Music Theory for Cellists Part Four: Seventh Chords

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By Miranda Wilson

A seventh chord is defined as a chord composed of a triad, plus a fourth note that forms the interval of a seventh (diminished, minor, or major) above the root of the chord.

In the classical music theory classroom, students are usually called upon to be able to notate and identify five types of seventh chords:

  • The fully diminished seventh chord (solfege: ti re fa le), a chord composed of stacked minor thirds that functions most commonly as chord viio7 in minor keys.

  • The half-diminished seventh chord (solfege: ti re fa la or re fa le do), a chord composed of a diminished triad stacked under a major third, that functions most commonly as chord viiø7 in major keys or chord iiø7 in minor keys.

  • The minor-minor seventh chord (solfege: re fa la do or la do mi sol), a chord composed of a minor triad stacked under a minor third, that functions most commonly as chord ii7 or chord vi7 in major keys.

  • The major-minor seventh chord (solfege: sol ti re fa), a chord composed of a major triad stacked under a minor third, that functions as chord V7 in both major and minor keys.

  • The major-major seventh chord (solfege: do mi sol ti), a chord composed of a major triad stacked under a major third, relatively uncommon in classical music but still common enough to make it a good idea to study and recognize.

In one of the appendices to Cello Practice, Cello Performance, I wrote an exercise in arpeggios in which I supplied fingerings for these five types of seventh chords, beginning each one on D for the sake of intervallic comparison.

My views on how best to learn these chords continue to evolve, and these days I think it’s even more helpful to learn about seventh chords using their harmonic function as a context. Chords don’t exist in a vacuum — they are always part of something bigger than themselves — so I composed some (I hope) fun melodies that do just that.

In them, I placed the seventh chords in the kind of context that you might find them in when you come across them in repertoire. For example, I place the fully diminished seventh chord in D minor, beginning on ti in D minor (C-sharp) and resolving it, just as the fully diminished chord resolves in diatonic harmony.

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Some of the seventh chords have more than one common function in diatonic music, such as the minor-minor seventh chord. I put a little musical “in-joke” into my exercise here — a quote from Debussy’s Girl With the Flaxen Hair that is one of the most famous melodic uses of this type of chord.


Click here to download a free, high-resolution PDF of the whole etude.

Leadership, Gratitude, and Experimentation in Chamber Music

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By Miranda Wilson,

Today, during a chamber music coaching, I decided to stop micromanaging my students and let them figure out how to fix their intonation, time, and group sound themselves. I jumped in when needed, and when I wasn’t, I backed off.

I could do this because I trusted them and trusted myself. I knew I had taught them task mastery: of their instruments in their studio lessons, of the language of music in the theory classroom. Using a set of guidelines, it was now up to them to become their own best coaches.

I call this method inquiry-based rehearsal technique.

Here are the guidelines I gave them.

  1. Every member of the group is a leader.

    • If there’s only one leader, that means there are then three followers, and if you’re following you’re already behind the group.

    • Each member is allowed an allotted time as the director of the rehearsal. That person gets to pick the places she or he wants to work on, and shape the conversation about how to work on them.

  2. Criticize experimentally; listen generously.

    • It’s OK to offer constructive criticism to colleagues. Remember, though, that they have feelings. With this in mind, crux criticism as an experiment:What would happen if Jane put her F-sharp a little flatter in that D major triad?”

    • When you are the one receiving criticism, remember this: criticism is a gift. It is for you, to help you improve. Be available to this gift, even when it feels hard to accept it.

  3. Acceptance and gratitude

    • Be grateful for your colleagues. You could not make this music in this moment if they were not available to you.

    • Accept yourself and your colleagues as the players you are right now. You are all travelers on the same journey. All of you will improve on this journey if you are available to criticism.

    • Be grateful for your colleagues’ ideas, and try them out as wholeheartedly as if they were your own. Accept that sometimes, other people’s ideas may be better than what you wanted to do.

    • It’s OK if your idea that seemed great in practice doesn’t work in rehearsal. Embrace your failures. They are the wellspring of your creativity.

  4. Questions to ask yourselves that no one can answer for you:

  • How will we start?

  • What are our shared goals for intonation, interpretation, and everything else?

  • Is our group sound unified? If not, why not?

  • What is going wrong?

  • How do we fix it?

And the biggest, most important question of all, one that you should ask yourself at all times:

Are we making each other sound good?

Because it’s not about you, the individual, any more. It’s about you, the group.

Further Reading:

Cello Practice, Cello Performance by Miranda Wilson (Rowman & Littlefield, 2015)

  • The principles of group sound, Chapter 3

  • The principles of keeping good time, Chapter 5

  • The principles of just intonation, Chapter 6

Music Theory for Cellists Part Three: Compound Intervals

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By Miranda Wilson

I love to begin a fundamentals workout with shifting exercises, since the process of getting from note to note isn’t necessarily straightforward.

In Cello Practice, Cello Performance, I wrote some exercises in shifting between first and fourth positions, and another shifting exercise dealing with octave shifts in a variety of fingerings. These exercises comprise part of my daily workout, and the purpose of them is to help me feel absolutely comfortable with the goals, mechanics, and success rate of shifting.

The Thinking Shift

What do I mean by “goals”? Well, when you have a big shift, you have to know what you’re aiming at. What pitch are you trying to hit, and how will you know if you’ve done it accurately? Therefore, this is an exercise in shifting and thinking. For this reason, I highly recommend the study of moveable-do solfege, a method of speaking the principles of theory so that you can navigate all the intervals with ease.

How to Set a Goal

Audiate — imagine in your mind’s ear — what your goal note sounds like. Make sure you prepare your shifts with the slight backward pull (see Cello Practice, Cello Performance for details) that will give your arm the release it needs to shift. All the while, bow “through” your shift — remember, “all techniques are both-hand techniques.” Learn how far you must measure and judge your distance from note to note. Audiate again: have you reached the goal pitch?

Improve Your Compound Intervals — and Your Shifts

In a previous post, I shared a warm-up exercise that illustrates how best to hear and assign solfege to all the simple intervals — that is, the intervals we can find within the octave. Today, let’s work on compound intervals — that is, the intervals wider than an octave. The benefits of this are multifaceted. You can improve your solfege, your interval recognition, and your large shifts all in one go. Here’s what it looks like:

Compound Intervals Shifting Warmup-1.jpg

Music Theory for Cellists Part Two: Modal Scales


By Miranda Wilson

I love to multi-task, which is why I've started to compose fundamentals exercises for my students in the University of Idaho cello studio that reinforce the fundamentals they learn in Theory I-IV and Aural Skills I-IV at the same time as building their proficiency in the principles of cello playing.

A couple of years ago, I wrote three posts on creative ways to practise scales (click on the links to read The Multifaceted Gift of Scales Part One; Part Two; Part Three). 

This post is specifically about scales in the diatonic modes. I'll leave it to the music historians to explain why their names are Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. The short explanation is that modal scales are major scales that may not start on the tonic of the key signature. Ionian is the common major scale, and Aeolian is the natural minor scale, and the others all bear various resemblances to other scales -- Dorian has a lot in common with the minor scale, for example.

There are two ways to label modal scales using moveable-do solfege: the "start on do" method, which involves altering degrees of the scale accordingly, so the Lydian scale, for example, would be spelled "do re mi fi sol la ti do." Another method, which I prefer, is to keep the solfege of the Ionian (major) scale and simply say that each mode starts on a different scale degree. By this method, the Lydian scale would be spelled "fa sol la ti do re mi fa."

I've noticed that a lot of college students arrive in Theory I without having heard of the modal scales. I believe it's never too early to teach theory concepts -- in an age-appropriate manner, of course -- and that near-beginners can easily master them. Here's a way of explaining modal scales for a student who isn't yet shifting. (For a free, higher-resolution download with complete instructions, click here.)

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Advanced players can combine the theory of modes with their daily thumb position work. In my chapter on how to practise in Cello Practice, Cello Performance, I demonstrated how a difficult scalar thumb position passage in Beethoven's A major sonata could be made easier through practising it in modal scales. Below is an exercise I use every day in practice and lessons to keep our thumb position in good shape -- and improve my students' recognition of the diatonic modes. (Click here to download a free PDF of the full exercise complete with instructions.)

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In Cello Practice, Cello Performance, I strongly advise against the concept of unthinking mechanical practice, or "mindless practice," as I called it. When we combine the fundamental principles of how music works with those of how cello playing works, the building bricks of expressive cello playing are literally at our fingertips

Music Theory For Cellists Part One: Solfege & Intervals Warm-Up


By Miranda Wilson

This is my first post in a projected series on learning and using music theory in cello practice. As well as my cello studio at the University of Idaho, I also teach a class in aural skills -- essentially the laboratory class for what students learn in music theory. In most theory methods, the material is taught in a piano-centric way, and I've been looking for a way to make it more applicable to the cello. Over the next few weeks, I'll be sharing some exercises that "kill two birds with one stone" -- that is, teach the principles of music theory at the same time as getting a good cello warm-up.

Intervals and Solfege

Intervals quizzes are the bugbear of many of my students. Most of us hear intervals just fine within melodic and harmonic contexts; what's hard is taking them out of context. I find that assigning certain solfege syllables to every interval based on the commonest melodic context in which we're likely to find that interval is the key to correctly identifying them. I also like to use intervals from the major scale for this in the earliest stages of teaching interval theory, to avoid confusion.

Er, so what exactly is this solfege....?

I'm a relatively late convert to movable-do solfege, since I grew up in New Zealand, where most people use the Associated Board of Royal Schools of Music theory and practical syllabuses. Solfege wasn't really part of the conversation for us. When I moved to America, however, I had to learn the American theory system, which relies heavily on solfege, and I have to say I like it. The syllables -- which it turned out I already knew from The Sound of Music -- provided an easily memorable way of articulating music theory.

 Well, mi re do, actually, but who's quibbling?

Well, mi re do, actually, but who's quibbling?

Essentially: "do" is always the tonic of the key we're in (so this may change within the course of a piece, since we'll be modulating to other keys). Therefore, in D major, D=do, A=sol, and so on. We use solfege to train our brains to understand the relationship between a note and its predecessor and its successor -- that is, training ourselves to have relative pitch. (A concept that is far more useful than its more famous relative, perfect pitch.)

scale with solfege syllables.jpg

Common Interval Associations

Certain intervals are associated with certain melodic and harmonic roles in diatonic music. There are multiple possibilities for solfege for any interval; however, certain solfege associations are more common than others. For example, the interval of the tritone is associated with diminished 7 chord, and the V7 chord, and for that reason we assign it the solfege ti and fa (or the other way around). The minor seventh is associated with V7 and the dominant function, so we assign it the solfege sol and fa. It's tempting to relate every interval to "do," but I discourage this: there really isn't much of a context in diatonic music for, say, "do-te" for the minor seventh, whereas "sol-fa" is omnipresent in music from the past hundreds of years. (Don't believe me? Try singing "There's A Place For Us" from West Side Story, where you'll hear that intensely strong pull of the dominant seventh towards resolution on mi.)

Why the emphasis on the major mode? Well, I find this the easiest way to teach beginning intervals. Therefore, I like to use "do-mi" for the major third and "mi-sol" for the minor third. Of course "do-me" is a perfectly acceptable way to label the minor third, but I prefer not to do this because the major and minor thirds are commonly muddled, and assigning them both parts of the major triad (do-mi-sol) helps sort them out.

By the same token, the major third is the inverse of the minor sixth, so it makes sense to assign the same solfege syllables to these intervals (and the same goes for the minor third-major sixth combination, since most native English speakers know the very useful song "My Bonnie Lies Over The Ocean," which begins with a major sixth).

With this in mind, I created a cello warm-up that goes through the intervals together with their commonest solfege contexts. This is great for multi-tasking because it also gives you a good shifting workout.

Just like for the shifting exercises that I wrote in Chapter Three of Cello Practice, Cello Performance, you'll need to establish a consistent contact point between bow and string, and ensure that your stance is balanced and relaxed.

Step One: sing through the exercise using solfege to the best of your ability (it doesn't matter if you're a bad singer, that's really not the point).

Step Two: play it on the cello! Use the bow from frog to tip. Shift slowly, "feeling" the shifts with your bow. Try to imagine that your shift is "powered" by the efficient pull of your bow, and that your bow's consistency and friction against the string are powered by the efficiency of the shift. As I stated several times over in Cello Practice, Cello Performanceall techniques are both-hands techniques.

Going further: theory is part of practice, and practice is part of theory.

Step Three: Using movable-do solfege, transpose the exercise into any key you like. You can play it on any string, using any finger. Five minutes of this every day will transform your ability to recognize intervals by assigning them with solfege contexts, and it'll improve your shifting and bowing. Win-win!

Exercise below, or download a free PDF complete with instructions here.

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Banish the Buckling Pinky (Bow Hand Edition)

In a previous post, I addressed the technical issues faced by cellists with "double-jointed" (more correctly, hypermobile) left-hand fingers. An equally common problem that you'll see on cellists with otherwise decent bow-hold setups is a hypermobile right fourth finger that "buckles" on the bow. 

This "collapse" isn't so much caused by the person's hypermobility, but by a misconception of what the fourth finger is supposed to do on the bow, in combination with finger shaping that places the finger on the bow in a way that's likely to cause buckling.

What do I mean by "misconception"? Well, I've heard a lot of teachers say that the index finger, fourth finger, and thumb are the fingers that "hold the bow up" so it doesn't fall. I disagree. The force of gravity is on our side: the string is what prevents the bow from falling; the fingers are there to be guides more than holders. In most cases, the fourth finger can sit relaxedly aside the ring finger without overworking.

The second part of this is the hand and finger shaping.  Buckling happens when the cellist's finger touches the bow at a sub-optimal part of the finger, as shown in this photograph of one of my students, J. Unlike me, J. has short arms and small hands, and in this photo she is demonstrating how she used to "compensate" by pushing the top joint of her fourth finger on the stick, causing it to buckle. Some people find this painful and some don't; either way, it's tense and we ought to avoid it.

 How not to do it: the buckling fourth finger

How not to do it: the buckling fourth finger

Looking at this from a side view, you can see because the bow hair is "flat" on the string, the fourth finger of J's small hand is forced to touch the bow almost at its tip, violinist-style. (For this reason, I don't use the widespread pedagogical practice of correcting a non-pronating bow-hand by having the student place the tip of her/his fourth finger on the stick to encourage pronation. It's a nice idea, but it simply causes too many other problems to be useful.)

 How Not To Do It, side view

How Not To Do It, side view

There's a very simple solution to this very common problem: don't play with flat hair! In the next picture, J. angles the stick towards her so that the bow's hair appears to be "pushing down" to the bridge (this has the by-product of improving tone quality). She's allowing the top joint of her fourth finger to come down the frog a bit so that the tip of her finger nestles in the hollow in the front of the frog. That way, a cellist can maintain good hand shaping without buckling the joint.

 Better: bow stick angled towards you, relaxed and curved fourth finger

Better: bow stick angled towards you, relaxed and curved fourth finger

Here's what it looks like from the side:

 Rounded hand shape, side view

Rounded hand shape, side view

I sometimes joke that this bow-hold has such a rounded position, you could take the bow out of the student's hand and replace it with a banana!

And because I always like to check the back view of both hands, here's what J's hand looks like from behind. (Questions about the student's thumb placement? Check out my post Rethinking The Bow Hold.)


Long, Long Ago: Wisdom From Your First Cello Teacher

 Turns out it's almost impossible to make a terrible bow hold when you're "spidering" up and down the stick...

Turns out it's almost impossible to make a terrible bow hold when you're "spidering" up and down the stick...

There are some things that are quite common in beginning cello pedagogy that I don't like much. The beginning bow hold with the thumb under the frog, for example, which teaches--for no good reason--a habit that has to be unlearned later. Another is the "left thumb as anchor," which teaches little hands to hit pitches chronically out of tune, and little ears to accept this poor intonation. I know why some otherwise good teachers are doing these things: because we all want to get a student set up with decent hand shaping so that they can advance to playing pieces quickly and not get bored and quit. But the fact is, poor setup leads to fundamental misunderstanding of how the body can be used to our advantage in playing the cello, and this in turn sets the student up for endless technical challenges later on. 

It's not all doom and gloom, however. When I thought back to some of the exercises I was taught as a child, it seems that many of them make a lot of sense, even if children don't know what they're doing them for. When the teacher tests whether the student can stand up from a seated playing position without shuffling their feet or moving the chair, what they're actually doing is encouraging a balanced sitting position. You simply can't stand up directly from sitting if your legs are splayed out or wrapped around the chair legs, or if you're hunched up. This is a great "reset" for those children who grow faster than their cello technique can keep up with. (And a good reminder for teachers to keep checking whether the chair is at an ideal height!)

Another great "reset" is the "bow hold spider." This is universal among string teachers and it's actually a really great exercise. You hold your bow with the stick vertically, and "walk" your fingers up and down it, sometimes while singing "Incy Wincy Spider" (a song my American daughter assures me is called "Itsy Bitsy Spider" here in the United States). It's harder to spider back to the frog than it is to spider to the tip! Back when I taught children in Saturday morning Suzuki classes, they always complained if I forgot to include Spider in our preliminary warm-ups. (I may or may not have sometimes placed Life Saver candies on the tips of their bows...) 

Spider is a fun game, but what's so great about it is that it's practically impossible to do it with a bad bow-hold. I know this, because I just tried to do it. I tried supinating my hand, and almost dropped the bow! I tried spreading my fingers in a widely-spaced, tense "claw," and I couldn't "walk" my fingers at all. I tried wedging my fingers together in a salute, and couldn't do it that way either. I tried "bracing" my fourth finger hard against the bow, and nearly whacked my bow into the wall. Holding the bow in a vice-grip? Neglecting to curve the fingers? Those don't work either.

Spider quite simply trains you to keep your fingers naturally spaced, curved, and relaxed on the bow, with thumb opposing the middle fingers, and the whole hand slightly pronated, playing-style. There's a reason for the hand shaping we have collectively deemed to be good for holding the bow--it's because our hands want to do it naturally. 

The takeaway from this is that despite all the misinformation about cello technique, there are certain exercises that are never-fail "resets" for your technique. Of which the ever-helpful Spider is one.

Want to know more about these resets? Check out Chapter 2 and Chapter 4 of Cello Practice, Cello Performance.

Buckling Fingers & "Double" Joints: Playing the Cello While Hypermobile

By Miranda Wilson

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Open up Google and type in "Can I play cello if I...". The first thing that came up for me was " double jointed?"

The answer is a resounding YES. Cello is for everyone. Humans come in all shapes and sizes and abilities, and that includes people with hypermobile joints. (Technically, there's no such thing as a "double" joint, but I use the term because it's common parlance for a common problem.)

I'm no contortionist, but I do have mild hypermobility, to the delight of my Alexander Technique teacher and the other children at my elementary school. Also, I've taught many college students with joints that can stretch way farther than mine. In cello playing, this manifests in fingers that buckle on the string and the bow, joints that lock painfully, excess tension, and pain.

Here's a little slideshow of some of the different types of wrongness that can happen -- and these are just the ones that have happened to me. (Not pictured is the very common problem of the locking pinky -- more on that in a minute.) Click the arrows to scroll through...


What can a person with hypermobile finger joints do to make cello playing comfortable?

1. Well, you could just ignore it, but that's not an option if it hurts or if you seriously want to improve.

2. You could do what I did with my hypermobile middle thumb joint: make it not buckle by force of will and lots of practice at never, ever hyperextending it. (Not recommended, as this takes a long time and is very frustrating.)

3. Wait to see if you grow out of it. I don't recommend this either -- why wait until a habit is so entrenched as to be unbreakable, and you start hurting yourself

The general consensus is that letting your fingers buckle is bad news. And yet there's so little information out there that can genuinely help the ambitious but confused super-bendy person. So...

4. Find some exercises that encourage rounded finger shaping so that this becomes habit.

I was excited to read this article by the violin teacher Lora Staples, where she encourages students to practice an exercise using a clothespin to build finger strength. Inspired, I found one in my laundry closet and tried it. But after a few repetitions, the tendons of my wrist started hurting, so I had to go to the grocery store to seek one that was more loosely sprung. Even that kind of hurt.

I did want to keep doing the exercise, however, because I was looking for solutions for my undergraduates, so I started thinking of other household objects that might do the same amount of good without causing pain. The answer came to me while I was cleaning my bathroom -- the trigger of a spray bottle! I tried the exercise on that and it worked brilliantly. Much "softer" than a clothespin, but with the same good results.

Here are some of the ways you can practice rounded finger shaping using a spray bottle.

Getting back to the cello...

5. Adjust your technique in a way that encourages rounded finger shaping and discourages buckling/locked finger shaping. For example:

a) Locking, tense left thumb? Avoid having the pad of the thumb press the cello neck. Look at how your fingers come together naturally -- your thumb comes in sideways. Let it do this on the neck too.

b) Fingers buckle on the string (especially in thumb position) and you can't find a comfortable angle that enables rounded shaping? You can, especially at high speeds, play on the side of the string and still get a good sound.

play on side of string.png

c) Fingers keep locking and causing pain? Try moving from finger to finger not by over-exercising the hand and fingers, but by thinking of the arm's weight as the agent that gets you from finger to finger-- like you're swinging from a bar at the gym. Keep your left thumb free (touching the neck with the side of the thumb helps with this, because you can't "press" so easily) so that it can move to "oppose" each of the fingers.

Further reading:

Intonation and the Opposable Thumb

Playing the Cello "Naturally"? Ask Your Hands How


Arm Weight, What It Means, How To Use It

Copyright Miranda Wilson, 2017. No part of this post may be reproduced without the author's permission.


Driving a Car, Driving a Cello

The first car I ever drove was a 1991 Ford Telstar with a manual transmission. At first, I was terrified of grating the gears, stalling, or simply not being able to move at all except in mortifying bunny-hops. After I'd figured out how to use the machinery, I realized that what frightened me more was steering the thing, parking it, judging how much space I needed to change lanes on the highway, and that sort of thing.

My instructor was a cranky elderly lady who was fond of reciting "Remember the six positions of the two-car crash!" as I clutched the steering wheel with white knuckles and tried not to hyperventilate. "Check your mirrors! You forgot to check! Never forget to check! Look behind you! No! In front of you!" The poor thing probably had permanently high cortisol levels from all the things her students did on the road. But eventually I was able to stop grating the gears, internalize the rules of the road, and pass my test (on my third attempt... hmm).

I thought fondly of my driving the instructor recently when I was on a visit to a high school orchestra. The teacher had done a great job of instrumental instruction and aspects of musicianship such as complicated rhythm. But I noticed that the majority of the students were buried in their music stands, barely looking up but for the conductor's cues. As a result, the ensemble's attacks weren't unified and the tempo got slower and slower.

And it occurred to me that playing in any ensemble isn't unlike learning to drive a car. Once you've mastered the task of playing tolerably well and have practised your part and studied the full score so you know "how it goes," when you get to rehearsal your gaze needs to be moving constantly. Of course you're going to look at your stand, but you constantly have to glance at the conductor, the concertmaster, the section principal, and so on. You have to be able to memorize short passages from the score so you can look up to give and observe cues without losing your place. It's as if having mastered how the gears work, now you have to make sure you're looking at the road in front of you, potential hazards in the distance, the rear-view mirror, the side mirrors, etc, with only occasional glances at the speedometer to check you aren't over the limit.

Successful driving and successful ensemble playing depend on having learned to do the thing in itself, i.e. master the equipment, so that it becomes automatic and you're liberated to do more things. If someone breaks a rule of the road and makes a mistake, alert and adept drivers can often adjust their own driving to avoid accidents. Someone comes in wrong in an ensemble? If everyone else is alert, adept at their own part, and knows the score well, they can "save" that person without having to stop.

Making music is inherently exciting. It's like driving down the freeway at high speeds, changing lanes, passing other vehicles, knowing where you're going, dodging hazards. If you can do the same thing in an ensemble -- get your head out of the stand and your gaze constantly moving -- you'll get to your destination much more smoothly.

Cello Cheats


Sometimes we encounter repetitive passages in the repertoire that tire the hands very quickly if we use conventionally "good" technique. Creative compositions call for creative performance solutions, including ways of playing that may initially look like "bad" technique. I call these "cello cheats."

One of my best cheats works well for long pizzicato passages. While pizzicato isn't inherently the hardest action to perform, repertoire that calls for a lot of it, such as the second movement from the Ravel quartet (pictured below), can be tiring to play -- to the point that the cellist may be worried about not being able to go fast enough at Ravel's specified tempo of 92.

If the repeated action of fast pizzicato causes feelings of weakness, try this simple tip: while holding the bow in the fist using the second, third, and fourth fingers, gently press the tip of the thumb into the pad of the first finger and pluck the string that way. You'll find that the strength provided by the thumb opposing the finger is enough to help you gain speed without tension (pictured below).

Another great cello cheat is the "vibrato trill." Most of us are taught that the motion of trilling should be initiated by a "hammering" of the finger that plays the upper note. But in repertoire with long or repeated trills, such as the excerpt from the first movement of the Dvořák concerto (pictured below), the trilling finger and the tendons of the hand can get overly tired if you do it that way. 

Why not play trills using the same motion as a vibrato, positioning the trilling finger so that it touches the string? In the pictures below, I demonstrate how the relaxed vibrating motion of the left arm in a trill can achieve the same effect as conventional trilling technique -- without the tension and tiredness.

I first thought of "vibrato trills" in my teens, and since then I've seen plenty of good players use them. It perplexes me that so many teachers won't let students trill like this. One of my mentors actually forbade me to do vibrato trills with no explanation other than that she thought it wasn't "classy." I wish now that I'd dared to argue. Why should we care what conventional technique is supposed to look like if we can achieve the same sound and feel more relaxed doing something else? Try it!