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.
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)
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 6th 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.
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 6th 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.
This is great. Thanks for your useful post. It really helped me. Greetings from Santiago de Chile.
ReplyDeleteI really liked your post. It is very informative, and time-saving. I have ABRSM Grade 3 Piano Practice Exam in two weeks, it saved lots of time for me to prepare for learning scale. Thank you :D
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