jwilzewske: Afflicted Fingerings, Biomechanics, and Energy Budgets

B and B-flat, vying; then C and C#: yow! … all of which as if to reveal some hidden perversity in the interval itself, to show some concealed possible corner of the second’s personality … what the Second does when he’s at home alone, when no one’s watching.”
— Jeremy Denk, More about Goldberg Variations, ThinkDenk blog, 11-MAY-2009.

M y hand shifts to make a gradual transition in this Bach sarabande. I never fail to be impressed by how deeply afflicted this piece is. I think of these passages as several competing storylines crossing each other... chains upon [Dutilleux-esque] chains of expressive dissonances in the French Suites.

Bach, French Suite, No. 1 in D minor, BWV 812, mm. 7-8

W hat fingerings might be best? Bach’s Inventions No. 1 and 2 have been the focus for studies by Yuichiro Yonebayashi, Hirokazu Kameoka, and Shigeki Sagayama at the University of Tokyo (link below). They represent the positions and forms of hands and fingers as Hidden Markov Model (HMM) states and model the resulting sequence of performed notes mathematically as HMM transitions. Or, for me just now, Bach’s French Suites, BWV 812-817, Markovian fingers, compelled by what other neighboring Markovian fingers just did.

F ingering would be no problem were it not that music notes are preceded and/or followed by other notes.”
— Yuichiro Yonebayashi, Hirokazu Kameoka, and Shigeki Sagayama.

O ptimal fingering is essentially a problem of finding an optimal sequence of [reasonably] smooth state-transitions, from one state of each finger to the next. But the issue is not just about ‘ease’ or ‘reliability’ or ‘evenness’, even though those are of course important. The matter has also to do with texture and emotion. In fact, a thoughtful composer who is also a pianist knows very well what biomechanical ‘cost function’ or budget for effort or attention or energy expenditure will likely prevail for performers. If the composer’s intent is to devise an especially afflicted expression, then the composer chooses a key-signature and sequences of notes specifically with the intention of beleaguering or defeating performers’ biomechanics cost functions and built-in instincts.

W hen pianos were first invented, they were similar in size to harpsichords. Hand size was rarely a limiting factor throughout the eighteenth century because the keys were short and narrow and the repertoire usually contained intervals no larger than the octave. However, at the beginning of the nineteenth century, the piano gradually expanded in range and key size. The use of cast iron frames led to an exponential increase in string tension, resulting in heavier and deeper actions that exacerbated problems for small-handed players. Nineteenth-century concert pianos typically featured actions with 6 millimeters of travel depth, requiring 23 gm of weight for full key depression and string tension in the middle register that ranged from 12 to 15 grams. By the end of the century, string tension had risen to 80 kg in the middle register, resulting in a heavier action with 9 mm of travel depth, requiring 45 g for full key depression. Today’s Steinway grands feature even heavier actions and larger hammers: 90 kg of string tension and 10.5 mm of travel depth, requiring 50 to 60 g of key depression force.”
— Lora Deahl & Brenda Wristen, American Music Teacher, JUN-2003.

I sometimes use 2-3-5 LH for triads and 1-2-3 for RH triads, leaving the thumb ready for 7ths or other contingencies. Also, my RH likes 1-3-5 or 1-2-5 when straddling black notes or for inversions or big gaps. But these produce tension in the hand—not just physical stretching but—I realize this now—brain stretching, too. Brain regions controlling the index finger and middle finger—fused under the influence of years of neuroplasticity—get anxious. They are apprehensive of more affliction that’s surely in-store.

T his Bach is undoubtedly about middle age and loss. Written in 1722 or a little earlier—two years after the sudden death of his first wife, Maria Barbara; now soon after his marriage to Anna Magdalena. Bach at 37—he hardly knew over-the-hillness first-hand, but he surely knew about loss. I realize that I am playing this differently now in my late 50s than I did 20 years ago, but I am not sure how to explain the difference in words.

I t has been more than 10 years since I played French Suites. The elapsed time is long enough to have lost any muscle memory I once had. Whole strategies and insights have vanished—and my old marked-up copy misplaced in one move or another along the way. Maybe my explanation for what is different is just that: beginning again, after some sort of catastrophe. Feels like physical therapy/rehab for someone who has suffered a stroke? You full-well know what your appendages ought to do, and you know the self-possessed sensations that you intend, but the body doesn’t cooperate—or even feel like your own self, really.

W hen working out your fingerings—even for a piece that is vexingly familiar and yet alien, like this one is for me right now—you often start at the beginning of a passage and plot your strategy forward from there. Sometimes, though, I prefer to first find the points that demand a specific finger. These points mark constraints such that you must have the requisite finger to proceed into the next phrase; such points are often the highest or lowest points in a passage. In the RH, you don’t usually want to end up with fingers 1 or 2 on the highest note (LH lowest note), nor do you want to end up on 4 or 5 on the lowest note of a RH passage (highest in the LH)—especially if the thing is going to immediately reverse direction. Once you’ve identified those constraints, you can work outward, both upstream and downstream, to plan your optimal fingerings.

I mark each place that involves a finger substitution, a change of fingering on a repeated note, or crossings (4-over-5; 2-over-1; 3-over-1; 4-over-1; 1-under-2; 1-under-3; 1-under-4; 5-under-4). I used to do this in pencil, and sometimes I still do this. But in the last couple of years I prefer to do it with e-markups in MusicReader™ software, which I use with my AirTurn™ pedal.

I mark more non-standard fingerings—the more afflicted the passage, the more non-standard it gets. For example, a passage may have a D minor scale in the RH, but it may continue to the octave E. One conventional fingering would cross to 1 on the high D and place 2 on the E. If it were then to return, you would have another crossing (1 - 4 on D to C) almost immediately. In this instance, a non-standard fingering such as 1-2-3-4-1-2-3-4 may be more effective. Bach as ‘rehab’; rehab as [self-] ‘discovery’...

jwilzewske

Wednesday, May 19, 2010

Afflicted Fingerings, Biomechanics, and Energy Budgets

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