Leverage and Sound
Chopin, Etude in C# Minor from Opus 25:
Irving’s brother came today. We wanted to get a rich cello-like / vocal-like tone out of the piano for the notes of the opening “baritone” melody for the left hand. It is in single notes without accompaniment, so it is very exposed. We need our entire sound/mechanical tool-kit to keep it resonant and sustained so there isn’t a moment’s break in the flow of the line. Their softness shouldn’t belie their resonance.
Our first exploration was with leverage, the principle being that the greater the leverage you have over the production of each sound, the more that sound approaches the ideal piano-resonance.
The effectiveness of a lever is a function of how long the lever is and where you place the fulcrum on which to rest it*. Leverage increases with the length of the lever and how remote the fulcrum is from the end of the lever that, from which in this case, the pianist initiates the motion of the lever. If, for example, the lever is solely the length of a finger, and the third knuckle is where the fulcrum is, there is little mechanical advantage to depressing the key through the motion of that lever. If the lever extends back into the wrist, and includes the finger, there is greater leverage on behalf of the movement of finger tip. So the question is, how we can create the greatest leverage with the human body.
We ended up using a curious combination of several different levers, that ended up being connected one to the other.
The length of the arm, from shoulder to finger tips, while perhaps not the longest lever we can make of the body, is a conveniently long one that is still easily manipulated.
We started by his holding out both his forearms; straight out in front of him so that they parallel with each other and were horizontal to the ground. We Left a comfortable distance between the two hands, about the same as the distance between the two shoulders.
We then had him move his arms up and down using just the shoulders as pivots. At their highest points the arms were aiming well above the horizontal, at an angle of about forty five degrees. At their lowest points the arms were just slightly below the horizontal.
Very soon, we changed it to an oscillating motion between the arms. One arm was at its lowest when the other was at its highest. And they exchanged these positions. We did this until he felt a sort of physical exhilaration from all that motion.
The next thing we did was to create a second, more imaginary, lever. At the same time the arms were moving, we pretended there was the plank of a see-saw that connects the two hands (traversing the empty space between the hands), which, as a result of the arm motions, was itself going up and down as if two people were seated at each end of the see-saw. The pivot of this imaginary see-saw was exactly half way between the hands, so that neither hand or arm had a mechanical advantage over the other – the advantages were equal.
I also had him imagine a secondary but similar see-saw between his two shoulders, as if an, albeit, small person was seated on each shoulder. We continued exercising the combination of these levers until he felt a definite exhilaration from making these motions.
We then ‘elected’ his two index fingers as the sole ‘beneficiaries’ of all the motions he was making, so that the each index finger was backed up by the entire arm and contributing see-saws.
While continuing the oscillation of the arms he used alternating index fingers to play first the opening note of the second note. The solo was no longer distributed solely to the left hand but alternately, from note to note, between one arm lever and the other. If he played the first note with his left index finger, then he played second note with his right index finger. Then back to the left index finger to sound the third note, the right again for the fourth note, and so on through the line.
During this procedure the fingers were to never loose their connection to the hand, and on to the wrist, the forearms, the elbows, all the way to the shoulders.
Sometimes the arms had to cross one another, but the more important thing was the swinging motion from one arm to the other regardless of which one was to the right or left of the other.
When he did this with physical abandon fervor, without thinking so much of the ‘proper’ or ‘usual’ way of pushing the notes down, the result, to our joint delight, was an unusually rich sound, one that he was unaccustomed to getting on single notes.
Even when consecutive notes were ‘next door’ to each, only a half step or whole step away, we did not diminish the feeling of the widest possible see-saw between the arms. In other words, while the objective distance between the consecutive notes might lessen, the subjective sense of how long that distance was always remained large.
The last step was to preserve the widest and most dynamic sense of an oscillating motion when going not just from one hand to the other, but from one finger of one hand to another finger of the same hand.
* The saying, concerning how levers work, as attributed to Archimedes, is: Give me the place to stand, and I shall move the earth.
Sometimes, it Really Is Black and White
Key signatures remain a stumbling block for certain types of students.
We were reading the middle section of the Mozart “Rondo alla Turca” – the section with the seemingly endless running sixteenths in the right hand.
If I am reading a piece in G Major, when I come to a note in a measure that that is printed on the top line of treble clef it simply doesn’t “look like” an “F” to me. It looks different, it “looks like” an “F#.” I’m lucky that way. For many students however F-s do not magically transform in appearance to F#-s.
I also carry around the inductive logic of the circle of fifths as a fixed and clear model in my mind. There is no trouble in remembering that if there are three sharps in the key signature they will be F#, C# and G#. I don’t have to examine the key signature to come to this conclusion. For many, though, regardless of experience, they have to look at the sometimes dense group of sharps or flat signs at the beginning of each line, an decipher for which line or space each is centered on, then try to remember, each one separately, to go through a check list, as it were, for each note they encounter in the piece to figure out of it is a natural or not.
These students have difficulty every developing more than a rudimentary sense of what a “key” is. They are apt to forget each time, for instance, that if there are three sharps in the key signature, they are always the same sharps, and that these F#, C#, G#.* Sometimes they will find it easier to they remember the three as C# F# G#, so at least they are sorted alphabetically. A typical question from such a type of student is “how do you know if the piece is major or minor?” “Can you tell from just looking at the notes at the beginning of the piece; or is it something to do with the sound?” Attempting to explain the answer to this question in terms of there being certain statistical likelihoods for certain notes and chords to show up in the first measures of the piece, further complicates and mystifies.
The inductive logic of the circle of fifths doesn’t establish itself firmly in their minds. They do not see an imaginary sharp or flat sign to the left of each note along a line of music, whose existence is confirms a sharp or flat that in the key signature at the beginning of the line. And practicing scales until they become automatic in the fingers seems a daunting task, as difficult and time consuming as learning entire pieces.
For many years I stubbornly retained the simple logic of he circle of fifths as the only unambiguous way of clarifying key signatures to students for whom this posed an issue. Logic, I felt, will always win out. It took a while to mature out of this notion.
At today’s lesson I chose a less elegant, a less logical, but simpler expedient. I told Rachael that my intuitive impression was that as she was reading the notes on the page it didn’t seem immediately clear to her whether the next note to play was a white note or black note. I took the first measure of the passage, and I asked her to play the passage as slowly as she needed to in order for her to say for each next note that she read, “this is a black note”, or “this is a white note”. How she determined this was unimportant, it was just the final experience of the hand on the keyboard that mattered.
This shifted the emphasis from remembering the key signature and how it applied within the measure, and raising to a higher level of conscious awareness the identity of that note as simply being a white note or a black note. There was no more key signature present. There was just the individual identity of each note as falling into the class black note or white note. If it was a black note it didn’t matter if it was written as a sharp or as a flat. Only key color mattered. The same with regard to white notes, whether their note names were naturals, or flats or sharps.
This first measure of eight sixteenth notes was just memorized as a sequence of words. Just as a binary number is a series of zeros and ones in a certain order, so the measure was a series of the words ‘back’ and ‘white’.
At first she seemed skeptical that this could work, since it seemed to beg the question of needing to know and retain in her mind the key signature. But it turned out otherwise. Now that there was only one of two things to choose about each note, and after putting in the initial downloading time it took to put the measure into this on/off, zero/one, black/white form, her confidence level in playing the notes correctly rapidly increased. She felt a certainty and a mastery over what to play. There were no questions left. No uncertainties. Just the color of the notes. She bypassed any worry about applying a ‘template’ of white and black notes, first to the key signature, and relate things from there to the notes of a measure.
*Or furthermore that the first two of those sharps are always the same as the sharps that appear when there is only two sharps in the key signature.
Lyricism, Connectivity and Shaping of Sounds
At B’s lesson today, he was playing Mozart’s Adagio in B Minor
He plays a series of notes from the piece, and stops because he is frustrated with how it just sounded. He says: “In order for me to even it out, ‘this’ note needs to be a little louder, and ‘that’ note needs to be a little softer.” He makes physical adjustments in how he plays each of those two notes. The result is a new set of inconsistencies in the sound. I try to explain that any difference in muscular action for which one can consciously in control will over-compensate for the problem. The only ways that reliably control evenness in sound, whether in a melody, or in a chord, are based on either the ear or finding a lever further up the arm that controls all the fingers alike.
Here are some of the spots that we worked on.
#1. The first chord in the piece: es3-b3- -gs4-d5.
If the chord is not coming out the way you want it to, do the following:
a) Play the es3, three times in a row, while doing nothing other listening to them. For, without your realizing, your playing mechanism is going to adjust the resonance of es3 your figurative, “inner” ear is satisfied with the sound. Just by gradually playing it over and over it comes closer to having the quality of sound you want. Hold the third one longer than the others.
b) Then pause a couple of seconds. Now play es3 and b3 together, three times in a row (as before). Again your instinctive ear is going to automatically cause the body to unconsciously change the enunciation of the two notes until both are equally resonant and well balanced.
c) Pause again for a couple of seconds, and play the es3, b3 and gs4 together several times. Let the same automatic balancing of the sound occur through the ear. You don’t have to do anything more than listen to the triads. You don’t have evaluate the balance each time you play it. It will simply gravitate towards an idea position. It’s an unconscious process of “practicing” something over and over until it pleases you or sounds the way you want.
d) The last stage is to play all four notes together – three times. Then, aslmost as an afterthought, play the four notes together again. Through the silence that elapsed between the last of the three iterations of the four note chord, and the ‘fourth’ one you just added on, you will have preserved, without the slightest change, the balance of the notes. It simply sounds the way you just heard it a few moments ago.
What we’ve done through this process is “taken apart” in time something that is meant to be heard “together” in time. Rather than that changing the nature of what we hear because we have broken it into repeating parts, we actually gain more automatic control of how the notes will sound when ‘together’ in time. One might say we have created a figurative lever of to gain a mechanical advantage of consciousness over simultaneous in time.
#2. The first three notes of measure one: b4, fs4 and d5.
We use a similar process to what we used in number 1. Play the b4 three times. Just listen to it. “Get to know it”. “What does it sound like when it sounds like a B”? Or, as in Ireland: “who is he when he is at home” (who is he really).
Pause and then play the b4 together with the fs4. Same principle, three times; getting to know the full tonal implications of the interval of the fourth between the notes. And something new: that there is an implication in that fourth that there is, latently, or about to be realized, another note that will complete the fourth and turn, as in this case, into a B Minor chord in second inversion.
Now ‘confirm’ your expectations, that have built up further and further during the last few moments in time, that you have patiently kept in check through the previous eighth note, and with an air of satisfaction / relief / puzzlement, etc.: any emotion will do, by playing the missing note (d5). If, for example, it meets your expectations, say to yourself something like “I knew all along it was going to sound this”.
What we are discussing in the last two paragraphs falls under the heading of “hearing the missing sounds”. Or, play it in such a way that even the listener can sense, vaguely, or more specifically, what the missing note or notes are.
If all we heard is the fourth between the fs4 and b4, and no other sounds from the universe, including from what we have stored in our musical memory, any of the following note (or notes) will complete the empty fourth:
fs4-b4-d5 or fs4-b4-ds5 or ds4-fs4-a4-b4 or d4-fs4-a4-b4 or d4 f4-af4-b4
Here is another approach to the same opening three notes. It is sort of the reverse of the process just described. Don’t begin with just one note, but with a B Minor chord of many notes (for instance: b2-fs3-b3–d4-fs4-b4-d5. Follow that by the single note with which the piece starts. That single note will still retain the coloring, or mood, that it possessed by virtue of the presence of the other notes sounding with it.
Or, we can start with the same, full chord, and then gradually strip away notes from that chord, until at the end we leave just one note, for instance the first note of the piece. Through each stage in this process the notes that are left remaining retain the full power and effect of a B Minor chord.
The end goal is, without physically playing the other notes of the chord, sound the b4 just as it would sound within the chord.
What applies to one note from a chord compared to a full orchestra, let us say, playing that chord in many voices and ranges, can apply to any chord we play in the piece, as compared to that same chord being elaborated over many octaves in a full symphony orchestra.
The process reminds me of the beginning of a poem by Wordsworth.
“There was a time when meadow, grove, and stream,
The earth, and every common sight,
To me did seem
Appareled in celestial light,
The glory and the freshness of a dream.
It is not now as it hath been of yore;
Turn wheresoe’er I may,
By night or day.
The things which I have seen I now can see no more.”
This is from the poem: “Ode: Intimations of Immortality from Recollections of Early Childhood”. The rest of the poem has to do with the possibility of retaining that celestial light or illumination that bathes even everyday things.
There is yet one more way of talking about this. It is also quasi poetical but scientific as well. When we play the piano, the sound of each individual note is already rich and complex in sound. Each such sound contains within it a firmly held together chord made up out of what are called the “partials”, or more commonly, the “overtones” of that note. So if we compare what we hear, when we listen to that note, to what, for example, a tuning fork (which has few overtones, and the ones it does last very briefly), sounds like intoning that sound, each individual piano note is found to be already rich and complex in sound. Bass tones evoke the higher overtones of heaven. And when our ears are open we hear the full panoply of pitches throughout the range of the piano.
When we play more than one note at a time, the higher notes in our chords often correspond to overtones of the lower notes in the chord, and these higher notes in the chord take upon them a fullness and resonance that they would not have minus the presence of the lower notes sounding with them.
A Thanksgiving Fantasy; Thank you to all my Followers
I had one lesson today in the early morning. The ubiquitous “Irving” was over and played the Scriabin Etude in C-sharp minor (Op. 2, No. 1).
My mind was running at a very fast pace dreaming of turkeys with enormous thighs and having visions Japanese sweet potatoes drowning in Vermont maple syrup. The result was that I gave, let us say, a ‘rambling’ lesson, one in which I let my imagination loose, which caused me to use a lot of mental imagery, flights of fancy and outre analogies. It definitely wasn’t a very ‘literal’ or scientific lesson. But it worked.
Here were the main points we covered.
Irving spent a long time sitting at the piano and figuring just how to play the first chord. I interrupted the process and said: too much time spent in preparation – just “evoke” the sound out of the piano. Feel like a magician who casts a spell or waves a magic wand and a beautiful, resonant, soulful, balanced, chord emerges from the piano. Then I said: and incidentally, do this over and over again for every sound that wants to come to birth out the womb of the instrument.
That had an immediate and positive effect on the sound quality, both within and between the chords. But we weren’t there yet. It wasn’t the sound I had in my memory and imagination. At that moment Irving happened to be doodling around with the B key on the middle line of treble clef, playing it -then listening to it. This inspired my next flight of fancy. I said: when you play that note, hear it crescendo after it starts. Every note grows while it sounds. There is no such thing as ‘decay’ or getting softer.
The great French philosopher Henri Bergson wrote: “What philosophy has lacked most of all is precision. . . (philosophical systems) are too wide for reality. Examine any one of them . . . and you will see that it could apply equally well to a world in which . . . men . . . born decrepit . . . would end as babes in arms.”
Or, if you remember the TV series “Mork and Mindy” with Robin Williams: they have a son together, who hatches out of an egg fully grown, looking surprisingly like Jonathan Winters. Mork explains to Mindy that their son from this point on will grow younger and younger over the years.
I mentioned both of these things just to say that others beside me have had fantasies in which things defy the ‘arrow’ of time, or in my case, that a piano string, once set into motion and left on its own, will vibrate more and more strongly rather than less and less so.
You can also imagine a group of billiard balls, all in motion, which grow closer and closer to each other over the next bunch of seconds, until at the last moment they have come together in a triangular arrangement. And other such ‘entropy’ defying feats.
At this point we were getting close to the desired sound. The sound had been transformed, was lush and lasting. One more thing was necessary, which had to do with mechanics of playing each chord. Each time there was a chord to sound (which was pretty much every eighth note in the piece) create the chord out of its lowest note which then, figuratively speaking, opens up to the entire chord – only this has to occur simultaneously.
This is how we approached. We began by taking one specimen chord and played it, with the pedal down, as a very slow upwards arpeggio. We did the same again to the same chord only the arpeggio moved a little faster. Then a little faster…
If I remember my calculus aright, if “delta t” represents the time duration of each note before adding to it the next note of the arpeggio, then, we simply let “delta t” shrink gradually to zero, at which point, though we still feel physically that we are arpeggiating, all the notes of the chord begin at the same instant.
At this point there is no longer a distinction between a simultaneous chord and an arpeggio of notes of a chord. It is a physiological feeling in the body that the lowest note is played first and that our energy then shifts rightwards. The listener hears the notes start simultaneously, but notices a richness to the sound.
The player has now been able to make ‘simultaneous in time’ identical with ‘sequential in space’. The simultaneous chord retains the imprint of the note by note arpeggio. In the calculus analogy, it like the straight line that connects two separated points on curve, which line, as those two points made to approach each other, changes its slant until, when the points converge, and the line looks like the tangent to the curve at that point.
Part of the retained ‘sequential’ physical experience is that each individual finger will feel totally in control physically of its note and each note sounds with an individual intent. The bonus is that this is not the result of trying to coordinate the actions of different fingers. For the feeling of the arpeggio remains, so that the body still feels a rotational change from one note to the next in the chord. The more notes in the chord the more this rotation seeks its origin and energy from the shoulders and the arms. In terms of our consciousness, something magical happens, it is as if the single instant at which all the notes start sounding has been expanded into lived duration.
We turned our attention next specifically to the contrasting section (when it switched from sharps to flats) where utmost anguish is suddenly replaced with great calm, as removed as possible from the original mood.
I made an analogy with a garden hose with a sprayer at its end that is held in the person’s hand, which sprayer contains a lever that makes the spray get stronger and stronger. There is usually a strong spring in the lever that progressively resists squeezing the handle further, so that if one wants a steady and strong flow. and squeezes it for too long, the hand may grow tired and need to relax, even if just for a moment, before returning the water to the same pressure. Without those moments of easing off the steadiness of the stream would not remain as continuous.
I wanted to have Irving feel this in relation to the keys going up and down. The goal in this section is to act like the keys always stay down, but with every eighth note the hand needs to release and retake the keys. The release of the keys has barely begun when a force from the arms and hands returns the keys to the depressed state. It’s almost like when having to play the same note over and over, legato, without any use of the pedal. We learn to strike a balance between there being just one continuous sounding note and the notes separating too far apart.
Looking around for a piano-key-like object, I seized on a pencil (it was the best I could find). I said: this is a piano key, and, not only is it a piano key it is “Every-key”, in reference to “Everyman” (the 15th century English morality play). I held one end of the pencil fixed, made the length of the pencil horizontal, and then manipulated the other end of it up and down. It is like, I said, we are manipulating the same key over and over, imagining the piano keyboard as having just one and not eighty-keys, and that all we were doing was, when playing, was raising that same lever up and down. And that made all the different pitches and rhythms.
Another way I described it was that part of the magic control that we have over time, when it came time to make the next chord sound, the keys were already down – even, already sounding.
Happy Thanksgiving and thank you to all, and especially to Sawyer Fuller, our web master. Save me a piece of dark meat!
The Challenges of Sight-Singing
Teaching sight reading skills to others is hard for me. It is the negative flip side of the positive fact of my having absolute pitch.
I start from the opposite end of the spectrum than most people. I know what the notes are going to sound as soon as my eye sees them on the page, even if I haven’t heard the piece before. If I am asked to identify an interval by its sound, I already know what the two notes are and from that I can, if I want, calculate the interval.
There is also for me a complete fusion between hearing the sound in advance and my hands going to take the notes on the keyboard that produce that sound. Additionally, I have a strong and well developed sense of harmony. Once I know what the chord is, which includes the particular spacing between the various notes of the chord, my hand simply distributes itself automatically on the keyboard to effect that chord. And, as I read, before I am conscious of the names of the individual notes in the next chord on the score page, I am conscious of the name (the root note, inversion, spacing… of the chord). It’s as if I see chords and not notes. It is a bit like the person who, before they are conscious of feeling any pain, has already withdrawn their hand from a hot object or a fire. As I recall from Junior High biology class, this results from part of a nerve signal making a U-turn in the spinal cord, and the other part of it making continuing to the brain. When the latter happens, then we know why we just drew our hand away.
I have a strong sense of pulse, which keeps the piece moving forwards even when sight reading. Part of that has to do with rhythm. As soon as I foresee a rhythmic pattern among the next group of notes in the score, my body also knows what that rhythm is going to feel like in its execution. This happens when or a fraction of a second before I read the identity of the pitches of those notes.
Anyway, Irving wants to continue with his diet of 10 minutes of sight reading every day. We talked for some time about it. I had to be very quiet and take in what he was saying, and not jumping in with half baked ideas that were based, without my thinking it through, on the things I do with greater ease when I sight read.
I learned from him one interesting point. If a person’s sight reading is too “slow”, and if there are too many misplayed notes, the pianist does not get a sense of what the music is like that they are playing. The latter, though, is what brings enjoyment to the sight reading process itself, and forms the motivation for continuing sight reading, both further into the piece and to want to spend time in general sight reading. The joy of discovery.
I have to figure this out… (I would love suggestions: please share your ideas)