Scale fingering made easy

Just a brief departure from my regular posts here. Having written up a categorisation of the simplest way of conceiving the coordination for every unison major and minor scale for my students, I thought I might as well post this on my blog too. While I cover standard basics in my teaching, one thing I don't want to do here is to put together posts containing information that has been stated elsewhere in exactly the same way 1000x over. However, while this covers something as standard and routine as scale fingering, I've never personally seen scales categorised in this exact way before and feel it warrants posting for that reason. Considering that 22 out of 24 keys actually use one of just two possible physical coordinations (!), I find it rather surprising that these simple time-saving observations have not been widely made. All too often, pianists do not understand just how similar seemingly different coordinations actually are. For this reason, a lot of time can be wasted on trying to get a "feel" for just running the fingers without understanding the basic trends (typically by repeating over and over). However, the process goes a lot more quickly if you realise that the coordination for virtually every scale is identical to that which will already have been learned elsewhere. The key to consistently sound fingering is understanding specific signposts or anchor points, that hold everything together. When properly understood, instead of having two separate coordinations conficting with each other, the two hands should actually help to guide each other. However, I must stress that hands separate practise is extremely useful. This is to show how to combine two hands with understanding- not to replace high quality separate practise altogether. 

When working with students, I use this basic material along with various demonstrations at the piano. I've filled in some additional details to the original summary, to clarify certain areas that might potentially cause confusion when viewed without that demonstration. However, I'll likely come back to this at some point in the future and perhaps illustrate certain points (that I typically accompany with a demonstration) with videos. Also- please note that this is specifically about understanding and organisation of fingering. This is not designed as a comprehensive "how to" for starting scales from scratch (although I may write an additional post sometime, about the quickest way to acquire a comprehensive mental grasp of the notes and key signatures for any possible key). 

Also, one final point- this is written to summarise the most significant features of each fingering- in an ultra-concise form. Some people may find it valuable or even necessary to cross-reference this skeleton with a fully notated and fingered version of each scale. That's not something I'd discourage at all- but remember to start focussing on the significant features straight away! Don't just follow instruction after instruction over and over- like a mindless automaton! The sooner you can reduce your mapping out of a scale fingering to its most significant features, the sooner each scale will be truly learned- and will stay truly learned.

Scale Fingering

Firstly, all unison scales that start on the white keys involve one of two coordinations. Most involve 343 (ie. for two octaves this means that the thumb turns under 3 then 4 then 3 in one direction, whereas 3 then 4 then 3 is turned over the thumb in the other direction). The only exception is anything starting on either a B or an F! For all 343 scales, practise the exercise of playing both thumbs together on the keynote and going back and forth, with a note on either side.

eg. for C major

R.H.  4 1  2  1 4  1  2

           B C D  C B C D etc.

L.H.  2 1  4  1 2  1 4

(apologies if the alignment is not quite right in some browsers) 

This gives you the location of every fourth finger in the whole scale (which will always sound at the same time as the second finger in the other hand). This is by far the most important point to focus on. Practise hands separate C major scales up and down passing exclusively under the third finger (and the third finger over the thumb), in order to develop a feel for this passing as being a "normal" default action to perform. Once this becomes habitual you are free to focus almost exclusively on the addition of fourth fingers (alongside the reference point of where the thumbs meet)- while everything else can be left to take care of itself. In this fingering, the worst possible sin is to fail to get the thumbs to meet- and especially to fail to even notice if it didn't happen! Even at the very fastest of speeds, there should always be conscious awareness of the thumbs meeting on the keynote. This is the anchor point that continues to hold everything together- even when other details start going on autopilot. Don't forget to keep looking out for that one moment of reference in each and every octave- even if the rest of the scenery is allowed to breeze by unnoticed! In the event that your fingers should start having their own ideas about which order they might wish to come in, a failure of the thumbs to meet here should send alarm bells ringing immediately! This sets up the chance to do immediate corrective work- before bad habits have a chance to set in.

Next up, we have B and F. Both the majors and minors use the next most standard fingering- which is that where thumbs ALWAYS land together, rather than only once per octave. This is very simple indeed as long as you plan for your thumbs and calculate the fingering accordingly. You should always be consciously aware of BOTH thumb notes before you even think of starting (which also applies when practicing any scale whatsoever hands separately)! Once the thumb notes are clear in the mind, practise firstly with a large pause on every thumb, both ascending and descending. When ascending, stop on the thumbs and think about the left hand. How far is the next thumb note for that hand? If it's a long way take 4 fingers. If it's nearer, take just 3. When descending, stop on every thumb note and apply the very same process to the right hand. Of course, this needs to lead to a "feel" for the movements, if the scale is to go quickly. However, by developing the "feel" in a way that is informed by a complete mental understanding of where the fingering comes from, it's far easier to train the reflexes to become reliable. 

Additionally you can look at the black keys to help guide this (although you should never use this as a replacement for knowing both of the thumb notes!). When there are two black keys you use the third finger (fitting 2 and 3 to the group of 2 black keys). When there are three black keys, you use the fourth finger (fitting 2, 3 and 4 to the group of 3 black keys). Note that the fact that the left hand starts B major and B minor on finger 4 is a mere passing detail- that true understanding of the thumbs will sort out automatically. If you realise that the first thumb meeting is on E, there's no other finger that could logically end up on the first note, other than the fourth. When a student starts on 5, it is clear that they have not given any thought to forward-planning. If they deal with this merely by memorising "start on 4" that tells them nothing except to start on 4- offering no guarantee of a better plan for the scale as a whole. Understanding nothing more than how to think around two reference thumb notes tells you EVERYTHING you need to know to reliably finger every note in the scale- saving a hell of a lot of time and effort!

Next up, we have the scales that begin on black keys. Firstly, D flat major plus its relative minor B flat minor and F sharp (or G flat) major plus its relative minor E flat (or D sharp) minor. All of these function around an identical principle where thumbs meet twice per octave. In particular though, take care with B major, F sharp major and D flat major. Note that each of these contains every black key- but different white keys. This is why it’s essential to be 100% clear on the thumb notes, as trying to play these by “feel” alone inevitably results in confusion. 

That leaves 6 more keys. Surprising as it may sound, 4 more of these are simply 343. C sharp minor and F sharp minor are most easily executed with an identical fingering to their relative majors (note the standard fingering for F sharp minor is different to what I suggest here, although I regard this approach as being far more practical and effective than having to learn the unique coordination required for the "traditional" fingering). Thumbs land on E for C sharp minor and on A for F sharp minor, with 4s on either side. A flat major and G sharp minor work much the same. Look where the thumbs meet and remember that the fours only occur immediately on either side. Be careful with G sharp minor here, however! Note that this time the fingering is different to the relative major of B (and that it does not correspond to the number of black keys!). Relate the fourth fingers to their location on either side of the B- but be careful not to think of B major (which does not operate on the 343 fingering we need here). All other black key minors involve an identical fingering to their relative majors and there is usually great benefit in directly associating their countless common features. It's very good to practise these relative majors and minors together. However, G sharp minor requires a different fingering- making it important to be careful not to associate too directly with B major. 

That covers everything other than B flat and E flat majors. For B flat, notice that there are no convenient meeting points. Odd as it may sound at first, the conflict between the hands on the black notes is exactly what holds it together most easily. When ascending the right hand has 4 on B flats and 3 on E flats and the thumb always follows the black note. The flats are the reference point- but the left hand never meets up with the right. One hand always has a 3 and the other a 4. On the way back down the left hand always has 3 on B flats and 4 on E flats and the thumbs turns under every black note. This time it is the right hand that must match the seemingly 'wrong' fingers to the left hand. 

E flat major is very similar but we have a natural meeting point to think around. 3s come together for a useful point of reference on E flat- but elsewhere 3 and 4 coincide with each other, as in B flat major. 

In the specific case of scales with flats in the key signature, an additional point to notice is that the right hand thumb always falls on C (or eventually C flat, in the case of G flat major/E flat minor) and F. Also, the third finger always lands on the E flat (or E natural, if we include F major) and the fourth finger always lands on B flats. It is only in the left hand that significant fingering changes occur. 

Fingering chart

343 scales: C, D, E, G, A (major and minor for each) A flat major, G sharp minor, F sharp minor (relative of A major), C sharp minor (relative of E major)

thumbs together scales: B major and minor, F major and minor, D flat, B flat minor (relative of D flat), F sharp/G flat, D sharp/E flat minor (relative of F sharp/G flat).

This leaves B flat and E flat as the two exceptions, with their own unique coordination. 

Addendum regarding melodic minors, issues of turning onto black notes and why I advise A major fingering for the BOTH hands in F sharp minor

Almost everything above applies equally to harmonic and melodic minors. However, F sharp melodic minor and C sharp melodic minor are slightly different. Due to the raised 6^th on the way up, it is necessary to adapt the right hand fingering when ascending. Simply conceive the ascent as a thumbs together fingering (thumbs on A and E sharp for F sharp minor, and thumbs on E and B sharp for C sharp minor). To return to the “normal” fingering, care must then be taken to start the right hand descent with 321- rather than to take the 2 that would normally be used on the keynote. From this moment onwards, the scale becomes a simple 343 fingering- involving wholly identical notes and fingering to the relative major. Additionally, note that G sharp minor melodic reverts to the fingering of the relative major (ie. B) for the descent.

Also, one commonly stated principle is that the thumb turns under black notes and that fingers are typically turned onto black notes. Personally, I would say that it is potentially disastrous to use this extremely superficial (and highly inconsistent trend) as a major part of what guides scales. There are simply far too many exceptions. It's considerably easier to use the two basic coordinations detailed here as the foundation. 

Some people use the premise that it is "easier to turn onto black notes" as the explanation for traditional F sharp minor fingering. Personally, I totally dispute that. Not only does the traditionally "correct" fingering make coordination of the hands vastly more complex, but I also believe it is marginally less comfortable. If it's somehow "hard" to turn the fourth finger over the thumb and onto a B, I cannot see why. If that movement is "hard", then A major contains the same difficulty anyway. Does anyone think something as routine as playing A major is "hard"? Personally, I actually feel far more cramped when turning my third finger onto C sharp. When turning onto the B, I feel I have plenty of time to get into position for the following notes. When going straight onto the C sharp, I feel slightly hurried. Having used the standard fingering for many years before switching to A major, I'm perfectly capable of using either. However, seeing as the left hand is marginally easier with a standard 343, I cannot see any justifiable reason to inflict a completely unique and confusing coordination upon anybody, as if it were somehow more "correct". In particular, I can't see why a clearly non-existant rule about turning under black keys (that is contradicted by the fingering for a wealth of other scales) should make it more "correct" to employ a fingering that is arguably less physically comfortable than the more obvious alternative.

Keybedding part ii- achieving a direct line of action without impact (plus an illustration of the REAL psychology behind prevention of muscle tensions)

This will be a fairly short post, but I just wanted to add an explanation of the second way of directing energy well away from potential impact at the keybed. Think of this as a kind of "half-way" post. As well as clarifying the basic theory of how this approach stops impact, these are extremely important concepts with regard to learning how to put this quality of movement into practice. From here, my next post will get right into the specifics of moving the keys with the fingers- with full relation to the arm's role (apologies for stalling, but I've wanted to be sure to get this part just right. A post with fully practical explanation and illustrative videos will follow very shortly now). Along the way, I'm also going to shed some light on the psychology of what really causes the worst tensions. I'm not necessarily denying that there is some relaxation value in positive thinking, lighting a couple of joss-sticks or taking in the sound of whale-song accompanied by pan-pipes. However, I want to show how achieving a suitable conception of movement itself has a vastly greater role to play.

Anyway, I've already covered the circular path that accounts for pure pulls from the knuckle- but there's a second type of finger action that is based on a more direct line of motion. Although this shares the same powerful "pulling" action from the knuckle itself, the finger as a whole is felt to "extend". Arguably you can even look at it as being something of a "push". However, thinking of a push can easily cause the truly harmful type of keybedding that Matthay spoke of! I'd like to use the analogy of a "press-up" against the wall to illustrate some significant issues that are hidden beneath the surface (see this post regarding issues of actions and reactions for some relevant information, and some background about the exercise). I'm going to use it to show what kind of background mindset leads to the equivalent of healthy pushing, compared to the type of mindset that results in an equivalent to Matthay's keybedding. Please note that this is not a vague or poetic metaphor! The basic practical issues are extremely similar- providing a better level of self-perception and awareness that can then be directly transferred to guiding finger actions!

Anyway, compare doing a light press-up against the wall with how you might act if you began from the same starting position, but intended to actually push the wall over (just to be clear, the motion of the arms here represents the action of the finger on a key- not the action of the arms on a key!). Although you can try out the latter- go easy if you do! There's probably little danger of toppling a building, assuming that it was constructed by a qualified team of certified builders (rather than a team of mobile-home dwellers, who some guy in the pub called Dave got you in touch with). However, you don't want to risk straining yourself. If in doubt do a rather light version of only pretending to act as if you want to bring the wall down. Alternatively, just imagine how your body might behave, were you to attempt this. Once you've done that stop and think for moment. What is the actual difference between the two acts, in terms of how the body behaves? Try it again and see if you can perceive what exactly is really going on.

If we looked at every individual detail it would likely be pretty complex. However, if we look at the bigger picture, the key difference is very simple. It's just that in one case you think of pushing your body AWAY from the wall, whereas in the other you think of piling your whole body in TOWARDS the wall. Yes, it's that simple. This basic concept is something that can play an enormous role in playing- if we can understand how to apply it to moving a key. I'll come back to this shortly. However, while keeping it relatively simple, I'd just like to go slightly beneath the surface for a deeper insight.

The weird thing here is that in both cases physics illustrates that you actually act TOWARDS the wall. Try doing the same motion of the arms in open space, with no wall to contact. Your elbows start bent and your hands extend away from your body (which stays in the same place). Most likely you won't even think about what your elbow does. You just feel where you hands begin and aim to move them directly away from you. The fine details of what makes that happen are left to the unconscious. However, when contacting the wall your hands stay in the same place and it's now your body that moves away. Basically, the wall gets in the way of the arm extension and sends the movement back in the opposite direction. To put it in a subjective (rather than scientific) manner, it's almost as if the wall serves as a mirror that reflects the movement back in the opposite direction. 

Anyway, while the press-up and the demolition press are spectacularly different acts, each is a type of "push".  Even when you think of going away from the wall, your hands will necessarily act towards it to make that happen. However, one of these is directly comparable to a healthy finger "push" on a piano whereas the other corresponds to the specific type of "push" that would be deemed keybedding. But if both involve pushing towards the wall, what makes them different?

The simple answer lies within the action/reaction concept. When you do a press-up, if you think of moving away, you will instinctively allow the REACTION from the wall to move you in the opposite direction. The brain figures out which muscles need to be moveable enough for the reaction to be allowed to push you away. When we think too much about aiming towards the wall, we are inclined to fight against the reactions and press through them with extra efforts or try to lock joints into rigid immobility. Here we have the underlying cause of most heavy tensions and of ongoing excesses of pressure into the keybed. Basically, the brain devotes too much attention to piling everything into the direction in which the key moves. There's not enough freedom for the reaction to act in the opposite direction.

Incidentally, when you get to the top of the press-up, there may be room for fine tuning. You should be careful not to lock the elbows or to push so hard that they double back. But there's obviously no question that the arms can release their effort altogether. If they did you would fall back in again! In fact, if you've done the movement optimally, it should be truly seamless. At the top, there should be nothing that you could possibly let go of without losing balance and there should be nothing that you would feel even slightly uncomfortable with. If you're balanced just right, the smallest fraction of release would slowly start you on the way back in again. Negative tensions do not come from keeping yourself away from the wall with sensitivity. They come from excessive efforts that are intended to act towards the wall. This tiny difference in the conscious mind triggers a wealth of different responses- that can gradually become ingrained into habit.

To take it half-way to what happens on a piano, imagine now if that wall could move an inch or two (offering moderate resistance) before stopping dead. If you think towards the wall, the mass of your whole body will likely be thrown towards the stopping point. That means more momentum and energy is heading into impact- and it doesn't necessarily go into aiding movement of the wall (as I'll demonstrate in a future post on efficiency). Imagine now if you think away from the wall. Your mass still acts to support and balance the movement of the arms into the the wall. But as it's mostly going away from the wall, there's less impact on landing.  Only a small amount of momentum from the arms goes into the moment of collision- with any other momentum being sent in the opposite direction. With just the right coordination, it may even be that the body doesn't end up moving in either direction, but simply hovers in balance (note that this balance is totally different to if you willfully fix it it into being immovable)

Interestingly, a "fall" into the wall would cause less impact than a full body press. HOWEVER, it will actually land vastly more momentum than when the muscles activate to press the body away. Falling through the wall certainly does not make for the least impact upon collision. Because the whole body is travelling, there is necessarily more momentum going into the stop. An inert collapse is superior to thrusting the whole body into a collision. However, a suitably controlled activation (that stops the body crashing in) is notably lower in impact still. This makes a lot of sense when related to "relaxation" technique. A flaccid arm that collapses makes for less impact than an arm that is pressed in hard against the keys. But compared to a hand that activates to push away from the piano in a suitable fashion, it's actually the dead arm drop that makes for the most impact. Later on things can start to get rather interesting when you learn how to "catch" an arm drop with hand activation (which does not mean a braced hand!)- like Artur Rubinstein:

Anyway, all of these issues translate into extremely direct equivalents, when moving a piano key. I suspect that this will have already given some major clues in itself, but I will show specifically how these concepts relate to putting finger actions into practice in my next post. In case you want to start experimenting now, I should stress that when you push away, it's very important not to let the arm be in a heavy corpse-like state! If you release too much weight, even an attitude of pushing away can be hard work. It needs to be very low effort when you start out. Don't even think of crashing your arms down like Rubinstein, but start by lightly extending the finger to ease your knuckles up and away, starting from direct contact. There should never be discomfort or a heavy sense of pressure!

Anyway, as you've probably guessed, the big issue here is that thinking away in piano playing requires you to think not down of pressing the key down but of causing yourself to go UP in the hand (and perhaps even in the wrist, in some instances)! This is something that Alan Fraser suggested to me, the first time I played to him. Although this provided plenty of benefit from the start, there are many issues that I've only recently been able to put into that context and fully make sense of in that light. I honestly don't believe it's any exaggeration to suggest that almost any action should be felt as to try to push back away from the key. Surprisingly, dropping onto the keys from a great height involves this too- I'd even say it's especially important in that scenario. Rubinstein doesn't get that big resonant sound from crashing into the keybed with an inert or braced hand. Redirection remains essential- and it's timed movement in the hand that best achieves that. Anyway, this post is effectively a fleshing out of the upward concept and an illustration of just some of the reasons why it is quite so significant. A future post on efficiency will go deeper into the reasons why this can also improve energy transfer and allow big sounds to come when expending relatively little energy.

Briefly, I should just add that the idea of thinking "up instead of down" may appear to be in contradiction to my post about two-sided thinking. To be clear, the difference here is that I am talking about acquiring a starting point in which you have first learned to allow the arm to respond freely to reactions. This is a missing link in the psychology of just about any technique that involves stiffness and fixation. Even some highly evolved techniques are held back slightly in this respect. Some of the exercises in future posts will give a clear illustration of how we'll still be building up towards a balanced understanding of both action and reaction as a single entity.