong places (out of tune, or not squarely on the desired string) because our body and brain gradually forget the fine details of exactly where each note is.

The more spatial information (coordinates) we can give to our brain and body, then the more security we will have at the moment in which we need to find (retrieve) that note. Fortunately, there are several mechanisms involved in the skill of “knowing” where the notes are before we actually sound them. We don’t just have one “positional sense”: in fact, our positional sense is made up of all our other senses with the exception of taste and smell! These different senses (mechanisms) overlap and reinforce each other. We will look now, one at a time, at these different components of our positional sense, working upwards from less sensory information to more.

THE DIFFERENT COMPONENTS OF OUR POSITIONAL SENSE

To build up progressively to our final, ultimate, refined, highly developed positional sense we will start from a situation with an absolute minimum of sensory input. There are four different stages in the progression from minimum to maximum sensory input, each stage corresponding to the addition of a new sensory mechanism. Each of these different sensory mechanisms has its own dedicated page (click on the highlighted link):

1: we are playing initially in absolute darkness, with our ears completely blocked, and with the tips of our fingers anaesthetized! Here, the only sensory signals we are receiving are the purely internal, subjective sensations concerning the position of our body parts without any relation to external objects or stimuli. This sense is called our Kinesthetic Sense. Here we are in the same situation as a deaf singer.

2: next, we will give our kinesthetic sense a bit of help. We are still blindfolded and deaf but now we will take away the local anaesthetic in our fingertips, thus adding another very important means of knowing where we are on the fingerboard: our sense of touch, or to be more scientific, our Tactile Sense.

3: next, let’s add another source (layer) of sensory information by taking off our blindfold (or switching on the lights). Now we have added our Visual Sense.

4: finally, we will unblock our ears to allow ourselves to receive the ultimate positional information: Aural Sense

POSITIONAL LOCATION ON DIFFERENT (NON-CELLO) INSTRUMENTS

For finding their notes, singers have no need for either the tactile sense or the visual sense because all of their positional references are internal: the musician is the instrument. Most other instruments have external visual (and/or tactile) reference points such as keys, holes, and frets, which tell the player exactly where their fingers are before they actually sound a note. Based on these physical reference points, the musician can see or feel exactly where their fingers are at all times, and thus know with absolute security, before even sounding (playing) a note, which note is going to come out. If the musician’s finger is not perfectly situated on the desired key (hole, fret etc.) they feel it immediately and can correct their position before sounding the note.

SPECIALITY OF STRING PLAYERS: THE NEED FOR BOTH VERTICAL AND HORIZONTAL POSITIONAL SENSE

For string players, finding our desired note requires basically two positional choices: the “vertical” (up and down the string = pitch) and the horizontal (on which string am I on?).

For our horizontal positional sense, we string players have the invaluable help of clearly defined tactile and visual-spatial references: our four strings. The strings are a lot like the valves on a brass instrument: thanks to them we know exactly where our fingers are on this horizontal axis (i.e. which string am I on?) before we sound them. Each string is a clearly defined visual and tactile spatial reference point. But, just like for a brass player, finding the right string (valve) is only a small part of finding our desired note. It is as though each string (or valve for brass players) was a different instrument. First, we choose our instrument (= string = horizontal placement) then we find our note (vertical placement). This “horizontal” aspect of left-hand positional sense is dealt with on the page “Left-Hand String Crossings“.

“Vertical” positional sense refers to our ability to know where our hand is in the vertical plane, running up and down the string (pitch). Finding the right string without any aural references is easy, because we can see and feel the different strings, but finding the correct pitch on each string is much more complicated. This is because on this vertical axis, we are seriously deprived of clear reference points: the fingerboard is totally smooth and our only real physical point of orientation is the corner (crook) for the thumb under the fingerboard at the end of the cello-neck (“4th position”). This is a much more difficult skill to acquire and is the subject of the rest of thisarticle.

LOST IN SPACE: THE STRING PLAYER’S VERTICAL SPATIAL CHALLENGE

This lack of tactile reference points on the fingerboard means that our vertical positional sense – our map of the fingerboard – has to be mainly internal. Finding notes without any physical references is the equivalent of “perfect pitch” for a singer: we often need to just “know” where a note is found, before sounding it, by how it “feels” for the arm and hand (and also by how it “looks”).

This lack of clear spatial references constitutes one of the principal difficulties of playing a string instrument: finding our way around the fingerboard is a little like walking around blindfolded. Sounding a note, for us, is the equivalent of a blind person touching something that allows them to know exactly where they are. Playing a note out of tune is our equivalent of a blind person losing their orientation and bumping into something accidentally: this is the negative feedback telling us that we are not where we hoped we were! On the fingerboard, it is almost as if our left hand was essentially “lost in space”, or more precisely, lost in four parallel outer-spaces (one for each string).

But at the same time, this lack of definition is also one of the main elements contributing to the expressiveness of string playing. We, like singers, are able to not only tune the notes exactly as we wish, but also to connect the pitches (vertically) exactly as we wish. We can choose the desired degree of separation anywhere between the extremes of a complete clean separation (finger articulation) to a seamless vocal connection (glissando), according uniquely to musical criteria.

“Knowing” where all the notes are on our 55 cm of fingerboard is a skill that requires enormous precision: a 1mm “error of judgement” can make the difference between musical life and death (beautifully in tune, or horribly out of tune). This is why so much of our practice time is dedicated to just “getting a feel” for exactly where the notes are (playing “in tune”). Consider the relative ease of finding notes on the piano – not only are they spread out over almost double the distance of the cello fingerboard, but also each note is clearly visible, and both clearly differentiated and equidistant from the others. They are much easier to locate accurately than the notes on a string instrument. No wonder pianists are able to play a lot more notes at the same time than we do! Finding notes on the violin requires even higher (finer) spatial precision than on the cello, because the violin fingerboard measures approximately half the length of the cello fingerboard.

THE SPACE WARP: EXPONENTIAL ? LOGARITHMIC ? DEFINITELY NOT GEOMETRIC

Navigating the fingerboard is made more complex by the fact that the distances between the notes on any one string are not geometric (regular, equidistant).

On keyboard instruments, the notes are all equally spaced over the entire range of the instrument, meaning that the physical distances between the notes do not change as the hand goes up and down in pitch. On string instruments however, the physical distances between the notes become smaller as we go higher up each string. For example, on the cello, the one-tone interval in the first position (for example between Bb and C in first position on the A-string) is produced by a finger spacing of approximately 7cm. But that same 7cm distance represents a progressively larger (wider) musical interval as we move it up the fingerboard. The following musical intervals are those that are sounded when we place our lowest finger on different notes (on the A-string) and reach up 7cm to a higher finger. This distance will be less than 7cm on smaller cellos, and greater on cellos with a longer string length.

In the above examples, we can see that the same finger-spacing (distance between fingers) produces gradually increasing musical intervals as we move up the fingerboard. To illustrate this same phenomenon from a different perspective we can measure the finger-spacing distance required to give the same interval in different parts of the fingerboard. The octave interval gives us a nice, clean, Pythagorean relationship: it appears that as we go up the fingerboard, each octave leap requires half the distance of the previous one. For example:

We can continue this curious and fascinating “game of distances” using the harmonic series. If we divide any string into equal portions (segments), on each of the nodal points (at which the previous section finishes and the new section starts) we can sound a naturally occurring harmonic. Let’s look at the distances (musical and physical) that result from dividing the string into three, four, five and six equal sections.

In the above example we can see that as we go up the fingerboard in equal-length steps, for each equidistant step (measured in cm), the size of the musical interval increases. And how extraordinarily beautiful is nature/physics in that when we start with the fundamental intervals of the perfect fifth, perfect fourth, and minor and major thirds, the size of the steps of these intervals above the open string correspond to the steps (vibrating string nodal lengths) that give us the notes of the harmonic series.

This is totally unlike the piano and all other keyboard instruments. For the keyboard player, the bottom and top notes of every octave are the same distance apart (17cm for the piano) no matter in what register they are played. The fact that the physical distances of musical intervals on string instruments are so variable (according to how high up the fingerboard our hand is) makes string instruments very “un-mechanical” …… and consequently difficult to play in tune. Even if the mathematical ideas of calculus and logarithms appear tremendously complex intellectually (on paper, in maths textbooks), as soon as we pick up our cello we are having to apply them in practice!

THE DIFFERENCE BETWEEN NAVIGATION AND FINE-TUNING

In our exploration as to how our left hand successfully navigates its way around this uncharted territory, we need to distinguish between “navigation” and “fine-tuning”. “Fine-tuning” refers to the corrections we make to our finger’s position after the note has sounded, in order to make the note perfectly in tune. This fine-tuning is done by ear (see “Aural Sense” above) but we can only make this correction once the note has sounded.

The art (or science) of “Positional Sense” refers to our ability to place any finger as accurately as possible before we sound the note, so that the need for correction is minimal. We could take an analogy from aviation: “navigation” is what gets the plane well placed over the runway, “fine-tuning” is the pilot’s last-minute dexterity that makes all the difference – even with perfect navigation – between a good and a bad landing. For the string player, good “intonation” is the combined result of good positional sense (navigation) + good aural fine-tuning. In other words, we need both a good GPS (“Global Positioning System” or “SatNav”) and a good ear.

HOW DO WE FIND A NEW POSITION/NOTE?? “SHIFTS” AND “PLACEMENTS”

We have two main techniques for finding our new note/position after a hand displacement up or down the fingerboard. We will call these two ways “Shifts” and “Placements”.

“Shifting” involves the use of a slide-glissando (audible or not) between the old and new notes (origin and target notes). This finger contact with the string during the shift (even when inaudible) allows us to measure the distance between the two notes, as well as to control and correct the horizontal placement of the finger on the string. The glissando is an enormous help for finding our new note in all of the regions of the fingerboard, but up high in the Thumb Region, it may be our only effective way of navigating very large intervals. When we play large intervals on the same string up high in the Thumb Region we are essentially “playing blind” with only our glissando to tell us where our hand is. Do the following shifts initially on the same finger, in order to have the smoothest most uninterrupted glissando. This is the easiest glissando to hear and thus the easiest to control:

“Placements”, on the other hand, are what we do when finding notes after a silence/rest or after an open string. Here, by definition, our finger is placed into its new position on the fingerboard from “midair”, rather than reaching its new position by sliding along the string (a “shift”) When finding a note in this way, we almost always find first the position of the thumb under the cello neck (or on the fingerboard if we are in Thumb Position), and only then do we place the finger. “Placements” are the subject of this page, while shifting is dealt with on its own page (click on the highlighted link above).

LEFT-HAND PIZZICATO TO CHECK INTONATION OF A “PLACEMENT” BEFORE PLAYING

Without the help of a glissando, it is hard to know exactly and precisely where our finger is when we place it after a silence/rest. Fortunately, if we have a moment of silence before our note needs to be played, then we can create an alternative source of aural feedback information that substitutes for that missing glissando. This vital “trick” involves the use of a soft Left-hand Pizzicato with which we can check the intonation of our note before actually play it “officially”. We thus use the silence before playing the note as invaluable “preparation time” in which to check and correct both the horizontal and vertical (pitch) placement of the finger. This is a lifesaver for our playing as it means we can correct these “starting notes” before sending them out into the public.

We have two types of left-hand pizzicato at our disposition for this note-checking:

Click on this Left-hand Pizzicato link for more discussion about this very important technique.

THE USE OF INTERMEDIATE NOTES TO FIND A NEW POSITION

Sometimes, when finding a higher finger,  instead of locating directly this new finger, we will place first of all a different finger in that same hand position, from which we will then locate the note (finger) that we need to play. This “stepping-stone” note is called an “Intermediate Note”, and is almost always on a lower finger. In other words, before finding our “target” finger, we will actually find a lower finger (usually the lowest) in the target position, and only when we have found that “intermediate” note, will we then place (and play) our “real” destination finger. This technique is used in both shifting and in finger placements. The finger used for the Intermediate Note is usually the first finger, but in the thumbposition it is most often the thumb.

WHY USE INTERMEDIATE NOTES

So why would we want to find our notes in this way, using an “intermediate note” rather than just finding our target note directly? There are two main reasons for this:

1: because our positional sense – both absolute and relative – is much stronger for the lower fingers than it is for the higher fingers. In other words, to correctly locate any one hand position, it is often easier and safer to find the first finger (or thumb in the higher regions) than finding the higher fingers in their corresponding position. This is especially true in the Intermediate and Thumb Regions of the fingerboard.
2: because the lower finger can be plucked gently by a higher finger Left-hand Pizzicato to check its intonation (see above). This has two advantages:

As soon as we get above the Intermediate Region, whacking is only possible when we have the thumb (or another finger) on the fingerboard.

For a larger discussion about the use of intermediate notes in shifting click on the following link:

The Use Of Intermediate Notes In Shifting

HIERARCHY OF POSITIONAL SENSE (NOTE FINDING) DIFFICULTIES

We can create a hierarchy of difficulty for the different circumstances in which we need to find a note in a new hand position. Here it is, in order of increasing difficulty. Each type is illustrated in the musical example that follows:

1: placements with plenty of preparation (checking) time [EX. 1]
2: shifts with an audible glissando [EX. 2]
3: shifts with inaudible glissando [EX. 3]
4: placements with no preparation time [EX. 4]

Placements for which we have ample preparation time (Ex 1 above) are the most secure and comfortable situations for finding notes on the cello because we have the possibility of checking and correcting either the target note or an intermediate note in the same target hand position. But we can only do this preparatory “trick of the trade” when we have that precious moment of silence before our note needs to be played. When our new position comes immediately after the playing of the (same) open string (or natural harmonic on the same string), then we have absolutely no time for any checking of the new finger’s position before we sound it (Ex 4 above). This is one of the most difficult circumstances in which we will ever have to find a new position: here, we not only have no possibility to check the note before sounding it, but also we have no aural or silent glissando to help us measure the distance (and to stabilise the finger’s contact with the string). This leads us to the following discussion:

POSITIONAL SENSE: “ABSOLUTE” AND “RELATIVE”

Up until now, we have considered the finding of each new hand position as an independent act, that has little relation to the note that came before the hand displacement, but this is often not the case. The GPS (SatNav) system in a vehicle doesn’t only know the exact coordinates of our destination but also calculates its distance from our departure point, and the best route to take to get there. Our internalised GPS (SatNav) navigation system (which, for a string player should probably be renamed as an FPS = Fingerboard Positioning System!) also works in this way.

“Knowing” the exact coordinates of our target destination could be called “Absolute Positional Sense” whereas finding our target position by measuring (sensing, feeling) the distance from our departure point could be called “Relative Positional Sense”.

ABSOLUTE POSITIONAL SENSE

“Absolute Positional Sense” (APS) refers to our ability to locate any note not only without the help of any aural references (i.e. without sounding either the target note nor any previous note which could serve as a reference) but also without any reference at all to the previous note. Our APS is what we principally rely on when finding notes “from the air” (what we call “Placements”) in the same way that a GPS might direct a helicopter to land at precise points on a huge fingerboard. It doesn’t matter where the helicopter is coming from or which route it takes, the only thing that is important is the coordinates of its landing point.

When finding a new position immediately after the (same) open string, we cannot use a glissando (neither audible nor silent) and are therefore deprived of both of our hugely informative tactile and aural sensory inputs. This exclusive reliance on our kinesthetic and visual senses is what makes finding notes in this way (from the air) significantly more dangerous (insecure) than when we can maintain finger contact with the string during our hand’s displacement. It is this lack of finger/string contact that is the main characteristic of finding notes with “Absolute Positional Sense”.

RELATIVE POSITIONAL SENSE

In contrast to this is our “Relative Positional Sense” (RPS), by which we find our target note according to its distance from the preceding note. Once we are back in contact with the earth (= finger contact with the string) then we can use our glissando to measure the distances between two positions. The glissando (audible or not) is a magnificent measurer of musical distances and is the basis of our Relative Positional Sense. For this reason, we use our RPS much more in shifting than in note placements from midair.

Let’s use a postal analogy to help describe these two terms: if we know the exact address of a house then we can go directly there with no need for landmarks or other references along the way: this is the equivalent of “Absolute Positional Sense”. If however, we know that our destination is three houses past the one we are presently at, then we are using “Relative Positional Sense” to get us to the right destination.

Using RPS corresponds to playing “by ear”, “by interval” rather than thinking “note names”. In other words, rather than thinking “go to C” we are more likely just to think “go up a fourth (or a third, a fifth etc) without necessarily knowing which notes (note-names) we are playing. Once we have sounded a note, we now know where we are and can find the next note relative to the note we have just played according to the musical interval that separates them. Thus “relative” positional sense works best for smaller intervals as it basically requires measuring the distance between the two notes.

When we place a new finger without any displacement of our hand’s position (no shift), then we are using our RPS. For larger distances (with a slide or an extension), our RPS imagines, measures and remembers the distance between the notes aurally, as a glissando or an extension.

We tend to use our Relative Positional sense a lot in the thumbposition because:

1: with the thumb up on the fingerboard we have a great lack of absolute positional information and
2: in thumbposition we have great possibilities for extending from the thumb.

It is easier to measure distances as extensions from the thumb than as shifts, which is why in Thumbposition it might feel safer  – when possible – to move around using “snake-crawls” (alternations of extensions and contractions) rather than shifts, as illustrated in the following example, based on the Prelude of Bach’s Sixth Suite. This is an excellent example of finding our new notes by RPS rather than by APS.

Relative positional sense can however be a little bit of a trap: playing by ear is a wonderful skill, but in order to constantly improve and refine our mental map of the fingerboard (our “absolute” positional sense) it helps very much to know which notes we are playing. This is especially true up in the thumb region.

ABSOLUTE OR RELATIVE: WHICH TO USE, AND WHEN?

We use both these positional senses, constantly and simultaneously but their relative importance varies according to the circumstances. We have seen that in “shifting” (with audible or silent glissando) our RPS tends to be more important, whereas in “placements” (from midair) we use more our APS. Other factors also influence the relative importance of these two ways of finding our way around the fingerboard:

CONCLUSION

When we are well-practised, we can have the equivalent of “perfect pitch” for a singer, whereby we know, before we actually play the note, exactly where it is. This skill uses all the available references: kinesthetic, tactile and visual and aural. Having perfect pitch must also be a great help to a cellist in knowing where they are on the fingerboard: not just knowing where each note is found (how it feels and looks) but also how (at what pitch) it will sound.