Chopin Etude in C, Op. 10, No. 1

Vladimir de Pachman
1848-1933

Here is an engaging performance by Vladimir de Pachman at a time well before the Chopin etudes became part of the Daytona 500 races. Think about it. Chopin Etude Op. 10, No. 1

     De Pachman studied with Joseph Dachs, a  pupil of Carl Czerny. He was nicknamed "Chopinzee" by one critic because he specialized in that composer and his stage manner was eccentric, including muttering and odd gestures. George Bernard Shaw reported that he "gave his well-known pantomimic performance, with accompaniments by Chopin." But his performances, almost exclusively Chopin, were highly regarded as authentic and he was considered one of the great pianists of his day.

Stories from Musical Life

Gentle Readers:

I'm happy to announce that THE GRAPEFRUIT CAKE INCIDENT AND OTHER STORIES INSTRUCTIVE AND CAUTIONARY FROM MUSICAL LIFE has been corrected, yet again, and is back on the shelves at Amazon. So, if you've been waiting for Santa's elfin editors to finish their proofing, now is the time. And to those of you who've endured the typos, please accept my apologies. If you didn't notice them, then never mind. 

                        

How to Practice

A student asks: "What is the most efficient way of approaching a new piece that has a wide range of technical demands (i.e. varies from sight-readable to very demanding)?"

           

            

                 At the risk of overkill, I've decided to post my mini-treatise on the topic of practicing. You may of course skip at will to the paragraph NEW PIECE.     

               There are three main types of practicing and many variables. The first type of practicing is employed in learning a NEW PIECE (or a new technical concept). The second type is for a piece that is IN PROGRESS; the third type is for a FINISHED PIECE, one that is ready or nearly ready for performance. In an ideal world, there will be fewer new pieces at any given time than in-progress or finished pieces. All practice requires intense focus and concentration. But I find that the concentration required in the solving of problems in a new piece can be the most intense and should therefore come at the beginning of the practice session, when the mind is fresh.

            Psychological impediments sometimes stand in the way of good practicing, or of even getting started. I call these psychological impediments “the committee” that sits on our shoulders giving negative feedback. “Just sit down whether you want to or not,” says cellist Gordon Epperson. And he’s right. The ritual of preparing to work itself can be cathartic.
            But there’s more to it than that, of course. While getting set up, think about a basic plan, i.e., what types of pieces will you practice: new, in progress, finished. Where will you start and what is the first thing you will do and how will you do it? In other words, THINK FIRST before the hand touches the keys. It is the thinking process that protects us from falling victim to what I call MINDLESS ROTE, which is when automatic pilot takes over from the deliberate act of thinking about what you are doing. If you find yourself thinking about what’s for lunch, take a break: a short walk, go for a coffee, read a chapter, play solitaire (but don’t wear out your thumbs texting). For most types of practicing, one hour at a time with a 10 or 15-minute break between hours is ideal. At the end of the break start the THINKING over again: where will I start, what will I do and how will I do it---WHERE, WHAT, HOW?

THE BASIC PLAN

NEW PIECE

1.  SCAN. Play through the piece at a comfortable tempo, stopping and starting as necessary, not to amaze yourself with what a fine sight-reader you are, but rather to identify problem spots. MARK THE HARD SPOTS.

2.  FOCUS. Having located spots that need extra attention, figure out possible fingerings, several even. WRITE THESE IN THE MUSIC in pencil. You won’t remember them, I promise. When deciding on fingerings, try to keep the musical intentions of the composer in mind. (See “Fingering Concepts.”)

3.  LIMIT. Reduce the amount of information you process, even down to just one interval or one leap. Start this very slowly and GRADUALLY, increasing the tempo to as close to the performance tempo as you can, but not faster than you can at this early point!

4.  PROCEED.  Go on to the next hard spot. Do not try to put the measures together yet. Make notes in the margin if you have questions about technical or musical issues. Do this very detailed work for as long as you can concentrate fully. (This type of practice has a learning curve, but in the long run it will cut your required practice time for a successful performance by at least 50%, probably more.)

5.  CONTEXT. Once a particular spot is feeling EASY and rather consistent, even if not quite up to tempo, try putting it in context with the material immediately before it and immediately after. Do this several times. DO NOT FORCE THE TEMPO. A good technique is one that feels easy, never rushed, even in speed.

6. TEMPO. Hard spots must be worked up through several tempos from very slow to the performance tempo. When you’re ready to work up the tempo, that is, when you have solved the technical problem(s), play NO SLOWER THAN YOU NEED TO and NOT FASTER THAN YOU CAN. The metronome can be useful here to keep track of your progress.

7.  MUSIC. The objective, always, is to make music. Keep in mind the quality of sound, the type of articulation required for the musical effect, the dynamic variety.

A PIECE IN PROGRESS

1.  EVALUATE. Make conscious decisions as to what sections need the most technical work. Start with those sections, working through several tempos. Most work should be under performance tempo. Keep in mind that the technique should always feel easy and unhurried.

2.  PERFORM. Try playing at tempo or near tempo in PHRASES or larger MUSICAL SECTIONS. For example, look at the musical form and select part of a section such as a first theme group or the development or the “A” section. This is also a good tool for examining the overall structure or architecture of the piece. Do not play through the piece non-stop at this point.

3.  SHAPES. Look for musical shapes. Where are the highest points in pitch? The lowest? What direction does a line seem to move over all? One approach to bringing the music to life is to play with increasing intensity as a line moves up and less intensity as a line moves down. This is just a starting point, of course.

4.  ARTICULATION. The length of individual notes has a great deal to do with musical expression. Should a group of notes be played very short or played with exaggerated length? What combinations of notes can be grouped under the hand without a thumb-crossing? The composer or editor often makes these decisions, but they are not etched in stone.

5.  DYNAMICS. Make some clear choices about how loud or soft a given passage will be. Where is the loudest place in the piece? The softest? Where are the crescendos? Are any passages especially accented?

FINISHED PIECE

1.  MUSICAL OBJECTIVE. As you worked through the previous section, particularly on SHAPES, ARTICULATION and DYNAMICS, you will have begun to form opinions about the meaning of the music. Ask yourself what the piece is about (happy?sad?). What is it that you like about it? How will you make your listener hear what you hear?

2.  PRACTICE PERFORMING SECTIONS. At this point it is time to start playing in large sections, i.e., an entire exposition or from point A to point B, without stopping. Try to incorporate everything that you have considered in the above. Don’t be discouraged if it doesn’t come off as planned on the first try. Keep in mind that the technique should always feel easy, unforced, unhurried.

3.  PRACTICE PERFORMING. Play the entire piece through up to tempo without stopping no matter what happens. This is a diagnostic tool and sometimes it can be helpful to record the effort. Afterward, consider how close you came to meeting your goals. It won’t be 100% the first time. Don’t expect it to be. Do whatever cleanup is necessary. Make notes in the score. Try again, but not more than 3 times in one sitting. After the final try, do whatever cleanup you need, i.e., slow technical work. Then LEAVE IT. Go on to something else or take a break.

4.  PRACTICE PERFORMANING SLOWLY.  Play the entire piece as a performance, but well under tempo. This removes much of the tactile memory, requiring more thoughtful, deliberate playing. It is also a very good test of memory


NINETY PERCENT OF PRACTICING IS SLOWER THAN THE PERFORMANCE TEMPO.

Smoothing Bumpy Scales

     A student writes: "I have noticed that if (during practice) scales or runs begin to feel a bit uneven or bumpy, this can often be corrected by playing the scale or run up and down four octaves at a moderate tempo while randomly stopping momentarily just before playing a particular note (i.e. stopping short and then continuing without any preconceived pattern in mind). The “stopped” finger (the one that would play next) is held back from playing for a quarter-note rest, and then I continue on for a few more notes before stopping again with another finger, etc.
     My best guess is that the sudden stopping of a finger and then releasing it has the effect of contracting and then releasing opposing muscles that I was allowing to tense up.  This random-stoppage approach seems to add something to the rag-doll relaxation-and-shake-out approach to creeping tension."

     Without seeing what he is doing, it is difficult to diagnose the unevenness of his scales. What he describes as a remedy strikes me as arbitrary and perhaps less reasonable than examining underlying causes. 
     

     Usually "bumpiness" is the result of a misunderstanding of how the thumb works in crossing. When anticipating a thumb crossing, allow the thumb to hang—yes, hang—behind the next finger. It should hang more or less behind the finger that is playing. Also, he should allow the forearm to move at an angle behind the playing finger in the direction of the music. This puts the playing apparatus in a perfect position to play the thumb rotationally. 

     But first, he should make sure that he is really completing each note of the scale before going on to the next. This is an opportunity to review basic forearm rotation. If the weight of the forearm is really transferred to each note as if walking, and if his fingers are each "at rest" at the bottom of the key, evenness should come easily. Feel the rotation a little exaggerated  at first, but then in speed don't think of it at all. I know, this is what confuses a lot of people. In speed we rely more on shaping and the "memory" of the sensation of completing each note.

     There are video demos under the iDemo tab above.

Chopin's Ocean Etude

A student writes: "Many of [Chopin's] etudes seem to require what feels like an impossible speed to sound even like a slow version of themselves. Short of just working on other things until my technique gets closer to what is needed, is there anything that can be done with the etudes themselves? The Op.25, #12, for instance, is more meaningfully expressive than the combination of groans, sighs and screams that suggest themselves as alternatives. Is there a general strategy to learning “impossible” pieces that is neither a waste of time nor harmful?"

Chopin's Ocean Etude

     The simple answer to the question is yes, there is a strategy for learning the impossible, which, of course, renders such passages possible. In this example the main technical issue—its "etudeness"–has to do with how the hand moves from one octave position to the next. 

     First, a word or two about the Chopin Etudes. These are concert pieces designed to show off different aspects of skilled pianism. They are not a pedagogical tool, at least not in the sense of so-called progressive studies such as Czerny, Hanon or method books. They require an advanced insight into piano technique. Having said that, any piece of music we study is at least in some sense an etude, especially if it contains passages that require special attention to mechanics.

     If this student enjoys the sound of the "Ocean" Etude, then by all means he should work on it. This means that he should first decide on the required movements and work them in gradually, short sections at a time. As always, we use the last note of one group to propel us to the first note of the next group. In this case, the right-hand fifth finger takes the hand rotationally to the thumb. (The left hand is the same movement, thumb to five.) For a succinct demonstration click here:

Rotation in the Ocean Etude

     Even if he doesn't get the tempo up right away, he will develop important technical concepts and in the process have a head start on a piece he enjoys. 

Instructive and Cautionary Stories from Musical Life

The Grapefruit Cake Incident and 

Other Stories from Musical Life

     

   

   

   One of my readers, a former student, found a few typos in the first edition of my collection of autobiographical stories (sigh). What can I say? Everyone needs an editor. So, I looked at it yet again and made a few changes. Those of you who already have the first edition should hold on to it, perhaps have it bronzed, because one day it will undoubtedly be very valuable. 

Chopin Etudes

   

Chopin

A number of readers have asked me, repeatedly, to write about the Chopin Etudes—all of them. This, needless to say, would be a huge undertaking. It's a request I've not taken seriously. Call me daring (foolish?) but now I've decided to at least explore the challenge.  

    The catalyst is a student's gleeful reminder of Alfred Cortot's edition, which carries the misunderstandings of the 19th century to the nth degree, that all we have to do is stretch and pull our limbs until they are "strong"(sic). 

   

Alfred Cortot

Cortot was himself a remarkable artist, his artistic feet planted firmly in the 19th century. He was supremely gifted as a youth, if not a child prodigy in the usual exploitative sense, as he was admitted to the Paris Conservatory at the age of nine. His professional debut came in his 19th year. This suggests to me that it is unlikely he practiced the etudes using the guidelines he later published, which he did, I'm sure, in good faith. This is just a supposition on my part, not unlike my supposition that Czerny never practiced his exercises. Czerny made his official debut at the prodigious age of nine, although he began private concerts much earlier.

     My purpose here is to inquire of you, gentle reader, whether you have particular technical issues in any of the etudes that I might be able to shed some light on. If so, identify the passage using measure numbers and I'll try to include it. Use the  Contact Me tab above or the comment button below, which, I've just discovered has been out of order..

     

Brahms Paganini Variations

   

Brahms in his study.

A pianist writes asking for suggestions on technical approaches to the fourth variation in this technically challenging set of etude-like variations. I use the word etude advisedly. Everything we play that is of consequence requires us to figure out its etude-ness, the how-tos. 

   "The first 4 measures require a trill," he writes, "presumably on the top note, seemingly with 4 and 5, with other notes of the chord beneath it briefly played by other fingers and then released.  Certainly trills with 4 and 5 are difficult." In his quest for information, he "found a heated debate about whether it is acceptable to use other fingers on the top trill when they become available after releasing the lower notes, especially for smaller hands, or whether one is obliged to employ the very difficult 4/5 trill in these 4 measures." I believe, according to his report, that the word cheating may have been bandied about. (As far as I know, Brahms did not indicate any fingering.)

Brahms Paganini Var. 4, MM 1-2

   Such an important issue has been raised here—yet again. I'm very familiar with the "cheater" school of thought. My answer to that is the score tells us how the music should sound, not how it feels in our hands. This means that we get to choose fingerings and redistribute notes between the hands in any manner that suits us as long as in so doing we don't hamper the musical objective, even uncross hands if it makes the music more technically accessible. The audience doesn't care what fingers you use. They just want a nice concert.

   Most of the concert music we play on the piano was written by great (mostly) pianists for themselves to play. So I read these scores assuming that some built-in accommodations are intended. The composer can't really give technical explanations in his score, if you follow my logic. In the above example, the octave chord is one unit, the trill another. By that I mean, play the chord with 1, 3, 5, bouncing immediately to 5 on the F (yes, 5-5) and trill with 5-3, the F being the second note of the trill. This works very well if the arm is kept at a slight (slight!) angle, the elbow a tiny bit in toward the torso. (It is also possible to begin the trill by starting on 4, yes, over 5, and trill with 2-3 until the triplet [see below], which would be 2-4-3 in order to get the thumb closer to the next octave position.) The D-sharp is the end of the group, which provides the spring-board (slight up) for landing down again on the next chord. This is really rather easy once worked in carefully.

Brahms Paganini Var. 4 M1
Fingerings and Rhythm

   

More important than fingering, though, is the rhythm of the trill. Many pianists make the mistake of seeing trill and throw themselves at it. All ornaments indicated with a symbol require a place in time. Figure out how many notes you will play and in what rhythms and how they fit with the left hand. Try starting with four groups of two 16ths for each of the eighths in the left hand, making a 16th-note triplet on the fifth eighth. Depending on your tempo, this might actually be enough of a trill. If you want a faster trill (slower tempo?) try making triplets on each eighth. (I think duple is fast enough.) The upshot here is that once this coordination has been well worked in, it is possible to abandon the precise rhythms, letting the trill find its own number of notes. The process teaches the hand what it feels like to be free, and not jam, which is what can happen if tackled without thought.

   In sixty years of playing the piano, I have never felt required to play an extended trill with four and five. If you know of such a passage in standard repertoire, I'd be glad to know about it.

Stories from a Musical Life

I've just published a collection of autobiographical stories. Call them sins of my old age, if you like (apologies to Rossini). Strange as they may at first seem, these stories are as close to the truth as words on paper can achieve. Distinguished young cello virtuoso Sarah Mae Spieler really did receive a dire warning in a Chinese restaurant under the watchful eye, singular, of a lime-green dragon. And only moments later, the oddest coincidence involving a pastry she’d never heard of changed her life. Axel Stowne, in a muddle over a Beethoven piano sonata and, well, his life, really did find a Goldfish on Palm Avenue. Gilbert Trillweiler without a doubt took the most circuitous route possible on the way to finding his way in music. The offspring of British actress Margaret Rutherford makes an entrance at a very unusual tea party in the garden of an historic home in Charleston, South Carolina. 
    The thoughtful reader will notice here an overlapping of certain incidents, the retelling of stories in different contexts, which, if nothing else corroborates their veracity. Sarah Mae, Axel and Gilbert are pseudonyms, as are Dorothea, Cheryl, Susan and Morris. The others are real. Here you will find, gentle reader food for thought, or at the very least, entertainment. I can attest to the fact that the incidents are all true because I was there.
     Read an excerpt here: The Grapefruit Cake incident.

Alfred Cortot and "The Poet Speaks"

Alfred Cortot
1877-1962

     My pianist friend reminded me the other day of the great early 20th century French pianist Alfred Cortot. He made many recordings, some more accurate than others, but always with the musical objectives in tact. Don't bother with his editions of Chopin Etudes with endless examples of mindless exercises meant to strengthen the fingers. They are at best a waste of time and potentially harmful. Personally, I doubt he ever used them himself, as he was a prodigy. 
     Still, he was a fine musician and eloquent teacher. Here is his explication of the final piece in Schumann's Kinderszenen, Der Dichter Spricht: Cortot and "The Poet Speaks."

Bach-Philipp and Issues of Pedaling

     

J. S. Bach

     My far-flung student, the one who prefers not to Skype but rather send videos with written questions, startled me with some unusual pedal issues. He is playing the Isador Philipp transcription of the "Little" G Minor organ fugue of Bach. He complained of cramping in his calf as the result of pedaling in this piece. Well, I've never before heard of leg injuries from playing the piano. Since I

Isador Philipp

didn't have a clear view in the video of his foot, I responded first to his written statements with some basic pedaling techniques in Bach.

      In unadulterated Bach, which this isn't, pedaling is almost non-existent. That is, we pedal in such a way as to avoid blurring textures. So, we can use pedal on a single chord for warmth or accent; we can use pedal to assist in making a legato connection in a melodic leap (rarely necessary). In Philipp's transcription, I would begin with these ideas in mind, particularly regarding clarity of textures—where he allows for that possibility. We can think of this piece as more romantic than Baroque, imagining a large organ resonating in a cathedral.

     Now, for the more pertinent issues of pain in the leg. Remember, playing the piano is easy and doesn't hurt, not even when using the pedals.  The ball of the foot remains on the pedal, rising only to the point where the dampers release. More than that is overkill. With a properly adjusted pedal, the movement of the foot is almost imperceptible. The basic pedal technique is the so-called syncopated pedal in which the pedal acts on a note to sustain it while the hand moves to a different note, at which time the pedal is reactivated. A flutter pedal is used to release some of the accumulated sound, but not all of it. You can experiment with this technique by playing a chord, putting the pedal down, releasing the keys just to near the point of sound and allowing your foot to come up only part way, not all the way to a complete release of sound. 

     Listening to the sound you make is, of course, always a good

approach, particularly apropos of clarity. I think most advanced pianists pedal "by ear." That is, listening for the degree to which sonorities overlap and how much of that is desirable. If there are passages that are particularly confounding, you can take a technical approach to the use of the pedal, deciding when or if it should be applied and on exactly which note it should be depressed. Do this slowly and thoughtfully, gradually working in the pedal technique the way you would other techniques.

     I concluded that his piano has to be some how out of adjustment if he can't depress the pedal easily with the ball of his foot. He should not have to stomp on it.

     

Beethoven's Waldstein Sonata: Food for Thought

     One of the questions tossed at me during my doctoral orals had to do with the importance of music theory when making interpretive

decisions. In other words, why bother to analyze a score? Isn't this a little bit like having to understand how a car works in order to drive it, as one colleague put it?
     If in performance our objective is to convey meaning or emotion, then one question is, whose meaning or emotion are we offering? Is it our own, the performer's point of view? Or the composer's? Both? If the performer is the interpreter, then what is he/she interpreting? For me, performance begins with the score. There we find the composer's precise intentions, that is, precise as notation and words with all of their limitations allow. The notes and other markings are surface directions; in order to go deeper, we performers have to think.

   This, it seems to me, is why we need to understand how the piece was put together structurally. Where are the sign posts, the guard rails, the inn at the side of the road? In Beethoven's time a diminished seventh was still a scary chord. A deceptive resolution was still a surprise. In other words, we need to learn how to take the scenic route and enjoy its offerings. Stay off the interstate and much more will be revealed. And no, we don't have to be an auto mechanic to drive a car. We just have to know how to tell it where to go.
     So, I propose some questions. What does it mean that, in his Waldstein Sonata Beethoven  repeats the opening statement on B-flat, pianissimo? How incongruous is that? We are prepared for sunshine on a field of poppies and instead we get a small lake. Soon, with all those borrowings from the parallel minor, we get a sliver of doom, perhaps precipitation, on the horizon, only to be saved again by the sun. What do we think about the choice of keys? Is that incongruous B-flat a hint that things are not going to be as expected? What should we—could we—do about the second subject appearing in E Major instead of the usual dominant? E major seems to me even warmer, after  C major and especially after that soggy B-flat.
     Hah! I'll bet you thought I would tell you the answers, as if there were absolute answers. No, this is my way of thinking aloud, my way of getting the engine started. To view one person's analysis of the first movement, visit Waldstein. And do enjoy the view.
    



http://www.teoria.com/articles/waldstein/

Haydn Sinfonias for String Quartet

     Yes, I know this is off topic. But, I hasten to point out that many of my followers play string instruments, as do I. So it may be of interest to those folks that I have been at it again, transcribing from one venue to another, which would be considered quite normal in Haydn's day.
     

Joseph Haydn

Many of the symphonies of Joseph    Haydn, delightful as they are with wind doublings, work very well as string quartets. Titled "Sinfonias" by the composer, these charming morsels provide an informing glimpse into the musical development of one of the Classical period's great composers, the composer credited with inventing the string quartet. Do we really need more Haydn quartets, someone asked. Well, I respond, does one really need a slice of Sacher torte or a glass of schnapps? Play through these movements and travel along in time with the composer as he almost single-handedly invents the classical style.
     Have a look at these five Sinfonias, full score and individual parts, at Amazon: Haydn Sinfonias for String Quartet.

Jakob Gimpel Plays Johann Strauss: With the Help of Tom the Cat

   Every now and then I find myself reminiscing. This, I'm told, is a symptom of age. Never mind, I say. As long as I don't stay there in the past, it's okay to visit. And if I'm repeating myself, well just nod politely and pretend interest.

Jakob Gimpel

   When my undergraduate piano teacher, Muriel Kerr, died, her replacement was Jakob Gimpel. Gimpel was a distinguished Polish pianist with an established European career, although he lived in Los Angeles. I hadn't heard of him, though, until I met him that fall of 1963 when he took over Kerr's studio. I hadn't heard of him, but I had indeed heard him without knowing it.
   Gimpel was the go-to pianist in Hollywood. He provided the piano in "Gaslight," in which he appears on screen, "Possessed," "Letter from an Unknown Woman," "Strange Fascination," "The Story of Three Loves," "Planet of the Apes" and "The Mephisto Waltz." But perhaps most notably were his performances in two Tom and Jerry cartoons, one of which, "Johann Mouse," won an Academy Award for best short.
   I had been admiring Gimpel’s virtuosity, albeit unwittingly, since childhood. Some afternoons in the summer of my tenth year I would be allowed to visit a school friend, Marlene Harkelroad, who lived on my street several houses down. Her family owned a television, a rarity in those days. My mother was suspicious of the contraption, so these cherished occasions would be rare. Marlene and I watched “Sheriff John’s Lunch Brigade” and ate along with one of the sheriff’s many cartoon characters, Crusader Rabbit. The sheriff was a remarkable man, as he could see into TV land and would know if we had finished our milk and made our beds. If we were good, that is, if we didn’t talk back to our mothers, Sheriff John played special cartoons for us, one of which was  “Johann Mouse.” 

"Johann Mouse"

   Narrated by the distinguished actor Hans Conreid, the cartoon begins: "This is the story of a waltzing mouse. His name was Johann and he lived in Vienna in the home of Johann Strauss."  Jerry is the waltzing mouse who can’t resist coming out of his mouse hole when Strauss plays the piano. While the maestro is away, Tom, a cat with homicidal aspirations, learns to play the piano in six easy lessons in order to entice jerry back out into the open. It’s Jakob Gimpel who provides Tom’s virtuosity with his own extravagant arrangements of “The Blue Danube,” “Kaiser-Walzer” and “Trisch, Trasch Polka.” I didn’t realize it at the time, but it was Tom’s remarkable piano playing—after only six lessons—that gave me the courage to stamp my little foot and demand that I be allowed the same. If you've made your bed and finished your milk, you can watch some of it here: Tom and Jerry

Khachaturian Toccata: Polyrhythms

   

Aram Khachatrurian

A student writes that she struggles in Khachaturian’s Toccata with the polyrhythms in the slow section—mainly measure 110.

Khatchaturian Toccata MM 109-110

   Without seeing what she's doing, I can only make some general suggestions. I'm guessing her problem is with the combined rhythms and not so much the technique. That is, she is able to play the hands separately.
   On the first beat of M 110, notice that the right hand is duple, the 16th-note triplet equals one eighth. So in the RH you have the equivalent of 2 eighths. Against that in the LH you have an eighth-note triplet, which makes this first beat 2 against three:

Khachaturian Toccata M 110

Try it that way first, then add the extra 16ths. The hands come together pretty much as printed, at least close enough.
   The 3rd beat of M 110 is also 2 against three, but with 16ths, so it feels faster. One way to solve this is to first set a constant eighth-note pulse and fill in the spaces once that pulse is in your bones:

Khachaturian Toccata M 110

   I'll keep you posted as to whether this helped.

Beethoven Op. 111: Double Trills in the Arietta

     

Beethoven
 Notice the Evil Smirk

A student writes asking for help with this pesky passage in the trill variation. He wants to know how to practice it without damaging his fourth finger, which, no doubt, feels inadequate. This is a very good question indeed.

    

                                           Beethoven Op. 111, M 121

     I use a trill of a 4th to a 6th, 2-4 to 1-5. (Some folks have tried to trill in fifths, which can be done, but is not worth the trouble. I also think that is not what is meant.) Since this pianist expresses concern about his fourth finger, I conclude that he is isolating fingers, separating them from each other, trying to make a "clean" trill. 

     

     I suggested he not think fingers so much as shaping, that is, a tiny (tiny) move in for the thumb (1-5) and back out (tiny) for the 2-4. He should practice it rhythmically feeling pulses, remembering that, even though he's identified a technical issue, it isn't what is featured here. So, show the bells in the left hand. If truth be told, and please don't yell at me, a tremolo works just fine, and it wouldn't surprise me to learn that the master played it that way. It'll be one of my first questions in the great beyond.