(39) Damper (Sustain) Pedal, Physics of the piano sound

Practice any new piece without the (damper) pedal, HS and HT, until it can be played comfortably HT at final speed. All good teachers use this method. It might feel difficult, at first, to practice musically without the pedal where it is indicated; however, this is the best way to learn precise control. The "difficult" feeling arises because, without the pedal, you need to play every detail correctly. Students who practice with the pedal from the beginning will become sloppy players, develop numerous bad habits, and will not learn the concept of precise control.

Rank amateurs often over-use the damper pedal. The obvious rule is, if the music doesn't indicate a pedal, don't use it. The action feels lighter with the damper pedal down, because the foot is holding the dampers off the strings instead of the fingers. Some pieces might seem easier to play with the pedal when playing very slowly but this is one of the worst traps a beginner can fall into. Most beginners do not realize that where pedals are not indicated, it is usually impossible to play the music at speed with the pedal because all the notes will run into each other, and you lose control over the individual notes. The pedal is a crutch because you never have to lift the fingers accurately. Such crutches ruin the technique because they allow you to "play" (slowly) without adequate technique.

One major objective of practicing without the pedal is to practice keeping the fingers down to hold the hammer still using the backcheck, see [(11) Basic Key Stroke; Legato, Staccato], after every note. When not in use, the hammer must be held still so that it is under control at all times; otherwise you lose control and can miss notes or play them too loud even when you play them correctly, because the hammer was flopping around. Do not push down hard, the "force of gravity" (arm weight) is adequate.

The pedal did not exist before Mozart's time; for example, no pedal is used in any of J. S. Bach's music. Mozart did not indicate any pedaling although, today, some pedaling is considered optional in some of his compositions and many editors have added pedal markings in his music. The pedal was fully developed by Beethoven's time, although it was not yet totally accepted as a serious musical tool. Beethoven used it with great success as a special effect; therefore, he tended to use it a lot (first movement of his Moonlight Sonata, third movement of Waldstein Sonata) or non at all (Sonata #1 and Pathetique Sonata, first and second movements of the Waldstein). Chopin used the pedal extensively to inject an additional level of harmonic logic into his music and fully exploited all the different ways of pedaling. Therefore, Chopin (and many later composers) cannot be played correctly without adequate training in pedaling.

See the references for all the different ways to pedal, when to use them, and how to practice those methods (Gieseking and Leimer, Fink, Sándor, Rubinstein, and "The Pianist's Guide to Pedaling" by Banowetz). These references provide helpful exercises for practicing proper pedaling. Try to master all these methods before using the pedal with an actual piece of music. Example: depress the pedal before playing the note for exciting as many strings to vibrate as possible. For sustaining only one clear note, depress the pedal after playing the note (but before you lift the finger); the longer you delay the pedal, the fewer sympathetic vibrations you will get. In general, develop the habit of depressing the pedal a split second after playing the note to produce a more harmonious tone. For producing a legato effect without too much blurring, rapidly lift and depress the pedal at every chord change. It is just as important to know when to lift the pedal as when to depress it. Clearly, the pedal must be "played" as carefully as you play the keys similarly to the basic keystroke.

Physics of the piano sound. Unlike the simple picture of fundamental and harmonic frequencies that are used when tuning a piano, the actual string vibrations consist of a complex time dependent series of events. Therefore, I summarize here some general knowledge based on the physics of the piano sound. The piano produces an initial prompt- sound and a sustaining after-sound (Weinreich, Askenfelt). The string vibrations can be polarized, either parallel to the soundboard, or perpendicular to it. When the strings are struck, vertically polarized traveling waves are generated that move away from the hammer in opposite directions, towards the agraffes (capo bar) and towards the bridge. See Grand Piano Diagrams or Reblitz for names of piano parts. These waves travel so rapidly that they reflect back from both ends of the strings and pass the hammer several hundred times before the hammer bounces off the strings; in fact it is these waves that eventually throw the hammer back. Horizontally polarized waves are generated from the vertical waves because the piano is asymmetric. These traveling waves decay into standing waves consisting of harmonics (including the fundamental) because the standing waves are "normal vibration modes" (see a mechanics text book) that transfer energy slowly to the soundboards and are therefore long- lived. However, from the very beginning, the concept of fundamentals and harmonics remains valid because the Fourier coefficients (see a math or physics textbook) of the fundamental and harmonic frequencies are always large, even for the traveling waves, because the ends of the strings are rigidly fixed. The rigidity is supplied by the mass of the piano, which explains why good pianos are so heavy. The initial vertically polarized waves transfer energy more efficiently to the soundboard than the horizontally polarized waves and therefore produce a louder sound and decay faster; they create the prompt sound. The horizontally polarized standing waves produce the after-sound which gives the piano its long sustain. Energy is transferred back and forth from the vertical to horizontal polarizations, which produces the singing property of piano sounds.

If the damper pedal is depressed before a note is played, the initial time dependent traveling waves will excite all strings, creating a soft, but slightly dissonant, background roar. That is, in the prompt sound, the non-harmonic Fourier coefficients are significant; i. e., there is some white noise. If you place a finger on any string, you can feel it vibrate. However, octave and harmonic strings will vibrate with higher amplitudes than the dissonant strings, which is a consequence of the larger Fourier coefficients for the harmonics because the ends of the strings are fixed. If the pedal is depressed after the note is struck, there will be sympathetic vibration in octave and harmonic strings, but all the other strings will be quiet because the traveling waves have dissipated and the remaining standing waves contain only harmonics. This produces a clearer sustained note. The lesson here is that, in general, the pedal should be depressed immediately after striking the note, in order to produce a more harmonious sustain.

For Für Elise, use the pedal only for the large LH broken chord accompaniments (bar 3 & similar), bars 83-96 and the RH arpeggio passage (bars 100-104). Practically all of the first difficult interruption should be played without the pedal. Of course, everything should initially be practiced without the pedal until you have basically finished the piece. By not using the pedal, technique improves fastest because you can hear exactly what you play, especially the hold and lift components of the basic keystroke.