The Technique of “Isolating” Variables
Whenever a passage involves an intricate balance between two concerns, such as rhythm and pitch, pitch and fingering, etc., there is a method by which one of the two can be “held constant” while allowing only the other one to change.*
In the following examples we separate apart two intertwined issues, putting emphasis first on one and then the other, by holding the other one constant. Each is mastered singly before putting them back together again.
If rhythm and pitch are changing at the same time:
Make all the pitches just one and the same pitch, and play that note in the rhythm of the passage.
Play the sequence of pitches as written but do so in a “neutral” rhythm, (for instance giving each note the same duration).
If loudness and pitch are changing at the same time:
hold the loudness constant and let only the pitch vary.
hold all the pitches to one repeating note, and only let the loudness vary.
If an intricate series of notes also requires a difficult pattern of fingering:
Play every note with one and the same finger.
Stay on one note, but use the fingers in the order that they will need to be used when playing the passage in its normal form.
‘bunch’ up the finger tips and use them as a single unit on just one note and play the rhythm of the passage.
If the two hands are doing things that are quite different from one another and, thus, hand coordination becomes an issue:
Have both hands play the right hand’s notes, but in two different octaves. Then reverse the procedure, and have both hands lay the left hand’s notes in two different octaves.
If a melodic line involves sudden changes of register (octave).
Put all the notes of the melody into one and the same octave (a perfect example is Brahms: Op 117 No. 3, the middle section).
If it is difficult to play a melody in octaves in one hand. Use the pinkie to play just the pinkie notes. Then use the thumb to play just the lower notes.
If there is a variety of articulation marks within a small group of notes.
Play it all very legato; then all very staccato; then all accented; then all sotto voce.
Then add back the articulation. By this time you will be practiced in executing each type of articulation.
If it is difficult to play something slowly (or rapidly) enough:
Play it first at the opposite extreme of tempo. This procedure is especially useful for learning to sustain a long phrase or melody, that evolves over many measures. First play it extremely rapidly.
You will get a sense of the main outlines and directions in the phrase. Then slow it back down, and you will notice that the way the notes adhered to each other in the fast tempo is preserved into the slower tempo.
Mention is also made of these types of procedures in the blog:
* In mathematics, when there are several different ‘variables’, all intermixing and interacting with each other in a single equation, mathematicians, in order to gain understanding of how the equation behaves as a whole, use a procedure in which they treat all of the variables except one as if they were no longer capable of varying but were held constant. Then, one can go through each of the original variables in turn, each time making it, for the nonce, the only one varying. This is called partial differentiation.
“Outsourcing”. Comparing Through Exaggeration or Contrast
“Outsourcing” is a term I use when I use a second piece of music, one other than the one I am practicing at the moment, as a model on which to base out some quality or other in the practice-piece, but which I find difficult to bring out clearly when limited to how it appears in just the practice-piece.
To select a model piece, I free-associate for something very well known, in the same meter practice-piece, not always in the same tempo, but in which the quality I am seeking to bring out in the practice-piece is already shining brightly on the surface of the model.
Here are some examples:
If there is an element of subtle humor lurking in the passage from my practice-piece, I chose as a model something that exaggerates the comic element in it to an extreme. Or, if there is a subtle sadness passing over the surface of a passage in my practice-piece, then I would choose a model-piece that goes way over the top in sadness and tragedy. With a little careful “gene splicing” I can insert the characteristic found in the model piece into the way I play the practice piece.
In the same way that comedy and tragedy and two complementary lenses through which view the one and the same issue in life, so I can affect other such diverging comparisons. If the practice-piece sounds too ordinary or too beautiful (too affected, too precious) then, for the time being, my model would be a piece that is either too banal and insipid, or too beautiful, respectively.
The model-piece can also be used as a counterbalance to the practice-piece, to prevent some quality in the practice-piece from becoming too predominating.
Here are some examples:
When the practice-piece is in 3/4 time and a saccharine, waltz-like feeling is taking over the piece, I will play a blatant “oom-pah-pah” figuration in my left hand while continuing with the written notes in the right hand. The left hand definitely spices up the right hand. If I am giving a lesson, I will often do this left hand figuration at the second piano. It creates an irresistible force which transforms the student’s notes. Thus, while sometimes I need a model of the caliber of a Da Vinci or a Rembrandt, I can gain as much insight into my passage from a line drawing or caricature. In either direction, exaggeration is just as bona fide a way to bringing out the inner quality of something as is the process of trying to go deeper into it. The process is similar to looking through a fun house mirror, when suddenly we become aware of a curve or line went unnoticed until it became exaggerated or bent out of shape.
Another example of using a contrasting model:
A piece in a slow 2/4, that goes on and on, may eventually become bogged down in its own over-seriousness. I can be bring it back to life by superimposing on it a John Philip Sousa march like the “The stars and stripes forever”. I’ve done just this when playing a solo piano arrangement of the second movement of Beethoven’s 7th Symphony. If that piece is as deep and melancholy as I believe it to be, then these latter characteristics won’t disappear if some good humored fun is poked at it.
Origin of the process in my life:
I developed this tactic of out-sourcing a number of years ago after making a comment to my friend Roy, that what lies on the surface of a “rock” piece, lies under the surface in a classical piece, while the reverse is also true. For example, the rhythm and harmonic progressions in a rock piece tend to live on the surface of the music where they are obvious and unmistakable. It is like the exo-skeleton of an insect. The inside is worn on the outside. The same aspects of the music light the classical piece from within causing it to glow with a more hidden light. So often outsourcing a passage of the piece I am practicing, it is just a matter of switching around what lies on the surface with what lies initially obscured under the surface.
When I “outsource”, I either look for a latent characteristic in the piece I am practicing and then choose a model piece that exaggerates that quality, or I look for a quality in the practice-piece that I am over-exaggerating, in which case I look for a model which scrupulously avoids that quality, or plays it down. In the first case the purpose is to balloon, magnify something latent, by momentarily making it blatant. In the other case it helps a passage from having “hubris” (taking itself or my self too seriously), or to prevent my musical ego from getting out of hand. Either way I learn more about my practice piece as a result of this process.
In life the beautiful exists side by side with the banal, the emotional with the desiccated, a rich harmonic under-structure with a I-IV-V progression, the rhythmically complex and sophisticated with the mundane ostinato of a person reading a poem that never departs or “modulates” from iambic pentameter.
An Addendum to Sight-Reading Blogs
Links to previous blogs on sight reading are at the end of this post.
Today, we devoted Irving’s entire lesson to sight reading. During the lesson we noticed that these things were recurrent themes.
Trust your ear to judge if there is you have played a wrong note, but that sometimes though a note sounds wrong to the ear it is still correct because you are playing the piece in a slower tempo.
Remind yourself of the key signature in each new measure that you read. If you have an excellent visual imagination, just place the key signature after each new bar line.
Keep track of accidentals that have arisen in the current measure and remember to honor them throughout the rest of the measure* (be on the lookout for a natural sign as one of the accidentals in a measure).
Make sure all the notes your fingers are pushing down are actually sounding.
Try to think ahead.
Try to make the bar lines “transparent”. See if you can use any of the time playing the current measure to read ahead and figure out some or all of the next measure.
Sometimes try to sight read in “real time”, I.E. with no pauses or hesitations. Keep up with the beats, even if it means skipping over notes or even measures.
* even though the accidental sign only shows up the first time it applies in the measure and not the remaining times that it may apply.
Links to previous posts about sight reading:
#1 Habits that produce good sight reading: https://joebloom.com/habits-that-induce-good-sight-reading-skills/
#2 New rule for Irving regarding Sight Reading. https://joebloom.com/a-new-rule-for-irving-about-sight-reading/
#3 Rhythm & rhythmic coordination in Sight Reading. https://joebloom.com/rhythmic-coordination-between-the- hands-in-sight-reading/
Simplifying A Difficult Passage
A simple example of the procedure.
Irving is a late beginner. He is playing just the right hand of one of the easier Bach pieces. He thinks it will be too hard to put the hands together. I suggest that the next time he plays just the right hand, he lay his left hand down on the keyboard hand and let it rest there passively. He says: I don’t see any advantage in doing this, it certainly is not going to make playing the two hands together any easier. But he tries it. He is immediately struck by the fact that the right hand seems harder to play when the left hand is simply present on the keyboard. He says the right hand feels different. I agree: what one hand does is influenced by the other hand. Still, he said, this is easier than playing both hands together.
What we had created is an in between point between playing just with one hand and playing with both hands. Instead of one larger ‘step’, going directly from playing with one hand to playing with both hands, we created two smaller steps: 1) right hand alone 2) right hand with left hand running interference, 3) both hands playing the written notes. Instead of going directly from step one to step three, all that’s left for Irving is to go from step two to step three.
However, what if going from step two to step three turns out to be too big a jump? We simply divide that jump into two smaller parts. Between step two and step three we insert this: the left hand, though not yet playing its part, now is moved around while the right hand plays. Not moving any place particular but just so he is conscious of motion occurring in the left hand while trying to concentrate of the right hand.
We were following in the foot steps of one of the great thinkers in the Western tradition. The philosopher René Descartes (1596-1650), in his “Discourse on Method” suggested that one follow a four-step plan for seeking truth in the sciences. The second of these was, in his words “to divide up each of the difficulties which I examined into as many parts as possible, and as seemed requisite in order that it might be resolved in the best manner possible.”
We interpolate new steps as needed. As soon as the transition from one step to the next is not easily accomplished, we interpolate another step. The beauty of this procedure is that one can interpolate as many steps as one wants between the starting state and the final state we are aiming for. The more intermediate steps there are, the smaller becomes the change in difficulty from one to the next. In its ideal form, when using this process, the pianist will not be aware of any increase in difficulty when going from one step to the next, and the final state, the one desired all along, will, when attained, seem no harder than the first step.
A careful analysis:
The trick is how to define the first state. It must bear a direct relation to the last state. In Irving’s case it was easily found: “I’ll start with one hand at a time before trying both hands together”. Other technical and musical difficulties require a more penetrating analysis. Often the starting state is found at the end of a reverse process that starts with the final state, and gradually simplifies it, step by step, each time by removing what is most difficult to execute from what is left, and/or what is least essential musically, until a simplest state is left or revealed, one that is simplest to play yet still bears a resemblance to the final state.* During this process, each stage, while simpler than the last, should still contain the essence of the previous stage.
We operate like a grammarian who diagrams a sentence in a manner that reveals its more essential and less essential parts and clauses. Or like a chemist who by analysis reduces a complex compound into smaller and smaller molecules until at last the atomic structure of the compound is revealed. Or like a philosopher who seeks into an issue to find the more basic principle on which it rests. In my case, it is a procedure I use especially when teaching ear training: taking an ear training ability that is presented as being simple and whole, but then refracting it through a prism and showing that there are other, simpler component abilities that underlying the target ability. And even some of the simpler abilities turn out to be, themselves, complex in relation to even simpler abilities. Start with the simplest abilities and build back up.
* By removing notes without compromising the general meaning of the passage. By removing melodically unessential notes from a melody leaving only the salient notes. By simplifying a complex rhythm into simpler rhythms (simpler in nature and simpler in execution). By simplifying a complex harmonic progression to a simpler one that is easier for the ear to track, and easier for the fingers to play.
5 Shorter Blogs on General Technique and Jazz
How to start a run (#1). Scales can help us execute arpeggios and vice versa (#2). Symmetric motions in the hands (#4) Jazz improvisation (#4). A deeper meaning to a group of notes (#5)
#1 How to start a run
It’s the second note that precisely defines the tempo of the run.
How quickly does a listener determine the tempo of a piece. Not by the first note, but they can judge the tempo by hearing the first two notes. It is the precise duration from the beginning of the first note to the beginning of the second note that is the clue. This proves to be important for the pianist when starting a run, a scale, etc., any series of notes that are all share the same rhythmic value. If we are careful to play the second note at exactly the right moment after the first note, then we know what precise duration to give to each of the notes follow.
#2 Using arpeggios to help play scales, and vice versa.
When I am playing a scale, and it isn’t coming out the way I want, I play instead an arpeggio starting on the tonic note of the scale.
For instance, instead of: C D E F G A B c
I play C E G c
If at that point, without any time taken off in between, I play the scale again, the scale sounds more evenly and controlled.
The arpeggio in effect seems like a scale that has been sped up. I just have to fill parenthetically the notes the arpeggio left out.
The reverse situation applies as well. When I am playing an arpeggio, if it isn’t coming out the way I want, I play stead a scale whose tonic is implied tonic in the arpeggio.
For instance, instead of: C E G c
I play C D E F G A B c
This slows down the arpeggio because I am filling in the notes between the notes of the arpeggio. It now takes longer to get from one note of the arpeggio to the next. I just have be aware of the notes that I’m leaving. Especially the interval is more than a third, as well as when I bring over thumb, or come under the thumb.
#3 Mirror motions. The “target hand” and the “helping hand”
The body is freest and happiest when the two bilateral side of the body (the arms in particular) are moving in opposite directions. The physical sensation in the arm when moving away from the a central position (I.E. rightwards with the right hand, leftwards with the left hand) is different than the physical sensation in the arm when moving towards a central position (I.E. leftwards with the right hand, rightwards with the left hand). The body is happier when the two sensations are more alike. This is one of the reason that scales played in opposite motion in two hands seems easier than the usual practice of both hands moving rightwards, or both hands moving leftwards.
One hand helps the other: the helping hand and the “target” hand
In my playing, if I feeling awkward playing a passage or group of notes in the right hand, In what follows the right hand is the “target” hand and the left hand is the “helping” hand. The situation can be reversed if one is having difficulty with a passage in the left hand.
I will take the helping hand and move it in the empty space above the keyboard in a course that is a mirror image of the the directions that the right hand is going. It goes leftwards when the target hand goes rightwards, It goes rightwards when the target hand goes leftwards. As i said, the helping hand traces in empty space, just above the keyboard, the mirror motion of the target hand.
After doing this for a brief time, I go back to having the helping hand play the notes indicated for it in the score. The helping hand can retain the sensations of trying to mirror the target hand even though it is restrained from doing it fully by the notes it has to play that are in the score. But that doesn’t stop it from “trying” to start making such motions to mirror the other. Muscles can contract as if attempting a motion in one direction even if the hand at the same time busy playing notes that go in a different direction.
#4. Jazz improvisation
Not stopping the flow of notes every once in a while simply because you are not sure where to go to next.
During one year I had a jazz pianist come for lessons. He thought he would gain some additional perspectives on jazz by working with a classically trained teacher.
At first I showed stuff about classical music. It went OK. However, then I decided that it would be more interesting to work with him while he was improvising. My absence of technical knowledge in jazz would not prevent me from evaluating his improvisation on more general musical grounds such as sound, musicality, and motion.
I asked him to improvise for me on a standard tune. What I noticed was that when he would begin to play a series of rapid notes, after a certain number of notes went by he paused, but then went on. The pause to me always sounded artificial: not done for a musical reasons. I was curious to determine whether the pause was for stylistic reasons or occurred because his fingers were momentarily ‘stumped’ as to what to do next. It turned out to be the latter. Ideally he would have preferred continuing the series of notes in the improvisation.
I invented a curious exercise, one that is good for classical as well as jazz pianists. I had him wiggle his fingers rapidly in the air and simply do so without stopping. That set up the notion that the note-stream does not ever need to stop. The next step was to bring that finger motion to the keyboard and to play random notes. The notes need not have any musical significance. It was purely for him to get used to the idea that it was technically possible to generate an indefinite series of notes. In the last stage he applied that technique to improvising on a standard melody and, every time he was on the verge of stopping because he hadn’t yet figured out the following notes, he was to use stage two and to continue playing notes they were random notes. This opened up for him the possibility of creating a stream of fast notes at any speed, one that would last as long as he chose.
#5. A deeper meaning to a group of notes.
Sometimes it is not enough for me to play through a group of notes, just once, a part of a theme or a motive. It is as if I am taking a cursory swipe at what I think is contained in those notes: looking especially for something that is consistent with all the notes around it. But with repeated swipes I begin to unmask what is really going on in that group of notes. And that something is often easily glossed-over by me to make it seem like it is just another neutral, undifferentiated part of the whole nexus of notes of which it is a part.
By the second or third time I repeat the target group of notes (usually anywhere from 2 – 8 notes), I begin to see that it has a life of its own, one that is easily submerged in the general flow of the measure. Would I be encouraging anarchy on the part of those notes to give special care to bring out its authentic properties independently of what the rest of the surrounding passage is trying to state musically.
The answer I find is usually that bringing out the individuality of a group of notes, based on its shape, rhythm and harmonic implications, only adds, and does not detract, from the general flow of the piece; that it enriches meaning in the passage and not goes off on a tangent.