Major and minor arpeggios in all inversions- a comprehensive explanation of how to understand patterns via fingering groups, for efficient practice

Introduction

Quite a few years back I wrote a post breaking down scale fingering. When it comes to scale fingering resources, we are typically treated to reams of details, on a note by note basis. The normal approach is to simply read these off and repeat by rote until the scales are fluent. Instead of working that way, my post was designed to show a small number of defining features based on relationships between hands. With understanding of merely two basic unifying relationships, all major and minor keys (excepting only B flat and E flat major) can be covered within a simple premise, that will easily allow you to find any smaller detail by association. This saves a huge amount of time, that can be wasted when swamped in the least relevant details. Although nothing can altogether replace rote practise, the process is more efficient when we have a clear and simple vision of the foundation which holds lesser details together- ie thumb locations (particularly those where both thumbs coincide). 

In a sense, arpeggio fingering is so much more straightforward that it doesn't actually require a similar post. I'll give a brief summary. When an arpeggio begins from a white key you should start with the lowest available finger. That will be the thumb in the right hand and the 5th finger in the left hand (which leaves no spare fingers unused beneath the starter note, in either hand). However, this 5th finger is a one off substitute, on what would usually be the thumb's note. In following octaves, both thumbs land here as your chief reference (until the right hand uses 5 at the top- again as a substitute for the usual thumb). You then just need to decide on the other fingers. All major/minor arpeggios are built on a basic hand shape of 1235 or 1245. Your sole choice is between 3 or 4. Looking at the width of the spaces between notes should usually make it easy to tell which fits a chord shape best. However, if the arpeggio starts on a black key, you must look to see if there is a white key included in the chord.  If there are none, you can still apply the original principle- as if the black keys are really white keys. When white keys are available, however, you will assign your thumbs here, rather than to the starting black key. You can build the basic hand shape around this primary thumb location- in the same manner as if the arpeggio had begun here.

I've skimmed over a couple of extra details and that may be a little too condensed to make sense to all, right away (especially if you haven't already learned a few arpeggios to reference back to this). You may first want to start from a fingering chart and relate the details there back to this logic. Nevertheless, once you start to recognise the mechanics of this deeper premise, you really won't need much more. However, this post also runs far beyond which fingers go on which keys. Although studying this should soon ensure that you would never need to check an arpeggio manual again, the main focus is on making logical groupings of arpeggios for practice purposes- based on physical similarity. When putting similar arpeggios alongside each other, you will quickly come to understand them on a far deeper level. In fact, if you're the kind of person who doesn't particularly enjoy scales and arpeggios (but grudgingly recognises that they have value) you might assume that this post isn't particularly for you. Actually, you're exactly the kind of person who needs this- so you can get the basics ingrained permanently, with as little fuss as possible and only a bare minimum of drilling. The groups I'm going to show are extremely logical, yet far from obvious. It wouldn't be easy to stumble upon this approach for yourself. While plenty of the background is common knowledge elsewhere, I'm not aware of any other source that offers these groupings. Feel free to skip to the end section for the lists, if you don't find anything new to you in the middle section.

Chord positions vs hand positions

Before showing the specific organisations into groups, I'm just going to show how the number of black/white keys within a chord directly contributes to the features that determine which group a chord belongs in. Although an arpeggio can be played in the shape of the three different chord positions (ie root position, first inversion, or second inversion), only some of these are what I'll refer to as a "physically natural" shape, from which the thumb can pass. While some chords are best served by having a different hand placement for each of the three possible shapes, elsewhere we must recycle a single hand placement for two or more shapes. You'll see what I mean through the following examples.

Basic arpeggios with only white keys/only black keys:

In the key of C major, say, C is the lowest note in root position, with E as the lowest for first inversion, or G as the lowest for second inversion. In traditional approaches, as I said earlier, the standard fingering for any of these shapes starts from the thumb in the right hand and 5 in the left hand, as long as the lowest note is a white key. Seeing as every note of C major is a white key, we thus have three physically natural chord shapes to fit the hand directly upon. Our chord positions and hand positions are one and the same thing.

I show all of these at the start of the film above. Before practising the arpeggio in each shape, I first get my hand used to that shape by playing it as a four note chord. Then I go quickly up and down the notes of that chord, using plenty of side to side arm movement to keep everything free. Do this as the norm for every arpeggio you practise until you have such a good sense of the shape, that you can imagine it in full detail. There's no sense in even trying to play through a whole arpeggio, unless you can easily go up and down the basic chord shape within an octave. Once the hand feels fully "tuned in" to the shape, I execute the actual arpeggio by passing the thumb. Each of the three chord shapes has a new placement of the hand to match. Notice how the thumb always defines which shape we are aligned to. Rather than demonstrate super-slow, to save both your time and mine I only went moderately slow. However, you don't need to try to watch every small detail closely. I want you to put almost all of your attention on where the thumbs occur, and notice how this governs the shapes.

As an alternative, we could also take the way the hand was set to the root position shape and simply recycle that. Root position fingering (in terms of which finger was assigned to which key) can now be applied to the inversions of the chord. I show this next in the film. Although this might sometimes be an option, I'd have to stress that it can't truly replace what I showed before. Particularly when doing the first inversion arpeggio, it becomes awkward to turn around rapidly on 1 and 2 at the top. To prove this, I show a 1st inversion run right up the piano, similar to one that features in a Pletnev arrangement from the Tchaikovsky Nutcracker. I first match my hand to the first inversion shape and then try it with the hand set to a root position shape. It should be very clear how much more sweep is possible when you start and finish from a full open hand shape, by matching the hand position to the chord shape. I can survive it when I use root position fingering but the awkward reversal at the top stops it coming alive. It's physically more fiddly at both top and bottom, which causes greater caution and restraint. To truly master white key arpeggios, you absolutely need a fingering for each position. 

Aside from the many arpeggios with only white keys, G flat major and E flat minor exist upon three black keys. Seeing as we have no choice but to place the thumbs on a black key, here we treat them no differently to if they were on white keys. With three available keys to put the thumb on, we again have three chord shapes to match with three hand shapes.

Arpeggios starting from a black key, with at least one white key

However, lets look now at E flat major (E flat, G, B flat). There are always three different positions available for a chord, as defined by the lowest note. However, according to the premise of traditional arpeggio fingering, we need to avoid taking the thumb on a black key- as long as there is a white key available. This is because the thumb is shorter than the fingers and it is generally more awkward to have to reach forward into the black keys, during thumb passing (I should point out that this rule is occasionally broken in advanced piano playing, although this lies outside of the standard foundations). In the following video, I start by including these "wrong" fingerings, just for illustration purposes.

Again, I start by getting the hand used to the shape of the chord. Notice that there's nothing awkward about merely being on any of the basic shapes. It's solely when going on to pass the thumb, that the thumb on a black key is seen to be a problem (I'm not bad at these, but you might notice my loss of legato on the 2nd inversion). Seeing as there is only one white key, we only have one superior option available. Regardless of which chord position we play the arpeggio in, our hand will be built around the thumb note G- in a first inversion shape. By the way, I show with my right hand, but the left hand will be building positions around the exact same notes. Our premise is universal, not specific to either hand. Unlike C major, it makes no difference as to which which note the arpeggio begins from. Instead of matching the hand position to the specific chord position that starts the arpeggio, we take the one physically natural shape (via the white key) and base everything upon it.

When we base fingering around thumb awareness, it's easy to find the other details from there. It's important to recognise that the thumb is always the main unifying feature of arpeggios and thus needs to be given far more attention than any mere starter note. For black key arpeggios where we have a white key available for the thumb, the finger for the first note is an extremely minor detail. The first note is only the most meaningful in our thoughts, if it also happens to be a thumb note. Giving more attention to a starting black key than to the thumb location will radically slow down understanding and progress. In fact, it doesn't even matter what finger you take on the first note. I took 2 on E flat, but any finger is fine- as long as it gives control over the sound and leads you comfortably towards the thumb and the following shape. 

I have always found it rather odd that the ABRSM introduces the E flat major arpeggio in root position early on, yet waits until the advanced grades to include even a single first inversion arpeggio. It makes little sense to start E flat major in root position, if your prior experience is only of white key arpeggios in root position. They may both be root position chords, physically speaking, but the physical foundations have nothing in common. To go straight to root position conceals the true simplicity of the arpeggio, by prematurely throwing the student into the deep end. The natural course of events would be to first learn a white key first inversion arpeggio, such as C major. This prepares for the basic feel of a similar physical inversion. The next step is to also learn E flat major in the physically natural first inversion. The final step is to go back to play the arpeggio in root position- with an existing feel for the 1st inversion position you are headed towards. When a student doesn't begin with the fundamental physical shape for an arpeggio, the movement is bound to be awkward. This is simply due to feeling mentally and physically disoriented- not because the technique includes any remarkable demands. 

Just a final point for this mixed group- B flat major is the only root position arpeggio that starts on a black key, where there are two white notes available. This means that when playing it in root position, you have two locations available for the thumbs. There are two physically natural shapes to form, around either the D or the F. As long as you practise the arpeggio in both of these inversions, it doesn't necessarily matter which note you choose to place the thumb on, when returning to root position. In this video I practise a B flat arpeggio in both available inversions. 

Once these shapes are familiar, I can use either arrangement of the hand to execute the root position arpeggio. When using two hands at once, I recommend matching both thumbs to the same white key. However, note that many scale books put one thumb on F and the other on D. For me, this is the fingering equivalent of wearing odd socks ie if you're happy and comfortable with it then feel free, but it wouldn't be my idea of a default style. Don't do it just because a book says so! Take control over your thumb options and find your own preference. The same applies with first inversion arpeggios on a chord that has one black key in the middle eg. D major. There are two physically natural shapes based on each of the white keys. I show both from the thumb notes and then show the first inversion D major based on both possible hand shapes.

That covers the general concept of building everything directly from the physically natural shapes (ie. those in which thumb passing is convenient), before reusing them for other chord positions. What's left is how to organise the arpeggios together into logical practise groups via...

The 3 Groupings

We have three categories to practise, corresponding to the three basic chord shapes. This isn't quite as it might seem, however. As I said earlier, a root position chord of E flat major has nothing physically in common with a root position C major. When we practise in relation to the physically natural groups, E flat major would go into our first inversion group, even if we execute it starting directly from the root. The only physically natural way to use the hand is in the first inversion shape- thus it's in the first inversion category where E flat belongs. We get consistency when we work from the shapes built around our thumbs on the white keys. Getting the pattern is more complicated than merely taking every chord of a particular inversion and thinking we can therefore lump them in together. However, the root position group has the fewest surprises. We basically just omit those that would start on a black key (other than the two in group c, in which every black key functions as a "virtual" white key). Every arpeggio we'll look at throughout is built on the thumb/5th finger. The simplest way to order this is as follows.

Group 1- root positions

1a C maj, D min, E min, F maj, G maj, A min, B min

1b C min, D maj, E maj, F min, G min, A maj, B maj

1c G flat maj, E flat minor

I show what is happening in the following video.

However, I didn't want to waste your time by playing every arpeggio for you. I just play the chord shapes to show the same order as above. First, play open fifths ascending on the white keys, from C and G. Each of these will go on to create two root position chords- one minor and one major. Every fifth is on two white keys until we arrive at B. For B, the needed fifth is an F sharp, thus making it the odd one out. Group a is found by filling in the third as a white key and working through. Group b is slightly more complex. If the one in Group a was a minor chord, raise the third by a semitone and get a major chord. If it was a major chord, lower the third and get a minor chord. I show the process of adjustment first, but then play straight through the order of group b on its own. Every one of these chords now has a black key in the middle. Whereas the whole of the first group is literally identical physically (aside for the unique B minor), there are more subtle differences here. The minor chords have the black key very slightly lower than for the majors. The physical shape is not identical but merely very similar. To go deeper into fingering now, you might include this into your consideration for the left hand. Every right hand shape here is 1235, beyond question. In the left you may use 4s or 3s. You might consider 4 for such chords as C minor and 3 for such chords as A major. This naturally corresponds with those subtle differences of distance between keys. For myself, I mostly use 4s with occasional 3s, although with no particular consistency. I have practised them all both ways and can do either, so I'm now happy enough to simply do what feels right in a given moment- as long as my hand is properly set to the arpeggio shape. Whatever you should choose, putting these subtly different arpeggios side by side is a quick way to build a feel for them all. Finally, group c is the very small group of the two black key only chords. 

I'd spend at least a week or so practising Group 1 alone (you might want to get that done first, before reading on, and then return for another group). That will mean you have worked at every single arpeggio in which the hand is physically matched to a root position shape. Those chords that were omitted don't feature ever feature in root position setup, for arpeggios. We instead see them in the other groups.

Group 2- 2nd inversions

2a C maj, D min, E min, F maj, G maj, A min, B flat maj

2b C min, D maj, E maj, F min, G min, A maj, B flat min

2c G flat maj, E flat minor

I show second inversion next, because it's mostly rather similar to what we already did. However, notice the one difference in the fifths. Remember that the premise is always based on narrowing down to chords with a thumb on a white key (excepting our "virtual" white keys in of group c). The thumb needs to be on F, so we get our perfect fifth by adding a B flat to it. Also, this time the left hand will definitely need to take a 5321 fingering to fit to all chord shapes. It's now the right hand that can choose between 3/4. We can carry similar reasoning over from the last group (although it's now in major chords the right hand has the smaller gap between a black key and the top, whereas in minor chords the bigger gap might suggest a 3). One extra thing of note is that this group contains the only physically natural position for B flat minor- so the other two forms for the arpeggio are built from this same second inversion hand shape.

Group 3- 1st Inversions

3a C maj, D min, E min, F maj, G maj, A min, B min

3b C sharp min, D flat maj, E flat maj, F sharp min, G sharp min, A flat maj, B flat maj

3c G flat maj, E flat minor

The good news on this one is that the fingering is very easy. Both hands should always be based on 1245. The widest interval is in the centre for each hand, so the spare 3rd finger is best left 'spare' in that gap. The bad news is that this is probably the single most difficult group to understand conceptually. You may want to read through the written chords quite a few times, before you start to practise the arpeggios in the sequence. However, there is still a pattern here that you can get used to. For the first group, there's another chance to merely cruise along on the white keys until you get to B minor- again the odd one out. For group b, what you need to remember is that our thumb note will always be marking the third of a major or minor chord, which has to have a black key as its root. Where E had been the 3rd of a C major chord in group a, the only other chord it can be the 3rd of is a C sharp minor chord. Note also the adjustment to get from group a to group b. If you come from a major chord, the middle notes slide up a semitone. If you come from a minor chord then they both slide down a semitone. You need to know your basic chords very well before this becomes easy to remember. However with a certain amount of repetition, it will become familiar. It's worth the effort, because even a relatively small amount of practise in this highly organised setup can give rather quick results.

Remember that this is truly comprehensive in setting the physical foundations for all inversions of any major or minor chord. We didn't directly practise all of these here, but we covered every hand shape that might serve as a foundation for the remaining ones. I've been working this way for many years and I can assure you that I checked every possibility. It's all there. With these down, you'll be ready to try using the common orders in method books, which can require you to dart between physical positions without the same consistency. By then it won't matter, as you should have the tools to cope with this. 

All that remains for the other chords or inversions is to picture one of the practised shapes and either begin somewhere in the middle of it, or use a substitute finger to lead into it. For example in D flat major right hand we usually take 4 on D flats, but we can begin from 2 or 3, as long as there is a strong sense of the first inversion shape that we are headed for.  If you do work through these groups systematically, you should find that it would barely take a moment's thought to picture the two different chord shapes around which you could arrange the hand for a B minor 2nd inversion, say. Also, I won't list them right now, but I also apply a similar formulaic breakdown of all the diminished 7th and dominant 7th chords- again arranging the thumb for every possible white key based inversion of these chords. You can take it further still into plenty of chromatic chords and ones that you might make up for yourself. Once you appreciate thumb anchors in just about any context, a very wide number of possibilities open up. Fitting your hands around the shapes of the keyboard becomes incredibly fluent, as if it were nothing more than some inborn natural instinct. Perhaps some pianists really do get there that way, but it's a lot easier to cheat your way there via systematic practise.