Wednesday, January 25, 2012

A Preliminary Exercise for Polyrhythm (2 against 3, 3 against 4)

One of the most mind boggling things I've ever had to sort out in my musical education was how to play polyrhythms. My teacher called it "2 against 3" but it actually encompasses any figuration wherein two or more independent rhythms need to be played together. Some of the most iconic examples from classical piano music are the following (click on the image to download the score):

1. Debussy Arabesque No. 1 in E major (YouTube):

2. Brahms Intermezzo in A major Op. 118 No. 2 (YouTube):

3. Chopin Fantasie Impromptu Op. 66 (YouTube):

Practically all major composers use polyrhythms in their music yet there are very few technical exercises that offer a "friendly" introduction to the early intermediate pianist. For instance, there are no polyrhythms in Hanon (or rhythmic variation exercises for that matter). Brahms wrote 51 exercises that incorporate it but they have other technical difficulties that suit the late intermediate pianists:

For the newbies to polyrhythms, I suggest the following steps to learning it:

1. Let the ear and mind internalize this rhythmic peculiarity. Try listening to the following examples: Example 1 and Example 2. Count the beat as you listen. Some have suggested to verbalize the notes for 2 against 3 as "Not dif-Fi-cult" although I must confess I have not really gotten the hang of it.

EDIT: I've just discovered this tapping exercise using "George Wa-Shing-ton" verbalization and I really find it useful. Check it out!

2. Download and print the exercise I have written. Do not play it right away.

3. Listen to the exercise in slow tempo (42 bpm, download), follow the score, and count the beats:

4. Play the first part of the exercise (2 against 3, up to the double bar) hands separate (start with the left hand and then the right) at 60 bpm. It is essential to use a metronome.

5. Play both hands at 42 bpm until flowing.

6. Gradually increase the tempo. I recommend the following tempi increases:

60 bpm download

78 bpm download

96 bpm download

108 bpm download

7. Work out the second part of the exercise (3 against 4).

A closer look at the exercise: It is actually a twist on the Hanon exercise #46. Each hand plays a trill while the other plays broken chords in triplets as accompaniment. There are two main parts.

The first part is an exercise in 2 against 3 or 3 against 2. The right hand begins playing short trills while the left hand provides a broken chord accompaniment.

The second part extends the first part as an exercise in 3 against 4 or 4 against 3. The broken chords remain as quarter note triplets but the trills are now in sixteenths notes, squeezing more for each beat. Each hand has the opportunity to play the trill and the accompaniment. Just like in the previous part.

When learning this exercise,  begin by playing it forte but as soon as you are comfortable, the trills must be louder than the accompaniment.

EDIT: For variety, transpose this exercise in C minor. It's basically the same notes but all Es, As, and Bs will be played flat. Alternatively, play it as a harmonic minor (B is natural) or melodic minor (A and B are natural ascending and become flat descending).

Where to go from here? After the exercise is mastered, it makes sense to reinforce this newly learned skill with a real piece. Any of the pieces illustrated above (Debussy's Arabesque, Brahm's Intermezzo, or Chopin's Fantasie Impromptu) would be a good goal.

However, to lessen the frustration of learning a lengthy piece, one might attempt Chopin's Nouvelle Etude No. 1 in f minor first Youtube. It's only two pages long but it has just the right technical issues (wide arpeggios, polyrhythms) as well as interpretative challenges fit for the intermediate pianist.

Good luck!

Saturday, January 14, 2012

Top 10 Hanon Exercises

A few days ago, I chanced upon my old, shiny, red Hanon book (online version). I remember my teacher assigning a couple of them to me but I never understood the underlying principle of these exercises. After much research around piano forums, I've realized that many pianists consider the Hanon exercises as antiquated, unmusical, obsolete, a waste of time and worse, injurious to one's hands (click here for more info). I immediately dropped these exercises but saved the scales and arpeggios.

Who is Hanon? See this related article. How important were the Hanon exercises? Read this interesting link.

Now, as a mature pianist and having learned much over time, I leafed through the Hanon book once again with critical eyes. Indeed, repetition of predictable patterns is the key concept of the Hanon exercises. It's just full of short and long repetitive figurations (trills, tremolos, repeated notes) written in many permutations (but mostly in the key of C). 

The principle is the same as physically training an athlete or working out in the gym. By doing repetitive drills, one's speed, stamina, and strength improve over a period of time.

After reviewing all of the exercises, I've arrived at the following conclusions: 1) about 80% of the exercises are indeed a waste of time, 2) most of them seem to be illogically ordered; but 3) about 20% have real applications in classical pieces.

I have picked 10 of the most useful ones, to be studied in the following order (please see end of list for my practice suggestions):

1. #46 - The Trill

Virtually all major composers (Bach, Beethoven, Mozart, et al) used trills in their compositions. When properly executed, the trill mimics a bird call or even a vocal vibrato. When combined with the right dynamics and tempo, it has a penetrating effect on the listener.Technically, the trill is one of those best-kept secrets in improving overall speed and dexterity.

For this exercise, it is best to master them hands separate (HS). The trill of outer fingers (5-4-3) cannot simply compete with the trill of the inner fingers (1-2). On their own, they can achieve a degree of speed not possible when played hands together (HT). Play close attention to the following fingers: 5-4 and 4-3. Never trill them too much as to strain them.

For beginners: The exercise looks menacing and may be overwhelming for newbies. I suggest you reduce the exercise as follows: eliminate the extra trills on the 3rd and 4th beats (i.e, just do 2/4 instead of 4/4 time). Work the first 6 measures only.

For variety: You could try the exercise one octave lower. The hammers in the lower register are heavier, thus you will encounter more resistance. It's exactly like working out on an elliptical stepper. Once you're comfortable with a certain resistance, you increase it a bit. You can also transpose this exercise in practically any key if you get bored playing just white keys. Try in the key of A and E.

2. #44 - Repeated Notes

There are plentiful repeated notes in the music of Bach, Beethoven, Prokofiev and other composers, often representing a drum or some percussion instrument figuration. In some of Scarlatti's keyboard sonatas, they mimic the strumming of a Spanish guitar or mandolin. A newbie is often tempted to use only one finger for the repeated notes when different fingerings are clearly written for each note. This simplification often results in the loss of "color" of the repeated notes and a build up of tension on the poor finger that plays everything.

For beginner: This exercise is also best practiced HS and if needed, reduced to 2/4 from 4/4 (eliminate third and fourth beats). The first four measures are a good warm up but once mastered, the student may simply skip this and start on the fifth measure up all the way to the last measure of the page. No need to do the repeat.

For the more experienced: After mastering the first four measures, skip to the second page. No need to do the repeat.

For the advanced: You may replace this exercise with #47. The repeat is unnecessary.

3. #6 - Basic Extension

There is big stretch from the first note to the second note of every measure--a sixth in fact. The real interesting thing are the inner notes that descend from a fixed upper note (played by the 5th on RH and 1st on the LH) in every measure. The descending notes are played by 4-3-2 on the RH 2-3-4 on the LH, as if a mirror image. This figuration is very common in Baroque and Classical period pieces (just look at some of the preludes of Bach, sonatinas of Clementi, variations of Beethoven, etc.).

If this exercise can already be played perfectly, the pianist may replace this with #31. This time, the stretch is an octave span. This should be very effective in preparing the hands for octave studies.

4. #40 - Chromatic Scale

The chromatic scale is one of those enthralling effects in classical music. In Beethoven's Fur Elise, there is the ever famous descending chromatic scale after the climax. Without a good grasp of chromatic scales, it is hard to interpret the music of Chopin, Beethoven, Liszt and so many others who exploited chromaticism in their music.

The chromatic scale is actually easier to learn than the major and minor scales because the thumb, wrist, and arm movements are simpler. In some ways, it's a good preparation for the study of scales. Most chromatic scales are played "leggiero" or light. To do this, practice each note staccato in slow speed. As you increase speed, make the staccato lighter. This should produce a "feather-like" articulation.

For beginners: Study "At an octave" and "In contrary motion, beginning on the octave".

For the advanced: Add "At a minor sixth" and "In contrary motion, beginning on the major third".

5. #38 - Running notes

Every pianist must eventually deal with rapid running notes. It's just part of the trade. This exercise offers a  fair introduction to the role of the thumb in facilitating the execution of running notes.

There are two schools of thought regarding the use of the thumb: Thumb Under and Thumb Over. I won't go into detail regarding the merits and demerits of each but suffice it to say that from Hanon's thumb turning exercises (#32 to #36), one could deduce that he advocated the Thumb Under method. Whichever is most effective depends on the situation.

For the advanced: Play this C scale in interval of 10, i.e, the LH plays as is while the RH is raised a third up:

RH: e-f-g-a-b-c-d-e
LH: c-d-e-f-g-a-b-c

The fingering is also modified (numbers in bold are where the thumbs do their hard work):

RH: 3-1-2-3-4-1-2-3
LH: 1-4-3-2-1-3-2-1

6. #15 - Broken Thirds

Hanon is spot on with this exercise. Thirds (double or broken) is just everywhere in classical music and are one of the most difficult to execute convincingly. When played well, they sometimes mimic laughter or two persons singing together (tight counterpoint). It is said that Mozart conceded that his rival Muzeo Clementi played thirds better than him. Fast scales in thirds are so treacherous that some virtuosos cheat on the notorious D scale in thirds in the Brahms second piano concerto.

For the advanced: Add #50 (legato thirds) and #52 (scales in thirds).

7. #20 - Little Arpeggios

This exercise runs through the arpeggios (broken chords) in the second inversion based on the C scale. These chords are the C major, d minor, e minor, F major, G major, A minor, and b diminished. The general awkwardness in the LH fingering (5-4-2-1) and RH (1-2-4-5) in playing the first beat of every measure is the main reason why this exercise has to be mastered.

As preparation, play each first beat as a block chord until the grasp of the chords becomes very comfortable.

8. #53 - Octaves

Some of the most memorable moments in piano music are the big, thundering octave passages, such as in the concertos of Tchaikovsky, Liszt, Saint Saens, and others. Pianists work on their octave technique for hours on end to achieve the desired effect. This exercise is a good stepping stone.

Start wtih chromatic scale in octave which is actually the last part of the exercise. Go through it slowly and try to bring out the outer notes, i.e., those being played by the 5th finger of either hands. When sufficiently mastered, start with the second page of this exercise.

9. #39 - All scales

10. #41 - All arpeggios

Perhaps the most important among all the exercises in the Hanon book are the scales (#39) and arpeggios (#41). So important are they that most conservatories and collegiate music schools require the prospective students to play them during auditions and with good reason. All the most essential technique are codified in the scales and arpeggios and together with octaves, thirds, and sixths, they make up for 80% of the technical difficulty in written music. 

I will write a separate blog detailing my suggestions on practising scales and arpeggios.

When to take up the Hanon exercises: It makes sense to introduce the Hanon exercises after the third grade of the John Thompson method book or its equivalent. The student should concentrate on mastering the first eight exercises in the above list. To his/her delight, he/she may discover that the exercises will have prepared him/her well to study Beethoven's Fur Elise, Clementi's Sonatinas, and other intermediate level pieces.

How to practice Hanon: Make sure you practice this hands separate (HS) first, gradually speeding up without sacrificing note clarity and evenness. Keep the wrist relaxed to avoid strain. When either hands are sufficiently warmed up, play them hands together (HT) but choose a speed that both hands can handle. This is normally slower than either hands could achieve separately.

For the more experienced: Instead of playing the exercises mechanically, you may shape them through dynamics. Begin softly (p) on the first measure, gradually do a crescendo, reaching a mezzopiano (mp) after a few measures, then attaining an mezzoforte (mf), then a forte (f) on the first descending measure. From here on, do the exact opposite, i.e., a diminuendo, falling back to piano (p) on the last measure. Also, try doing an allargando as you reach the high point of the exercise, then resume "a tempo" until the last measure where you may do a slargando.

For the more advanced: Instead of a uniform crescendo from the first measure to the middle of the piece, you can do a mini crescendo-diminuendo in every measure, corresponding to the rise and fall of the notes within that measure. As you move to the next measure, you begin with a volume slightly higher than the first note of the previous measure, then proceed to do a crescendo-dimuendo. The effect is like the rising and falling of waves. On reaching the descending measure, apply the opposite dynamic, i.e., diminuendo-crescendo. Maintain a steady tempo all throughout. I would highly recommend using a METRONOME to reign in the tempo.