5. Playing Fast: Scales, Arpeggios, and Chromatic Scales¶

a. Scales: Thumb Under (TU), Thumb Over (TO)¶

Scales and arpeggios are the most basic piano passages; yet the most important method for playing them is often not taught at all! Arpeggios are simply expanded scales and can therefore be treated similarly to scales; thus we shall first discuss scales and then note how similar rules apply to arpeggios. There is one fundamental difference on how you must play the arpeggio (a flexible wrist) compared to the scale; once you learn that difference, arpeggios will become much easier, even for small hands.

There are two ways to play the scale. The first is the well-known “thumb under” method (TU) and the second is the “thumb over” method (TO). In the TU method, the thumb is brought under the hand in order to pass the 3rd or 4th finger for playing the scale. This TU operation is facilitated by two unique structures of the thumb; it is shorter than the other fingers and is located below the palm. In the TO method, the thumb is treated like the other 4 fingers, thus greatly simplifying the motion. Both methods are required to play the scale but each is needed under different circumstances; the TO method is needed for fast, technically difficult passages and the TU method is useful for slow, legato passages, or when some notes need to be held while others are being played.

For lack of a better terminology, I have named the TO method “Thumb Over” which is an obvious misnomer and might make it harder for a beginner to understand how to play it. I have tried other names, but none of them are any better than TO. The only possible advantage is that this outrageous nomenclature may call attention to the existence of TO.

Many piano teachers have been totally unaware of the TO method. This presented few difficulties as long as the students did not progress to advanced levels. In fact, with sufficient effort and work, it is possible to play fairly difficult passages using the TU method and there are accomplished pianists who think that TU is the only method they need. In reality, for sufficiently fast passages, they have subconsciously learned (through very hard work) to modify the TU method in such a way that it approaches the TO method. This modification is necessary because for such rapid scales, it is physically impossible to play them using the TU method. Therefore, it is important for the student to start learning the TO method as soon as they are past the novice stage, before the TU habit becomes ingrained into passages that should be played TO.

Many students use the method of playing slowly initially and then ramping up the speed. They do fine using TU at slow speed and consequently acquire the TU habit and find out, when they get up to speed, that they need to change to the TO method. This change can be a very difficult, frustrating, and time consuming task, not only for scales, but also for any fast run – another reason why the ramping up method is not recommended in this book. The TU motion is one of the most common causes of speed walls and flubs. Thus once the TO method is learned, it should always be used to play runs except when the TU method gives better results.

The main piano playing muscles for the thumb are in the forearm, just as for the other 4 fingers. However, the thumb has other muscles in the hand that are used to move the thumb sideways in the TU method. The involvement of these extra muscles for the TU motion makes it a more complex operation, thus slowing down the maximum speed attainable. The extra complication also causes mistakes. Teachers who teach TO claim that for those who use TU exclusively, 90% of their flubs originate with the TU motion.

You can demonstrate the disadvantage of the TU method by observing the loss of thumb mobility in its tucked-in position. First, stretch your fingers out so that all the fingers are in the same plane. You will find that all the fingers, including the thumb, have mobility up and down (the motion needed to play the piano). Now, wiggle the thumb up and down rapidly – you will see that the thumb can move 3 or 4 cm vertically with ease (without rotating the forearm), quite rapidly. Then, while still wiggling at the same rapid frequency, gradually pull the thumb under the hand – you will see that as it goes under, it loses vertical mobility until it becomes immobile, almost paralyzed, when it is under the middle finger.

Now stop the wiggling and thrust the thumb down (without moving the wrist) – it moves down! This is because you are now using a different set of muscles. Then, using these new muscles, try to move the thumb up and down as fast as you can – you should find that these new muscles are much clumsier and the up and down motion is slower than the wiggle rate of the thumb when it was stretched out. Therefore, in order to be able to move the thumb in its tucked position, you not only need to use a new set of muscles but, in addition, these muscles are slower. It is the introduction of these clumsy muscles that creates mistakes and slows down the play in the TU method. The TO method eliminates these problems.

Scales and arpeggios are some of the most abused exercises in piano pedagogy – novice students are taught only the TU method, leaving them unable to acquire proper techniques for fast runs and arpeggios. Not only that but, as the scale is speeded up, stress begins to mysteriously build up. Worse still, the student builds up a large repertoire with wrong habits that will need to be laboriously corrected. The TO method is easier to learn than the TU method because it does not require the sideways contortions of the thumb, hand, arm, and elbow. Beginners should be taught TU first because it is needed for slow passages and takes longer to learn. The TO method should be taught as soon as faster scales are needed, within the first two years of lessons. For talented students, the TO method must be taught within months of their first lessons, or as soon as they master TU.

Because there are two ways to play the scale, there are two schools of teaching on how to play it. The TU school (Czerny, Leschetizky) claims that TU is the only way that legato scales can be played and that, with sufficient practice, TU can play scales at any speed. The TO school (Whitesides, Sandor) has gradually taken over and the more insistent adherents forbid the use of TU, under any circumstances. See the Reference section for more discussions on TU vs. TO teaching. Both extreme schools are wrong because you need both skills.

The TO teachers are understandably angered by the fact that advanced students passed to them by private teachers often do not know the TO method and it takes six months or more to correct hours of repertoire that they had learned the wrong way. One disadvantage of learning both TU and TO is that when sight reading, the thumb might become confused and not know which way to go. This confusion is one reason why some teachers in the TO school actually forbid the use of TU. I recommend that you standardize to the TO method and use the TU as an exception to the rule. Note that Chopin taught both methods (Eigeldinger, P. 37).

Although the TO method was rediscovered by Whitesides, etc., the earliest account of its use dates back to at least Franz Liszt (Fay). Liszt is known to have stopped performing and returned to developing his technique for over a year when he was about 20 years old. He was dissatisfied with his technique (especially when playing scales) when compared to the magical performances of Paganini on the violin, and experimented with improving his technique. At the end of this period, he emerged satisfied with his new skills but could not teach others exactly what he had done to improve – he could only demonstrate on the piano (this was true of most of Liszt’s “teachings”). However, Amy Fay noticed that he now played the scale differently; instead of TU, Liszt was “rolling the hand over the passed finger” so that the thumb fell on the next key. It apparently took Fay many months to imitate this method but, according to her, “it completely changed my way of playing” and she claimed that it resulted in a marked improvement in her technique generally, not only for playing scales, because TO applies to any run and also to arpeggios.

b. The TO Motion, Explanation and Video¶

Let us start by analyzing the basic fingering of scales. Consider the RH, C major scale. We begin with the easiest part, which is the RH descending scale, played 5432132,1432132,1 etc. Since the thumb is below the hand, the 3 or 4 finger rolls over the thumb easily, the thumb naturally folds under those fingers, and this descending scale fingering works well. This motion is basically the TU motion; the TO descending motion is similar, but we will need to make a slight but crucial modification to this in order to make it into a true TO method; however, this modification is subtle and will be discussed later.

Now consider the RH, C major ascending scale. This is played 1231234, etc. In the TO method, the thumb is played like the 3 and 4 fingers; i.e., it is simply raised and lowered without the sideways TU motion under the palm. Since the thumb is shorter than the other fingers, it can be brought down almost parallel to (and just behind) the passed finger without colliding with it. In order to hit the thumb on the right key, you will need to move the hand and use a slight twitch of the wrist. For scales such as the C major, both the thumb and passed finger are on white keys and will necessarily crowd each other somewhat. In order to avoid any possibility of collision, the arm should be almost 45 degrees to the keyboard (pointing to the left), and the hand is rolled over the passed finger by using the passed finger as a pivot. The 3 or 4 finger must then be quickly moved away as the thumb comes down. In the TO method, it is not possible to hold the 3 or 4 finger down until the thumb plays, unlike the TU method. When you first try the TO method, the scale will be uneven and there may be a “gap” when playing the thumb. Therefore, the transition must be very quick even in a scale played slowly. As you improve, you will notice that a quick flick/rotation of the wrist/arm is helpful. Beginners usually find TO to be easier than TU, but those who learned TU for many years will initially find TO clumsy and uneven. Also, rotate the forearm slightly clockwise (what Chopin called the “glissando position”, see c. Practicing TO: Speed, Glissando Motion below) which automatically brings the thumb forwards. The RH ascending scale is more difficult than the descending scale because for the descending scale, you pivot and roll over the thumb, which is easy. But for the ascending scale, you roll over the 3 or 4 finger, but there are fingers above the rolled finger and these can interfere with the roll.

The logic behind the TO method is the following. The thumb is used like any other finger. The thumb only moves up and down. This simplifies the finger motions and, in addition, the hand, arms, and elbows do not need to contort to accommodate the TU movements. Thus the hand and arm maintain their optimum angle to the keyboard at all times and simply glide up and down with the scale. Without this simplification, technically difficult passages can become impossible, especially because you still need to add new hand motions to attain such speeds, and many of these motions are incompatible with TU. Most importantly, the movement of the thumb to its correct location is controlled mostly by the hand whereas in the TU method, it is the combined motion of the thumb and hand that determines the thumb location. Because the hand motion is smooth, the thumb is positioned more accurately than with the TU method, thus reducing missed notes and hitting of wrong notes and at the same time bestowing better tone control to the thumb. Also, the ascending scale becomes similar to the descending scale, because you always roll the fingers over for passing. This also makes it easier to play hands together since all fingers of both hands are always rolling over. Another bonus is that the thumb can now play a black key. It is this large number of simplifications, the elimination of the stress that results from the paralyzed thumb, and even more advantages discussed below, that reduce the potential for mistakes and enable faster play. There are exceptions: slow, legato passages, or some scales containing black keys, etc., are executed more comfortably with a TU-like motion. Most students who had used only TU will initially have a terrible time trying to understand how anyone can play TO. This is the clearest indication of the harm done by not learning TO as soon as possible; for these students, the thumb is not “free”. We shall see that the free thumb is a versatile finger. But don’t despair, because it turns out that most advanced TU students already know how to play TO – they just don’t know it.

The LH is the reverse of the RH; the TO method is used for the descending scale, and the ascending scale is somewhat similar to TU. If your RH is more advanced than the LH, perform the explorations to faster TO speeds using the RH until you decide exactly what to do, then pick up that motion with the LH.

Because students without teachers have difficulty visualizing TO, we examine a video clip comparing TO and TU.

The video shows the RH playing two octaves TO, ascending and descending, played twice. This is then repeated using TU. To non-pianists, these may appear to be essentially the same, although the TU motion was slightly exaggerated. This illustrates why videos of piano motions are not as helpful as one might think. The TO motions ascending are basically correct. The TO motions descending has one error – a slight bending of the nail phalange of the thumb. At these moderate speeds, this slight bending does not affect the play, but in strict TO, the thumb should remain straight for both ascending and descending play. This example illustrates the importance of learning TO as early as possible. My tendency to bend the nail phalange is the result of using only TU for many decades, before I learned TO. An important conclusion here is keep the thumb straight at all times for TO.

c. Practicing TO: Speed, Glissando Motion¶

We now discuss procedures for practicing fast TO scales. The RH C major ascending scale consists of the parallel sets (PSs) 123 and 1234. First, use the PS exercises (7. Exercises) to attain a fast 123, with 1 on C4. Then practice 1231 with the thumb going up and then coming down behind the 3, quickly moving the 3 out of the way as the thumb comes down. Most of the sideways motion of the thumb is accomplished by moving the hand. The last 1 in the 1231 is the conjunction required by the continuity rule (see 8. Continuity Rule). Repeat with 1234, with 1 on F4, and then 12341, with the last 1 rolling over, behind the 4, and landing on C5. Play fingers 234 close to the black keys in order to give the thumb more area to land on. Turn the forearm and wrist so that the fingertips of 2345 make a straight line parallel to the keyboard; thus, when playing middle C, the forearm should make an angle of about 45 degrees to the keyboard. Then connect the two PSs to complete the octave. After you can do one octave, do two, etc.

When playing fast scales, the hand/arm motions are similar to those of a glissando. The glissando type motion allows you to bring the thumb even closer to the passed fingers because all the fingers 2 to 5 are pointing slightly backwards. You should be able to play one fast octave (about 1 octave/sec.) this way after a few minutes of practice (let’s not worry about evenness yet!). Practice relaxing to the point where you can feel the weight of your arm. When you become proficient with TO, you should find that long scales are no more difficult than short ones and that HT is not as difficult as TU. This happens because the contortions of the elbow, etc., for TU become difficult, especially at the high and low ends of the scales (there are many other reasons). It is important to stress here that there is never any need to practice scales HT and, until you become quite proficient, HT practice will do more harm than good. There is so much urgent material we must practice HS, that there is little to be gained by practicing HT, except for brief experimentation. Most advanced teachers (Gieseking) consider practicing fast HT scales to be a waste of time.

In order to control the phase angle (delay of successive fingers) in the PS accurately, raise your wrist (ever so slightly) as you play the PSs 123 or 1234. Then make the transition to the next PS by lowering the wrist to play TO. These wrist motions are extremely small motions, almost imperceptible to the untrained eye, and become even smaller as you speed up. You can accomplish the same thing by rotating the wrist clockwise (cw) to play the PSs and cycling back by rotating ccw to lower the thumb. However, the up and down wrist motion is preferred over the rotation because it is simpler, and the rotation can be reserved for other uses (Sandor). If you now try to play several octaves, it may initially come out like a washboard.

The fastest way to speed up scale playing is to practice only one octave. Once you are up to the faster speeds, cycle 2 octaves up and down. At high speeds, these shorter octaves are more useful because it is difficult to reverse direction at the top and bottom, and these short octaves give you more practice at the ends. With longer runs, you don’t get to practice the ends as often, and the added stretch of the arm to reach the higher/lower octaves is an unnecessary distraction from concentrating on the thumb. The way to play fast reverses at the top and bottom is to play them with a single downward pressure of the hand. For example, to reverse at the top, play the last ascending PS, the conjunction, and the first PS coming down, all in one downward motion. In this scheme, the conjunction is effectively eliminated by incorporating it into one of the PSs. This is one of the most effective ways of playing a fast conjunction – by making it disappear!

In the glissando motion, supinate or pronate the hands so that the fingers point away from the direction of motion of the hand. Now the keydrop motions of the fingers are not straight down, but have a horizontal backward component that enables the fingertips to linger a little longer on the keys as the hand moves along the keyboard. This is especially helpful for playing legato. Example: for RH ascending scale, turn forearm slightly clockwise so that the fingers point to the left. In other words, if the fingers were coming straight down (relative to the hand) and the hand is moving, the fingers would not come straight down onto the keys. By rotating the hand in the glissando direction, this error can be compensated. Thus the glissando motion allows the hand to glide smoothly. You can practice this motion by cycling one octave up and down; the hand should resemble the sideways motion of a skater, with alternate feet kicking sideways and the body tilting left and right while s/he skates forward. The hand should pronate or supinate with each change of direction of the octave. As in skating (where you must lean in the opposite direction before you can change the direction of motion) the rotation of the hand (reversal of glissando hand position) must precede the change in direction of the scale. This motion is best practiced by practicing one octave only.

For the RH descending TO scale, practice the PS 54321, and the other relevant PSs, with and without their conjunctions. You need to make a small modification to avoid letting the thumb fold completely under the hand while the next PS is rolling over the thumb. Lift the thumb as early as possible while keeping the scale smooth, by raising and/or rotating the wrist to pull the thumb up – almost the reverse of what you did for the ascending scale. If you fold the thumb completely under the palm, it will become paralyzed and difficult to move to the next position. This is the “slight modification” referred to above and is somewhat similar to the thumb motion for the ascending scale. For TU play, the thumb can be allowed to fold completely under the palm. Because this motion is somewhat similar in TO and TU, and differ only in degree, it can be easily played incorrectly. Although the differences in motion are small visually, the difference in feeling to the pianist should be like night and day, especially for fast passages.

For ultra-fast scales (over one octave per second), think not in terms of individual notes, but in units of PSs. For the RH, naming 123=A, 1234=B, play AB instead of 1231234, i.e., two things instead of seven. For even faster play, think in units of pairs of PSs AB,AB, etc. As you progress in speed and start thinking in terms of larger units, the continuity rule should be changed from A1 to AB1 to ABA (where the final A is the conjunction). It is a bad idea to over-practice fast, at speeds you can not comfortably manage. The forays into very fast play are useful only for making it easier to practice accurately at a slower speed. Therefore practice most of the time at slower than maximum speed; you will gain speed faster that way.

Try the following experiment in order to get the feel of truly fast scales. Cycle the 5 finger PS 54321 for the RH descending scale, according to the scheme described in the PS exercises (start with Ex. #1). Note that, as you increase the repetition speed, you will need to orient the hand and use a certain amount of thrust or rotation in order to attain the fastest, smooth, and even parallel play. You may need to study the arpeggio section below on “thrust” and “pull” (section f) before you can do this correctly. An intermediate level student should be able to get up to faster than 2 cycles per second. Once you can do this rapidly, comfortably, and relaxed, simply continue it down one octave at the same fast speed, making sure to play it TO. You have just discovered how to play a very fast run! How fast you can play depends on your technical level, and as you improve, this method will allow you to play even faster scales. Do not over practice these fast runs if they start to become uneven because you can end up with non-musical playing habits. These experiments are valuable mainly for discovering the motions needed at such speeds, and to train the brain to handle such speeds. Don’t get into the habit of playing fast and listening to it; instead, the brain must first have a clear idea of what is expected before you play it.

It is best not to start playing scales HT until you are very comfortable HS. If you feel a need to practice scales HT (some use it for warm-ups) start HT practice with one octave, or part of one, such as one PS. For practicing by PSs, the C major scale is not ideal because the thumbs are not synchronized – use B major, where the thumbs of the 2 hands are synchronized, see below. Cultivate the habit of transitioning to HT at a fast speed (although it may seem much easier to start at slow speed and then gradually ramp up). To do this, play one octave LH at a comfortable fast speed several times, repeat the RH at the same speed several times, and then combine them at the same speed. Don’t worry if at first the fingers don’t match absolutely perfectly. First match the starting notes; then match both the start and final notes; then cycle the octave continually; then work on matching every note. Then practice at slow speed, maintaining the same motions, until the scales are very accurate and under complete control, relaxed.

Before going too far with the C major scale, consider practicing the B major scale. See table below for scale fingerings. In this scale, only the thumb and pinky play the white keys, except for the bottom finger (4) of the LH. All other fingers play the black keys. This scale has the following advantages:

It is easier to play initially, especially for those with large hands or long fingers. Each key falls naturally under each finger and there is plenty of room for every finger. For this reason, Chopin taught this scale to beginners before teaching the C major scale.

It allows you to practice playing the black keys. The black keys are more difficult to play (easier to miss) because they are narrower, and require greater accuracy.

It allows play with flatter fingers (less curled), which is better for practicing legato and for tonal control.

TO play is much easier with this scale. This is the reason why I used the C major scale to illustrate the TO method. With the B major, it is more difficult to see the difference between the TU and TO motions. However, for purposes of practicing the proper motions, B major may be superior, if you already understand the difference between TU and TO because it is easier to get to the faster speeds without acquiring bad habits.

The thumbs are synchronized in the B major scale, making it possible to practice HT, PS by PS. Thus HT play is easier than for the C major scale. Once you become proficient with this scale HT, learning C major HT becomes simpler, thus saving you time. You will also understand exactly why the C major is more difficult.

This paragraph is for those who grew up learning TU only and must now learn TO. At first, you might feel as if the fingers get all tangled up and it is difficult to get a clear idea of what TO is. The main cause of this difficulty is the habit you have acquired playing TU which must be unlearned. TO is a new skill you need to learn and is no harder to learn than a Bach Invention. But the best news of all is that you probably already know how to play TO! Try playing a very fast chromatic scale. Starting with C, play 13131231313… The flat finger position may be useful here. If you can play a very fast chromatic scale, the thumb motion is exactly the same as for TO because it is impossible to play a fast chromatic scale TU. Now slow down this fast chromatic thumb motion and transfer it to the B major scale; think of B major scale as a chromatic scale in which only a few white keys are played. Once you can play the B major TO, transfer this motion to C major.

Of course, learning scales and arpeggios (below) TO is only the beginning. The same principles apply to any situation involving the thumb, in any piece of music, anywhere that is reasonably fast. Once the scale and arpeggios are mastered, these other TO situations should come almost as second nature. For this to develop naturally, you must use a consistent and optimized scale fingering; these are listed in the tables below.

Those who are new to the TO method and have learned many pieces using the TU method will need to go back and fix all the old pieces that contain fast runs and broken chords. Ideally, all the old pieces that were learned using TU should be redone so as to completely get away from the TU habit where TO is more appropriate. It is a bad idea to play some pieces TU and others TO for similar fingerings. One way to accomplish the switch to TO is to practice scales and arpeggios first so that you become comfortable with TO. Then learn a few new compositions using TO. After about 6 months or so, when you have become comfortable with TO, you can start converting all your old pieces.

TO and TU should be considered as the extremes of two different ways to use the thumb. That is, there are many other motions in between. One unexpected benefit of learning TO is that you become much better at playing TU. This happens because your thumb becomes technically more capable: it becomes free. And you gain the ability to use all those motions between TO and TU that may be required depending on what other notes are being played or what type of expression you want to create. The thumb is now free to use all of its available motions and for controlling tone. This freedom, plus the ability to now play much more technically difficult material correctly, is what transforms the thumb into a very versatile finger.

d. Scales: Origin, Nomenclature and Fingerings¶

Repeating scales and exercises mindlessly is discouraged in this book. However, it is critically important to develop the skill to play exquisite scales and arpeggios, in order to acquire some basic techniques and standard fingerings for routine playing and sight reading. Scales and arpeggios in all the major and minor keys should be practiced until you are familiar with their fingerings. They should sound crisp and authoritative, not loud but confident; just listening to them should lift up one’s spirits. The most important objective to achieve is to practice until the fingering of each scale becomes automatic.

Before describing the fingerings, let’s discuss some basic properties of scales: the key nomenclature and the question: what is a scale? There is nothing magical or musical about the C major scale; it arises simply from the desire to include as many chords as possible into an octave that can be played with one hand. This is a design feature (just as the most modern features are incorporated into every new car design) that makes it easier to learn/play the keyboard. From the size of the human fingers/hand, we can assume that the largest interval should span 8 keys. How many chords can these keys accommodate? We need the octave, thirds, fourths, fifths, and sixths. Starting from C4, we have now placed E4, F4, G4, A4, and C5, a total of 6 notes, leaving space for only 2 more notes, a full tone and a semitone. Note that even the minor third is already present as A4-C5. If you place the semitone above C4, you end up with one accidental (black key) near C4 and 4 accidentals near C5 in order to complete the chromatic scale, so it is better to place the semitone near C5 so that the octave is better balanced with 2 accidentals near C4 and 3 near C5. This completes the construction of the C major scale, with its accidentals (Sabbatella, Mathiew).

In the nomenclature process, it is unfortunate that C major was not named A major. Thus the octave numbers change at C, not A; therefore, at C4, the notes are numbered ... A3, B3, C4, D4, E4, ... For any scale, the first note is called the tonic, so C is the tonic of the C major scale. The lowest note of an 88-key keyboard is A-1 and the highest note is C8.

The standard major scale ascending fingerings are 12312345 (RH, one octave), 54321321(LH) for C, G, D, A, E major scales (with 0,1,2,3,4 sharps, respectively); these fingerings will be abbreviated as S1 and S2, where S stands for “standard”. The sharps increase in the order F, C, G, D, A, (G major has F#, D major has F# and C#, A major has F#, C#, and G#, etc.) and for the F, Bb, Eb, Ab, Db, Gb, major scales, the flats increase in the order B, E, A, D, G, C; every interval between adjacent letters is a fifth. They are therefore easy to remember, especially if you are a violinist (the violin’s open strings are G, D, A, E). The letters always appear in the sequence GDAEBFC which represents the complete circle of fifths, and this sequence is worth memorizing. Look at B or Gb major scales in a music book and you will see how the 5 sharps or 6 flats line up in the same sequence. Thus 2 sharps will have sharps at F, C, three sharps will be F, C, G, and so on. The flats increase in reverse order compared to the sharps. Each scale is identified by its key signature; thus the key signature of the G major scale has one sharp (F#). Once you learn to recognize the interval of a fifth, you can generate all the scales in order of increasing sharps (by going up in fifths from C) or in order of increasing flats (by going down in fifths); this is useful when you want to practice all the scales in sequence without having to refer to the printed scales. See table below (Table 1.III.5.a - Ascending Major Scales) for the ascending major scales (reverse the fingerings for descending scales).

Table 1.III.5.a - Ascending Major Scales¶

Right Hand	Left Hand	Scale	Sharps / Flats
S1=12312341	S2=54321321	C,G,D,A,E	0,1,2,3,4 sharps
S1	43214321321	B	5 sharps
12341231	S2	F	1 flat
41231234	32143213	Bb	2 flats
31234123	32143213	Eb	3 flats
34123123	32143213	Ab	4 flats
23123412	32143213	Db	5 flats
23412312	43213214	Gb	6 flats

The minor scales are complex because there are 3 families of them, and can be confusing because they are often just called “minor” without specifying which of the three, or worse, each has been given several different names. They were created because they produce moods different from the others. The simplest minor scale is the relative minor (also called natural minor); it is simple because it shares the same key signature as its major relative, but its tonic moves up to the sixth note of its major relative. I find it easier to remember this as a minor 3rd down instead of a 6th up. Thus the relative minor of G major has its tonic at E and the key signature is F#, and is called E (relative) minor. Another minor is the melodic minor; it is created by raising the 6th and 7th notes of the relative minor by a semitone only when ascending; the descending part is unchanged. The third, and the most frequently used, minor is the harmonic minor which is created from the relative minor by raising the 7th note a semitone.

Fingerings for the harmonic minor scales are shown in Table 1.III.5.b (the last column lists the raised note for the minor scale: thus A harmonic minor is ABCDEFG#A, and its relative major is C major). As stated earlier, there is nothing magical about scales; they are simply human creations constructed for convenience – just a framework on which to hang your music. Therefore, you can create any number of them, and the ones covered here, though most widely used, are not the only ones.

Table 1.III.5.b Ascending Harmonic Minor Scales¶

Right H	Left H	Scale	Signat.	Raised N.
S1(RH)	S2(LH)	A	natural	G sharp
S1	S2	E	1 sharp	D sharp
S1	43214321	B	2 sharps	A sharp
34123123	43213214	F#	3 sharps	E sharp
34213123	32143213	C#	4 sharps	B sharp
34213123	32143213	G#	5 sharps	F sharp
S1	S2	D	1 flat	C sharp
S1	S2	G	2 flats	F sharp
S1	S2	C	3 flats	B natural
12341231	S2	F	4 flats	E natural
21231234	21321432	Bb	5 flats	A natural
31234123	21432132	Eb	5 flats	D natural

We can never play scales too well. When practicing scales, always try to accomplish something – smoother, softer, clearer, faster. Make the hands glide, the scale sing; add color, authority or an air of excitement. Quit as soon as you start to lose concentration. There is no such thing as a maximum speed in parallel playing. Therefore, in principle, you can keep increasing the speed and accuracy all your life – which can be quite a bit of fun, and is certainly addicting. If you want to demonstrate your speed to an audience, you can probably do that using scales and arpeggios at least as well as with any piece of music.

e. Arpeggios (Chopin’s FI, Cartwheel Motion, Finger Splits)¶

Playing arpeggios (arps) correctly is technically complex. This makes arps particularly suitable for learning some important hand motions, such as thrust, pull, and the “cartwheel motion”. “Arpeggio”, as used here, includes broken chords and combinations of short arpeggic passages. We shall illustrate these concepts here using Beethoven’s Moonlight Sonata (3rd Movement) for the thrust and pull, and Chopin’s Fantaisie Impromptu (FI) for the cartwheel motion. Recall that suppleness of the hands, especially at the wrist, is critical for playing arps. The technical complexity of arps arises from the fact that in most cases, this suppleness must be combined with everything else: thrust, pull, cartwheel motion, glissando (or finger splits) motion, and TU or TO. One note of caution: the Moonlight is difficult because of the required speed. Many Beethoven compositions cannot be slowed down because they are so intimately tied to rhythm. In addition, this movement requires a minimum reach of a 9th, comfortably. Those with smaller hands will have more difficulty learning this piece than those with adequate reach.

Let’s first discuss how to play TO arps. Arps extending over several octaves are played TO just like scales. Therefore, if you know how to play TO scales, you know, in principle, how to play TO arps. However, the method of playing TO arps is a more extreme example of the TO motion than for scales and therefore serves as the clearest example of this motion. We noted above that the easiest TO motion is that used in playing chromatic scales (1313123131312 … for the RH). The chromatic TO motion is easy because the horizontal motion of the thumb is small. The next slightly more difficult motion is that for playing the B major scale. This TO motion is easy because you can play the entire scale with flat fingers so that there is no collision problem with the passing thumb. The next in difficulty is the C major scale; it is more difficult because all the fingers are crowded into the narrow white key area. Finally, the most difficult motion is the TO arp in which the hand must move rapidly and accurately. This motion requires a slight flex and flick of the wrist, sometimes described as a “throwing” motion. The nice thing about acquiring the TO arp motion is that, once you learn it, you simply have to make a smaller version of the same motion in order to play the easier TO motions.

The standard fingering for the CEGCEG ... C arp is 123123….5, RH, and 5421421….1, LH ascending, and reverse for descending. See Michael Aaron, Adult Piano Course, Book Two for fingerings of all arps and scales.

Because arps jump over several notes, most people spread the fingers to reach those notes. For fast arps, this is a mistake because spreading the fingers slows down their motion. The key method for fast arps is to move the hand instead of spreading the fingers. If you move the hand and wrist appropriately, you will find that it is not necessary to spread the fingers. This method also makes it easier to relax.

The Cartwheel Method (Chopin’s FI): In order to understand the cartwheel motion, place your left palm flat on the piano keys, with the fingers spread out like the spokes of a wheel. Note that the fingertips from pinky to thumb fall on an approximate semi-circle. Now place the pinky above C3 and parallel to it; you will have to rotate the hand so that the thumb is closer to you. Then move the hand towards the fallboard so that the pinky touches the fallboard; make sure that the hand is rigidly spread out at all times. If the 4th finger is too long and touches the fallboard first, rotate the hand sufficiently so that the pinky touches the fallboard, but keep the pinky as parallel to C3 as possible. Now rotate the hand like a wheel counter clockwise (as viewed from above) so that each successive finger touches the fallboard (without slipping) until you reach the thumb. This is the cartwheeling motion in the horizontal plane. If your normal reach is one octave with your fingers spread out, you will find that the cartwheeling motion will cover almost two octaves! You gain extra reach because this motion makes use of the fact that the center three fingers are longer than the pinky or thumb, and the circumference of a semi-circle is much larger than the diameter. Now repeat the same motion with the hand vertical (palm parallel to fallboard), so the fingers point downwards. Start with the pinky vertical and lower the hand to play C3. Now if you roll the hand up towards C4, (don’t worry if it feels very awkward), each finger will “play” the note that it touches. When you reach the thumb, you will again find that you have covered a distance almost twice your normal reach. In this paragraph, we learned three things:

How to “cartwheel” the hand

This motion expands your effective reach without making any jumps

The motion can be used to “play” the keys without moving the fingers relative to the hand.

In actual practice, cartwheeling is used with the hand somewhere between vertical and horizontal, and the fingers will be in the pyramid position or slightly curved. Although cartwheeling will add some keydrop motion, you will also move the fingers in order to play.

Believe it or not, the reach can be stretched even more by use of “finger splits” (Fraser), which is a form of glissando motion. Picture applying an exaggerated glissando motion to the arp, RH, ascending, CEGCEG... ; you can now spread the distance between fingers more than the cartwheel. To demonstrate this, make a “V” with fingers 2 & 3 and place the “V” on a flat surface, at the edge, so that only the “V” is on the surface. Spread the “V” as far as you can with comfort and ease. Then rotate your arm and hand 90 degrees clockwise so the fingers are now touching the surface with their sides. This is an exaggerated glissando position. Now you can spread the fingers even more. This works with any pair of fingers.

Therefore, by using a combination of TO, FFP, cartwheel motion and finger splits, you can easily reach and play fast arps with little stress on the stretching muscles. Notice that this complex combination of motions is enabled by a supple wrist. Once you become comfortable with this combination of motions, you will have enough control so that you gain the confidence that you will never miss a note. Practice the CEG arp using these motions.

We apply this method to the LH broken chords of Chopin’s FI. In 2. Cycling (Chopin’s Fantaisie Impromptu), we discussed the use of cycling to practice the LH. We will now add the cartwheel motion, etc., to the cycling. Cycle the first 6 (or 12) LH notes of bar 5 (where the RH first joins in). Let’s start with just the cartwheel motion. If you position the hand almost horizontally, then practically all the keydrop must be accomplished by finger motion. However, if you raise the hand more and more towards the vertical, the cartwheeling motion will contribute more keydrop and you will need less finger motion to play. Cartwheeling is especially useful for those with small hands because it automatically expands the reach. Cartwheeling also makes it easier to relax because there is less need to keep the fingers spread widely apart. You will also find that your control increases because the motions are now partly governed by the large motions of the hand which makes the playing less dependent on the motion of each finger and gives more uniform, even results. Use as much FFP as you need, and add a small amount of glissando motion.

The RH is an even bigger challenge. Most of the fast runs should be practiced using the basic keystroke (practicing slowly) and parallel sets (for speed). The part starting at bar 13 should be practiced like the tremolo (section 3.b), and then applying the parallel sets. That is, practice first (slowly) using only the fingers with no hand motion. Then use mostly arm/hand rotation to play the 15. Exaggerate these motions while practicing slowly; then gradually speed up by reducing each motion, then combine them to play even faster. Then apply parallel sets, playing all 4 notes in one down motion of the hand. Play white keys with curled fingers and black keys with FFP. Use the palm widening muscles (e. Playing (Wide) Chords, Finger/Palm Spreading Exercises) instead of the finger spreading muscles and practice rapid relaxation after playing each 15 octave.

f. Thrust and Pull, Beethoven’s Moonlight, 3rd Movement¶

For those who are learning Beethoven’s Moonlight Sonata for the first time, the most difficult section is the two-hand arpeggic ending of the 3rd movement (bars 196-198; this movement has 200 bars). By illustrating how to practice this difficult passage, we can demonstrate how arpeggios should be practiced. Let’s try the RH first. In order to simplify the practice, we skip the first note of bar 196 and practice only the following 4 ascending notes (E, G#, C#, E), which we will cycle. As you cycle, make an elliptical, clockwise motion (as seen from above) of the hand. We divide this ellipse into two parts: the upper part is the half towards the piano and the lower part is the half towards your body. When playing the upper half, you are “thrusting” your hand towards the piano, and when playing the lower half, you are “pulling” the hand away from it. First, play the 4 notes during the upper half and return the hand to its original position using the lower half. This is the thrust motion for playing these 4 notes. Your fingers tend to slide towards the piano as you play each note. Now make a counter clockwise motion of the hand and play the same 4 ascending notes during the lower half of the ellipse. Each finger tends to slide away from the piano as it plays each note. Those who have not practiced both motions may find one much more awkward than the other. Advanced players should find both motions equally comfortable.

The above was for the RH ascending arp. For the RH descending arp, let’s use the first 4 notes of the next bar (same notes as in preceding paragraph, an octave higher, and in reverse order). Again, the pull motion is needed for the lower half of the clockwise motion, and the thrust is used for the upper half of the counter clockwise rotation. For both ascending and descending arps, practice both thrust and pull until you are comfortable with them. Now see if you can figure out the corresponding exercises for the LH. Notice that these cycles are all parallel sets and therefore can eventually be played extremely fast.

Having learned what the thrust and pull motions are, you might reasonably ask, “why do you need them?” First, it should be pointed out that the thrust and pull motions use different sets of muscles. Therefore, given a specific application, one motion has to be better than the other. We will learn below that one motion is stronger than the other. Students who are not familiar with these motions may randomly pick one or switch from one to the other without even knowing what they did. This can result in unexpected flubs, unnecessary stress, or speed walls. The existence of the thrust and pull is analogous to the situation with TU and TO. Recall that by learning both TU and TO, you get to fully utilize all the capabilities of the thumb. In particular, at high speed, the thumb is used in a way which is about midway between TU and TO; however, the important thing to keep in mind is that the thumb motion must be on the TO side of dead center. If you are even slightly on the TU side, you hit a speed wall.

The analogy of thrust and pull to TU and TO go even further, because thrust and pull also have a neutral motion, just as TU and TO have a range of motions in between. You get the neutral motion by reducing the minor axis of the ellipse to zero; i.e., you simply translate the hand right and left without any apparent elliptical motion. But here again, it makes a big difference whether you approach the neutral position from the thrust side or the pull side, because the seemingly similar neutral motions (approached from thrust or pull side) are actually being played using a different set of muscles. Let me illustrate this with a mathematical example. Mathematicians will be horrified if you tell them that $0 = 0$ , which at first glance seems to be trivially correct. Reality, however, dictates that we must be very careful. This is because we must know the true meaning of zero; i.e., we need a mathematical definition of zero. It is defined as the number $\frac{1}{N}$ , when $N$ is allowed to go to infinity. You get to the “same” number zero, whether $N$ is positive or negative! Unfortunately, if you try to divide by zero: $1/0$ , you get a different answer depending on whether $N$ is positive or negative. $1/0 = \infty$ when $N$ is positive, and $1/0 = -\infty$ when $N$ is negative! If you had assumed the two zeros to be the same, your error after the division could have been as large as two infinities depending on which zero you used! In a similar way, the “same” neutral positions achieved by starting with TU or TO are fundamentally different, and similarly with thrust and pull. That is, under certain circumstances, a neutral position approached from either thrust or pull is better. The difference in feel is unmistakable when you play them. This is why you need to learn both.

This point is so universally important, especially for speed, that I will illustrate it with another example. The Samurai’s life depends on the speed of his sword. In order to maximize this speed, the sword must always be in motion. If he simply raises the sword, stops, and lowers it, the motion is too slow and his life is endangered. The sword must continually move in some circular, elliptical, or curved motion, even when it looks like he is simply raising and lowering it. This is one of the first lessons in swordsmanship. Thus the use of generically circular motions to increase speed has universal validity (tennis serve, badminton slam, etc.), and applies to the piano also.

OK, so we have established that thrust and pull are both needed, but how do we know when to use which? In the case for TU and TO, the rules were clear; for slow passages you can use either one, and for certain legato situations, you need TU; for all others you should use TO. For arps, the rule is to use the strong motions as a first choice and the weak motions as a secondary choice. Each person has a different strong motion, so you should first experiment to see which is strongest for you. The pull motions should be stronger because our pulling muscles in the arms are stronger than the pushing muscles. Also, the pull motions use the fleshy parts of the fingers whereas the thrust motions tend to use the fingertips which tends to injure the fingertips and to strain the attachment of the fingernails.

Finally, one can ask the question, “why not always play neutral - neither thrust nor pull?” Or learn one (pull only), and become very good at it? Here again, we are reminded of the fact that there are two ways to play neutral depending on whether you approach it from the thrust side or pull side, and for a particular application, one is always better than the other. As for the second question, a second motion may be useful for endurance because it uses a different set of muscles. Not only that, but in order to play the strong motions well, you must know how to play the weak motions. That is, you play best when the hand is balanced in the sense that it can play both motions. Therefore, whether you decide to use thrust or pull for a particular passage, you should always practice the other one also. That is the only way that you will know which motion is best for you. For example, as you practice this ending of Beethoven’s sonata, you should find that you make faster technical progress by practicing every cycle using both thrust and pull. In the end, most students should end up playing very close to neutral, although a few may decide to use exaggerated thrust or pull motions.

There is much more new material to practice in this 3rd movement before we should be playing HT, so at this stage, you probably do not need to practice anything HT, except as experimentation to see what you can or cannot do. In particular, trying HT at the highest speeds will be counter-productive and is not recommended. However, cycling a short segment HT can be quite beneficial; but this should not be over-practiced if you still cannot play it satisfactorily HS. The main difficulties in this movement are concentrated in the arps and Alberti accompaniments (“do-so-mi-so” type); once these are mastered, you have conquered 90% of this movement. For those without sufficient technical skill, you should be satisfied with getting up to about quarter-note = 120 BPM. Once you can play the entire movement comfortably at that speed, you might try to mount an effort towards presto (above 160). It is probably not a coincidence that with the 4/4 signature, presto corresponds to the rapid heart beat rate of a very excited person. Note how the LH accompaniment of bar 1 actually sounds like a beating heart.

We shall now outline our plan of attack for learning this movement. We started with the most difficult part, the two-hand arp at the end. Most students will have more difficulty with the LH than the RH; therefore, once the RH is fairly comfortable, start practicing the RH arp of the first two bars of this movement, while still practicing the LH part of the ending. One important rule for playing arps rapidly is to keep the fingers near the keys as much as possible, almost touching them. Do not lift the fingers far off the keys. Remember to use flat finger positions for black keys and the curled position for white keys. Thus in the first 2 bars of this 3rd movement, only the D is played with curled fingers. This habit of curling only specific fingers for each ascending arp is best cultivated by cycling parallel sets. Clearly, a major technical skill you must learn is the ability to quickly change any finger from flat to curl, independently of the others.

The pedal is used in only two situations in this piece:

At the end of bar 2, at the double staccato chord and all following similar situations

Bars 165-166, where the pedal plays a critical role

The next segment to practice is the tremolo type RH section starting at bar 9. Work out the fingering of the LH carefully – those with smaller hands may not be able to hold the 5th finger down for the duration of the 2 bars. If you have difficulty interpreting the rhythm of this section, listen to several recordings to get some ideas. Then comes the LH Alberti accompaniment starting at bar 21, and similar RH parts that appear later. The Alberti accompaniment can be practiced using parallel sets, as explained starting at 8. Continuity Rule. The next difficult segment is the RH trill of bar 30. This first trill is best performed using 3,5 fingering and the second one requires 4,5. For those with small hands, these trills are as difficult as the ending arps, so they should be practiced from the very beginning, when you first start learning this movement. These are the basic technical requirements of this piece. The cadenza of bar 186 is an interesting combination of a “scale” and an arp; if you have difficulty interpreting it, listen to several recordings to get some ideas. Don’t overlook the fact that bars 187 and 188 are adagio.

Start HT practice after all these technical problems are solved HS. There is no need to practice using the pedal until you start HT. Note that bars 163, 164, are played without pedal. Then application of the pedal to bars 165, 166, gives meaning to these last 2 bars. Because of the fast pace, there is a tendency to practice too loud. This is not only musically incorrect, but technically damaging. Practicing too loud can lead to fatigue and speed walls; the key to speed is relaxation. It is the P sections that create most of the excitement. For example, the ff of bar 33 is only a preparation for the following p, and in fact, there are very few ff’s in the entire movement. The whole section from bar 43 to 48 is played p, leading to just one bar, #50, played f.

Finally, if you have practiced correctly, you should find certain speeds at which it is easier to play faster than slower. This is completely natural in the beginning, and is one of the best signs that you have learned the lessons of this book well. Of course, once you have become technically proficient, you should be able to play at any speed with equal ease.

g. Thumb: The Most Versatile Finger¶

The thumb is the most versatile finger; it lets us play scales, arpeggios, and wide chords (if you don’t believe it, try playing a scale without the thumb!). Most students do not learn how to use the thumb correctly until they practice scales. Therefore it is important to practice scales as soon as possible. Repeating the C major scale over and over, or even including the B major, is not the way to practice scales. It is important to practice all the major and minor scales and arpeggios; the objective is to ingrain the correct fingering of each scale into the fingers.

Play with the tip of the thumb, not the first joint. This makes the thumb effectively as long as possible, which is needed because it is the shortest finger. In order to produce a smooth scale, all the fingers need to be as similar as possible. In order to play with the tip of the thumb, you may have to raise the wrist slightly. Using the tip is helpful at high speeds, for better control, and for playing arpeggios and chords. Playing with the tip facilitates TO and the “glissando motion” in which the fingers point away from the direction of motion of the hand. Do not exaggerate the glissando motion, you only need a small amount.

It is most important to liberate the thumb by practicing TO and a very flexible wrist. Except for TU, the thumb is always straight and is played by pivoting at the wrist joint and is moved into position by wrist and hand motion. One of Liszt’s most significant technical improvements occurred when he learned to use the thumb correctly.

h. Fast Chromatic Scales¶

The chromatic scale consists of semitone steps. The most important consideration for chromatic scales is the fingering, because there are so many ways to finger them. The standard fingering, starting from C, is 1313123131345 for ascending RH, and 1313132131321 for ascending LH for one octave (the top is fingered for a return) and the reverse for descending. This fingering is difficult to play fast because it is composed of the shortest possible parallel sets and therefore contains the largest number of conjunctions; it is usually the conjunctions that limit the speed. Its main advantage is simplicity which makes it applicable to practically any chromatic segment, starting from any note, and is the easiest to remember. One variation of this is 1212123121234, which enables a little more speed and legato, and is more comfortable for those with large hands.

In attempts to speed up the chromatic scale, several sequences using longer parallel sets have been devised; all of the “accepted” sequences avoid the use of the thumb on a black key. The most commonly used is, starting from E, 123123412312 (Hauer, Czerny, Hanon). One complication with this fingering is that the starting sequence should be changed depending on the starting key in order to maximize velocity. Also, the RH and LH are different; this sequence uses 4 parallel sets. You can shrink it to 3 parallel sets by playing, starting at C, 123412312345. With good TO technique, this scale might be playable, but even with TO, we rarely use a 51 or 15 transition, which is difficult. Clearly, the restriction of avoiding the thumb on a black key limits the choice of fingering and complicates matters because the fingering will depend on the starting note.

If we allow one thumb on a black key, a good scale is, starting from C:

1234,1234,1234; 1234,1234,12345, 2 octaves RH ascending,

5432,1432,1432; 1432,1432,14321, 2 octaves LH ascending,

with the thumb on G# for both hands and 3 identical parallel sets per octave - the simplest and fastest possible configuration. Reverse to descend. I call this the “4-finger chromatic scale”; as far as I know, this fingering has not been discussed in the literature because of the thumb on a black key followed by passing over the 4th finger. In addition to speed, the biggest advantage is simplicity; you use the same fingering no matter where you start (for example, use finger 3 for starting the RH with D), ascending or descending, the fingering is the same for both hands (in reverse), the thumbs and fingers 3 are synchronized, and the beginning and end is always 1,5. With good TO technique, this scale is unbeatable; you only need to pay attention to the 14 or 41 where 1 is on G#. Try this on the last chromatic run in the Grave of Beethoven’s Pathetique and you should notice a marked decline in the number of flubs and eventually a significant increase in speed. Once you learn it for this run, it will work for any other chromatic run. In order to develop a smooth run, practice with the beat on every note, every other note, every third note, etc.

In summary, although most exercises are not helpful, exercising scales, arpeggios and the 4-finger chromatic scale have a special place in piano technique acquisition. Because you can use them to learn so many fundamental technical skills, they must be part of a pianist’s daily practice program.