Playing Through vs. Spot Work

 

The quality of your practice time will largely determine your progress at the piano, or lack of it. Quality is far more important than quantity. Yet people often ask me "How long should I practice" before they ask "How should I practice." Many people still believe that if they just put in the hours, doing endless repetition, that someday it will just all come together and they will play really well. Unfortunately this is never the case. If you are spending many hours at the piano but doing the wrong things, you will certainly not improve, and your frustration level will be so high you will probably lose your desire to play.

With my students, I am always showing them how to practice. There are numerous aspects of practicing, many of which I have discussed in previous posts. The one I want to talk about here is the question of whether you should practice playing through the piece (or at least a large section), start to finish, versus doing what I call "spot work," that is, just practicing a particular measure (or measures) that seem to be more difficult. The answer is that you need both.

Let's say you are a beginner to intermediate-level student. You are starting a brand new piece. What should you do first? I strongly recommend that you outline the piece, start to finish. See my previous posts on outlining for more about this important skill. Essentially you are playing a sketch of the piece, but not all the notes. There is no right or wrong for how much to play and how much to omit; you just do what you are able to do. This way you get "the lay of the land" so to speak, and you hear what the piece sounds like. Continue outlining, gradually putting in more detail. At some point, you will discover that some sections, or particular measures, present more of a challenge, technically. At this point it would be entirely suitable to take those measures and "take them apart." You may need to do some hands separately, or play some of the voices separately, or you may need to do other technical work, to get those measures to improve.

At a recent lesson with a student who came to me having largely taught himself, he played a short piece, and at a measure near the end, he played it suddenly louder and more "aggressively," that is, it just had a different quality of sound than the rest of the piece. I asked him if he was aware of that, and if he knew why. The answer (which I already knew, based on my decades of teaching) was that he had "drilled" that measure because of something in it which he thought he was having trouble with. In his practice at home, he had played that measure over and over, to the point where he had caused it to sound, frankly, somewhat ugly. 

This is the problem with spot work. If you overdo it, that part of the piece may take on a different quality, and you probably won't realize it's happening. It eats up a lot of your practice time which might have been better spent in a different way. It also affects you psychologically, because when playing the piece through you are likely to think "uh-oh, here comes that spot." That will cause further problems because you will likely become tight and tense, which will, in turn, cause you to miss more notes, and create more anxiety about that spot. And so on, in a viscious circle.

I recommend a "gentle" approach to spot work. Do some if you think (or your teacher recommends) you need it, but not too much. See if just a little does the trick. Try to employ more creative problem-solving methods such as those in previous posts, rather than just repetition. Then play the piece through again and see what happens.

If you can play a piece through without doing any spot work, that would be wonderful, because you can focus on the musicality and just enjoy the experience of playing. However, it could indicate that this piece doesn't present enough challenge to you, and by choosing more challenging pieces, your skills would progress faster. On the other hand, if all of the piece is so challenging that you feel almost every measure is a "spot" you need to work on separately, then this piece may be too difficult for you at this stage. If it requires technical skills you simply do not have yet, then, with the guidance of a teacher, you can find pieces that will build up those skills.

It is important to strike a balance between playing through (including outlining) and spot work. This way, you don't ignore "problem areas" which need work, but you don't overdo it to the point where you lose musicality and beauty in your playing.

Do You Hear Voices?

 

When you hear about someone who "hears voices," it might make you a little worried. However, in music is essential to hear voices.

What I am referring to here is the phenomenon that virtually all of our music is made up of several lines, or voices, at least to some degree. The term "voice" comes, of course, from vocal music, which was the earliest music. In the middle ages almost all music was vocal -- largely religious music sung in church. As instrumental music began to be more prevalent, it still imitated vocal music to a great degree. Our music evolved as separate lines woven together. Melody preceeded harmony; harmony grew out of the fact that some tones, when occuring at the same time, were very pleasing, very "harmonious," and began to be viewed as entities in and of themselves. If you are a singer or instrumentalist on a single-line instrument, you will only have one "voice" to play or sing; but if you are a part of a choir or ensemble or symphony, your voice is one part of the greater whole. This is, hopefully, fairly obvious. If you are a pianist, however, you are very rarely just playing a single line melody, that is, one note at a time. You will be playing the whole gamut of melody and harmony. That is the beauty and the brilliance of piano.

When a new student comes to me who has studied with other teachers or is self-taught, I am still amazed that they don't seem to have any awareness of the concept of voices. They learned simply to "play the notes" that they see on the page. But piano music is never just monolithic. Let's consider a simple example. If you are playing a Bach two-part invention, you have two separate but complementary lines, one in right hand and one in left. One is not more important than the other. Yet I hear some people play it as if right hand has the melody and left hand has an accompaniment. This is not at all correct; instead it needs to be played as a dialogue between the two voices. Of course the same thing goes for a three-part invention. When you have a four-part piece, it could be a fugue (but not necessarily). You can't possible play a fugue well if you don't have understanding and awareness of the voices. Your practice should include playing each voice separately, so you can hear it clearly and "trace its path." Then play different combinations of two, and then three voices, and finally all four. Now you will more clearly hear the interweaving of these lines, and you will hopefully know which one(s) to bring out at any given point. If you can't hear each voice clearly, your listener will certainly not be able to either.

We call these voices soprano, alto, tenor and bass, just like actual voices in a choir.

How can you tell which voice is which? For one thing, the music is written in a way to indicate the voices very clearly. If it is a four-voice fugue, you may have two voices in the right hand and two in the left, although there may very well be a few spots where this isn't the case. On the treble clef, the soprano voice will mostly have the note stems (on quarter notes, eighth notes, etc.) pointing up, and the alto voice will have them pointing down. In the bass clef, tenor voice will be up, and bass voice down. Be aware that the voices can cross, with the alto being higher than the soprano, for example, at some point, just like in an actual choir. But regardless, the stem direction always identifies one voice versus another. In a piece such as a fugue, which is 100% polyphonic (multiple voices), this should be pretty clear. 

After the Baroque era, music became less polyphonic. An early Mozart piece, for example, could consist of a melody (in right hand) with a chord-based left hand. It may or may not be this way the entire piece, but if it is mostly that way we would refer to it as homophonic, not polyphonic. But in the more complex pieces of the Classical era, and most definitely by Beethoven, piano music is more often than not a combination of both. Take two examples of pieces by Beethoven that piano students love to play: the first movement of the so-called Moonlight Sonata (Beethoven did not name it this), and the second movement of the Pathetique sonata. In both cases there is a top-line melody, an inner voice of broken chords, and a bass line of single notes or octaves. In Moonlight, the broken C-sharp minor chord (the triplet) begins the piece, and the melody starting on G-sharp comes in a few measures later. In the Pathetique, the top melody is in quarter notes, with the middle voice in sixteenths. Together they make a complete chord, but they are still intended to be heard as two entities. In both cases, the stems of the top voice point up, and in the middle voice they point down. More to the point, the two voices have different rhythmic values, so they are clearly two things happening simultaneously. In both cases, if the notes of the top voice are not held for their full value, the middle voice will interrupt and will be indistinguishable from the main melody. Similarly, if you play both voices at the same dynamic level, the middle voice will compete with the top melody; the middle voice must be softer, more subdued. Another great example that students love to play (often before they are ready, in my opinion) is Traumerei by Schumann. This is essentially a four-voice composition, though in a few spots the alto and tenor split in two, making six voices. I recommend you make several copies of this piece, and in each copy, use a colored highlighter to trace the path of each voice. Sometimes the alto and tenor go from one hand to the other, so you have to look closely. After you've played each voice, play them in combinations of two, such as soprano and bass, then alto and tenor, and so on. I guarantee you will hear the piece differently than if you don't do this.

You would be hard-pressed to find any piece of Chopin, Schumann, Rachmaninoff, Debussy, Ravel, and just about any composer in the last 300 years or so, that isn't multi-dimensional. I've actually had many people tell me they had no idea these pieces had separate voices. If I hear someone play these compositions, I can tell immediately whether he/she is even aware that these are multi-layered compositions.

If you just play all the notes without this awareness, you essentially have a one-dimensional picture rather than a three-dimentional (or more) picture. It would have no "depth." Or, I make the analogy that you have a beautiful gourmet dinner on your plate, with several items, each with distinct taste and texture, and you take your fork and mush it all together. Theoretically you still have all the same flavors, but you can no longer taste each one, and the mushed-together flavor is very different from tasting each one by itself.

First you must understand that your pieces are multiple voices. Then you must learn to practice in such as way as to hear each voice. Then your technique must be advanced enough to enable you to play at different dynamic levels, even within one hand. If this is new information to you, and/or has never been mentioned or taught by your current teacher, it is imperative that you get a different teacher. If you are trying to learn on your own (not ideal, in my view) and this is new to you, take a fresh look at all the pieces you are working on in this new light. You can also listen to recordings (of professional pianists only) and direct your listening to the differentiated voices to refine your listening in this way.

You want to become one of those people who hears voices -- at least in music!

Progress Over Perfection

 

I recently saw someone wearing a t-shirt with this phrase, and thought it perfectly expressed my philosophy about learning to play the piano.

In my almost four decades of teaching piano, I have had many students, ranging from total beginner to intermediate to advanced. I would say that in almost 100% of students, the goal of playing "all the right notes" is their highest priority, at least when they start lessons with me. But over time, hopefully, I enable them to see that having this as your top priority (sometimes even their only priority), will be detrimental to both short and long term progress.

Some students who have come to me having had some lessons previously or having tried to teach themselves, focus so exclusively on "the notes" that the rhythm is totally ignored. Somehow they think they will "add the rhythm later." This is preposterous; the rhythm and the notes are inextricably enmeshed to make the particular music what it is. You cannot just take out the rhythm and try to add it back later. In focusing only on the notes, they ignore phrasing and dynamics and all the other nuances which make music beautiful. Again, they think they can add these later, but by the time they have "learned the notes," their habit of playing without these nuances is deeply entrenched and is almost impossible to change.

Students who come to me from other teachers and/or self-taught also tell me that they spent many months learning one piece, with great difficulty and a fair amount of drudgery. Then, I assume, they enjoyed playing it for a while, but if they stopped playing it for a short period, they could no longer play it. Then they would start the next piece and go through that process again. In the end, they really had almost no music they could just sit down and play, despite all the hours and months of work. This is because they learned notes but not skills. The learning was at a superficial level, so with lack of reinforcement (playing every day), it just disappeared. In focusing solely on the notes, they didn't work on developing their physical skills (technique) except for the minimum required by that piece. Nor did they develop their ear. So with the next new piece, which may require some different aspects of technique, they are starting from square one. If it takes you many months to learn a piece, you will only have exposure to very few pieces in the course of, say, a year, and you will not be able to acquire a broad range of technical skills. I might also add that most people who approach it in this way are trying to play pieces far too advanced for their skill level, so they don't have even the foundation of technique to be able to play that piece.

I always tell my students I am teaching skills, not pieces. The pieces are vehicles for learning skills. That doesn't mean that they are to play their pieces as exercises -- in fact the exact opposite. Playing musically, that is, with phrasing, dynamics, nuances of timing and so on -- is part of the skill set they need to acquire. They need to play pieces at the appropriate level of difficulty (which any good teacher must be able to assess), so that they aren't struggling too much, but yet are somewhat challenged. 

Perhaps the most important aspect of this approach is that you must give up on the idea of 100% correct notes 100% of the time. If this is your only metric of progress, you will do just about anything that you think will help you hit the right notes. These include, stopping and "fixing," looking at your hands, writing the note names in the music, listening to the piece on YouTube and trying to imitate, and a host of other things. These will actually take you backwards in your progress. They hamper your sight-reading, your kinesthetic awareness, your ear development, and your confidence. If you do these "cheater" approaches, thinking that one day you will magically play it all correctly, you will be sadly disappointed, to the point where you probably will consider giving up the piano.

In the course of learning to play the piano, or any other instrument, you will play many wrong notes. Get over it! It is part of the learning process. I often think of Olympic ice skaters who do those incredible jumps and leaps without falling. Do you think they never fell when they were learning to do these? Of course not; they fell all the time. If they hadn't been willing to fall, they never could have learned those techniques. It is the same with piano. Not only do you need to accept wrong notes, you need to embrace them. If you have a good teacher and also try to employ a great deal of self-awareness, you will start to see WHY you have the wrong notes. It is almost never random. Only if you know the reason for them can you take steps and practice in such a way to gradually reduce and/or eliminate them. But again, eliminating wrong notes is not the goal in itself. The goal is to have solid technique. If you are making progress in the areas of technique, ear-training, and musical expression, you will probably be quite happy and enjoy the process. 

I often think of this story: the student of a spiritual practice goes to see the Master and says: "Master, how do I keep from making so many mistakes?" The master replies: "Ahh...Experience." The student then asks: "But how do I get experience??" The master replies: "By making mistakes."

I hope you will keep this in mind in your piano practice. Experience, rather than avoiding mistakes, is the goal. Progress over perfection.

What chord am I on?

 

I am a firm believer that we must always try to approach music at the macro rather than the micro level. Unfortunately many beginners and even some more advanced players are so focused on "the notes" that they really do miss the proverbial forest for the trees. Although, yes, we play "the notes," they are always part of some larger entity: chords.

All of the music you are likely to play at the piano will be built of chords in one way or another. The only exceptions might be ultra-modern music and I can't really speak to that. But if you are playing Bach through 20th century music, it is built on chords. Even if you think Bach is polyphonic, meaning a weaving of individual lines, those lines created harmonies, that is, chords.

I ALWAYS know what chord I am on at any moment. It has become so second nature to me that I barely think about it consciously, but I just know at a deep level what the chord is. I never just see or hear it as a bunch of notes. I am referring to chords whether they are blocked, that is, played all at once, or broken, such as an arpeggio.

Here are some of the ways that knowing what chord(s) you are on will help you;

1. Reading. If you are still at the stage in your sight reading where you see several notes and need to identify them one by one, rather than seeing the whole thing (maybe 3,4,5 notes or more) as a chord, then your sight reading will be slow and inefficient. Think of a chord as a word. When you read English, you see the word, not the individual letters. Imagine if you still had to sound out the letters of every word when you read. That would be the equivalent of reading note by note.  If you've read my earlier posts on sight-reading, you know I emphasize reading by interval. If you see a group of notes and you immediately see it as a "shape," meaning its particular intervals, then you are much more likely to recognize it as a chord. That is the first step; the second step is to know which chord. Knowing the chord will always help you, but a situation where you will find it immensely helpful is when the chord is written with what I would call an alternate "spelling." Let's say you encounter the notes C-flat, E-flat, G-flat, B double flat; you might find that hard to read at first. But it is simply a B7 chord, written as a C-flat-7. (This would be the case if you were in a key with flats; it makes more sense musically to spell it in flats rather than sharps.) Once you see that, it becomes so easy, because it's something you are highly familiar with.

2. Memorizing. Although muscle memory is very important in learning to play by memory, it is not the only skill needed. Ear memory is probably the most important (see earlier posts). But sometimes those two skills need a little help, especially if, say, two passages in the piece are slightly different, and one chord progression leads to one place, and the other similar but not identical chord progression leads to another place. Knowing which chords are which will make sure you don't accidentally end up in the wrong place. Many a beginning or intermediate pianist has played, say, at a recital, and found themselves in a loop, or at the wrong place, to great embarrassment, because they just depended on muscle memory and didn't know the chord progressions.

3. Ear. Whether you realize it or not, you already hear chords as chords, because if you are playing, say, three or more notes, you hear the blended sound more than you hear the individual ones. But it is important to tie the auditory to the intellectual knowledge. Fusing the two together will make them both stronger. If your ear is very strong and well-developed, theoretically you wouldn't need to know the chord name. Some self-taught pianists may do this. But why would you want to be in the dark about this? I can assure you that jazz pianists, who play by improvisation and/or a "sketch" of the piece, would absolutely have to know every chord they play. In the moment of playing it goes by too fast to consciously "think" about, but at a very deep level they know all the chords. I believe classical pianists can and absolutely should do this as well.

4.Understanding musical forms and structure. The story of classical music is largely the story of harmony. While other cultures developed in different ways, classical music became more and more rich and varied in its harmonies through the last four centuries or so. The progression of the harmonies cannot by separated from the structure and form of the music. As an example: the sonata form has a first section which changes to a different key, then a middle section which may go through several keys, and a third section which must return to the original key for the ending. All of this modulating (key changes) depends on the harmonies to get it where it wants to go. There is simply no other way.

So how do you get this chord knowledge? If you don't have a teacher who knows it herself and can teach it, you can get a good book on harmony. But absolutely do not buy a chord chart or something which just tells you where to place your fingers for each chord; you will never have deep knowledge that way. You need to understand how chords are built, and then how they function. A textbook can be quite dry. But you need to start somewhere. Then I would encourage you to play songs, such as jazz standards, using a "fake book," where the chords are written as symbols rather than notation. In the course of playing many songs will get more proficient with chords. Then you can go through a classical piece and do what we call chord analysis. You will write (in pencil, please) the chord symbol over each chord. Don't do this with every piece you are working on; just do it now and then and see if your knowledge is progressing. Unless you have an enormous amount of time to spend at the piano, I think actually playing should be the bulk of your practice time. But you can supplement it with chord analysis.

Other instrumentalists do not have the opportunity to learn chords and harmonies as pianists do (with the exceptions or organ, guitar, and possibly harp). If you play a single line instrument, you may be aware of chords very little or even not at all. In the conservatory where I studied, other instrumentalists were required to take a few semesters of piano, for several reasons, but largely in order to understand harmony. In this area, being a pianist was a huge advantage. Chords are our "bread and butter." It is essential to gain this knowledge.

Should we be relaxed when we play?

 

Some people will say you need to be relaxed when you play. Or maybe they will say "relax your wrist." But what does that mean? Surely not relaxed like you are while lying on the couch. What is meant, or should be meant, is that you have no more tension than is necessary. My teacher, Joseph Prostakoff, used to say, "not relaxed like a cat lying in the sun, but like a cat ready to pounce." What we need when we play the piano is to be in a highly physically alert state; not tense, but not relaxed either. Your whole body, especially the arms and hands, feel animated and alert, and also supple and flexible. Like a cat.

To get a sense of this state of alertness, try the following: hold an object (it can be a pencil, a small rock, anything that is not breakable) in your hand with your fist closed, and your hand (palm and fingers) facing down towards the floor. Grip the item as hard as you can and feel the tension. Then, very slowly, loosen your grip, bit by bit, until eventually your grip will be too loose and the item will fall to the floor. The amount of tension you had in the moment before the item fell was just the amount you needed to hold it. You can do the same thing at the piano. Play a chord, and press very hard into the keys. While continuing to hold the keys down, ease up on the tension in your hand until it is so little that you cannot keep the keys depressed. Again, the amount of tension you need was just before that point. At the lesson, I do this this with my own hand, while the student grasps my palm. They can feel the easing of the tension as I do it. Then I have them feel their own palm with their other hand, to see if they can feel when it gets to the point of minimum tension.

With time, and keen awareness into your physical state at the piano, you can learn to feel this point. Sometimes, as you are playing, you may become aware you are "gripping" too hard, and you can then just ease up.

It is not enough for the teacher to say "relax." The teacher must show you how it feels to play with the minimum of tension and have you experience it yourself, as in the examples above. Unfortunately, the same teacher who says to relax may also be assigning you exercises which cause tension and strain. Most "finger exercises" encourage the antithesis of learning to play with minimal tension. They are designed to have you strain your fingers, supposedly to "strengthen" them. They will make your muscles tighter and you will have a harder time learning to play with no excess tension. As you've heard me say before, our piano training is more analogous to yoga than it is to weight-lifting.

Playing with too much tension over time will likely cause pain and strain, and will limit the types of music you can play, as well as speed, delicacy, etc.

What about playing "naturally?" What does this mean? There is nothing really natural about humans playing the piano; it's unlike anything else we would do in the course of our daily lives. The body must be trained to acquire skills, to move in such as way as it might not do "naturally." But we train it to do these things in a way that works with the body, not against it.

Repeated Notes

 

Repeated notes, that is, playing the same note in succession, sounds like it would be easy. And it can be. But once again, there is a lot of misinformation, or "300-year-old ideas," as I call them, on this subject. There is an old idea that, if playing the same note, you must use a different finger each time you play it. I have to assume that this idea came from the technique for harpsichord, which has an very different mechanism than the piano. The "key return," the speed at which the key itself comes back after being depressed, was slower on the harpsichord than on a piano, and certainly slower than our modern piano, assuming it is of good quality. (I am not an expert on the harpsichord, but I feel confident that my information is correct.) Theoretically, the fraction of a second it would take to change to a different finger would be enough for the key to return. But on our modern pianos, I can play a very fast repeated note using the same finger, by starting with a good strong pulse with the arm, and the rest of the notes "bounce" off of that pulse. A drummer does this with the drumstick to achieve rapid iterations. Since the drummer is not using his fingers per se, he has to use the power of the arm. Or think of skipping a stone in the water: after the initial impulse (the throw), the stone hits the water and then bounces several times. I can get quite a few repetitions this way with no change of finger.

However, if I had a great number of repetitions, I would change finger. But that doesn't mean the work is done by the fingers alone. It is necessary to get a good pulse going with the arm. Changing fingers slightly changes the angle of the arm and wrist to the fingers, and prevents the hand from stiffening as it might if playing with the same finger over and over. Take Scarlatti's sonata in D minor, K. 141, which has rapid-fire repeated notes for most of the piece. Since there are six sixteenth notes in the measure, I would do fingers 1 (thumb), then 3 then 2, twice for each measure. When you start the measure with the thumb, the arm does a small pulse and the other notes come from that pulse. In this way you can get speed without fatigue, because the bigger muscles of the arm are doing a lot of the work. Trying to do this with only finger technique would produce pain and fatigue in almost everyone. (Watch the Martha Argerich performance of this piece on YouTube if you want to have your mind totally blown!)

If the repeated notes are slow, and you want them to be legato, just as you would if they were two different notes, then changing fingers will almost certainly ruin your chance of legato. In the moment of changing fingers, the damper would come down on the string and make a fraction of a second gap between the notes. Instead, you must not let the key up all the way before depressing it again. If you look at the white keys from the side, you can see if you have let the key all the way up, or if you have let it come near to the top but not all the way. If you re-depress it before the damper comes down, you will have legato. This is absolutely the effect we should strive for in many instances. When you hear a not-so-good pianist you may notice they never achieve that effect. (If the composer has marked it detached, then obviously you don't need to do this.) 

One of my pet peeves is that when you see fingering marked in the musical score (usually by an editor, not the composer), you will see a change of finger on a repeated note, even when it is a moderate or slow tempo. This is very inefficient and has absolutely no benefit. And, as mentioned, you won't be able to make it legato. This is another example of people clinging to old, out-dated ideas that are not supported by the facts -- the physical properties of the piano itself or of the human body.

Non-standard divisions of the beat (complex rhythms)

 

If you are an intermediate or advanced player, and you play the music of Chopin and the other Romantic composers, as well as a great deal of the music since that time, you will have encountered places where the beat consists not of the usual divisions of two (such as eights or sixteenth notes) or three (triplets), but in what I will call "non-standard" divisions. In Chopin, for example, you will find many beautiful passages in the Nocturnes, Ballades, etc. where there is a run (sometimes written in eights, sometimes in sixteenths) with a number such as 5, or 15, or 17, or just about anything, written over the beat (or beats). This means, of course, you must fit all those notes in the beat as shown. Since it is Romantic music, you have the opportunity to have some nuance of timing, and the 15 notes, say, don't have to be exactly metrically equal. There can, and probably should be, some subtle slowing and/or speeding up within it, to enhance the musical line. But they must fit in the beat; you cannot change the length of the beat (except possibly the tiniest amount -- again, a nuance), and therefore the measure, because that would destroy the integrity of the rhythm.

If the number of notes within the beat is say, 15, it will probably be fairly fast. If it is only 5, then it may not be. But regardless what the number, or whether it is fast or slow, you need to learn how to play these. I cannot emphasize this point enough: if you have depended on "counting" to help you with rhythms, you will find it impossible and will be utterly at a loss as to how to approach it. If you try to break them down into smaller units, such as dividing up 15 in 3 groups of 5, it may seem to work but will probably sound stiff and unmusical. Remember, Chopin didn't mean for you to divide it in three groups of five, or he would have notated it that way. The idea is to make the passage sound flowing, and even improvisatory, not metric.

So how do you learn to do these? You learn by giving yourself a unit of time, and then "filling in." Start by playing (probably in your right hand) the note C and then the note G. The time between these is now your unit. Then you fill in the notes (white keys) in between. That's five notes, but the C is the beginning of the beat, and the G is the beginning of the next beat. It is important to remember that whatever number of notes you are filling in, it ends on the next beat. So if you fill in the notes from C to G (C-D-E-F-G) you will have actually played 4 sixteenth notes, again, ending on the G, which is the beginning of the next beat. Four sixteenths should be very simple and of course we do it all the time. You will find it helpful to pick a moderate to fast speed for this. Then, take the same time unit, but go from C to A and fill in. You will now have filled in 5 notes. Remember, don't even think about trying to divide it up into smaller units, which would defeat the whole purpose. Now do from C to B, filling in 6 notes, etc., continuing to make the unit larger each time, with more notes to fill in. Don't worry about perfect fingering, just do anything that works. We are not working on the physical aspect here, but rather, we are training the ear to hear these units and be able to fill them in. It's all about the ear. 

Later on, you need to do them randomly. In other words, start with filling in 7, say. Then the next time, start with 10. And so on.

The concept is the same as my approach to learning rhythm from the very beginning. The analogy is that you have a "log" and you learn to "chop" it in equal pieces without the benefit of a measuring tape. With an actual log, you "eyeball" it; with a unit of time, as in music, you "earball" it. See my posts on rhythm for more explantaion.

When you get to filling in really larger numbers, say beyond 12, it is really extremely challenging. But try to be able to get to at least 10 or 12.

You can also fill in using the chromatic scale. If you were trying to fill in 12, for example, you could go from C to C with the chromatic scale.

When you start this, you may not be able to tell if you are doing it correctly. If you start to slow down the time unit (the beat) each time, then you are not actually filling in, you are just changing the length of the beat. And remember, in the actual music we are talking about, you can't do that -- it would be a distortion and not at all what the composer intended. You might be tempted to set a metronome to the time unit, and see if you were able to do it correctly. But what would be even better is to be your own metronome. Slap you left hand on your lap, or tap your foot, and see if you can keep it steady on the time unit while your right hand fills in.

When I do this with my students, I play the "outsides" of the unit, in other words, the beat, along with them as they play. So if they didn't end with me, then they didn't keep to the beat. If they went too slow, then they know they just need to go faster. There is no way to "calculate" how much faster, you just keeping adjusting, trying again, adjusting again, until you get it.

Obviously, it it easier to do this when you are just playing a scale -- notes in sequence. The actual notes in a passage in Chopin will be harder, probably, but at least you now have a foundation.

Another reason why learning to hear these divisions of the beat is critical is so that you can do cross rhythms (also called poly-rhythms). I'm thinking of a Rachmaninoff prelude where the left hand has the beat dividing in 5, and the right hand in either 2 or 3, for the whole piece. Each hand has to be sinuoulsy smooth and silky-sounding. You can't try to "calculate" it out mathematically (like some people might tell you to do with two against three). The only way is to train your ear to hear two different rhythms, or more precisely, two different divisions of the beat.

Rhythm is probably the area that students of music have the most trouble with. Some never actually learn to read the rhythmic notation and instead they just go to YouTube to listen to the piece they are playing and try to copy the rhythm. But obviously, that is not a path to mastery. Rhythm CAN be taught, and CAN be learned, including complex rhythms.