What Some Dead White Guy Did: A Statistical Topology
Of Keyboard Usage In Beethoven's Sonatas For Pianoforte

Four Possible Solutions

To play an instrument is to exhibit a human weakness for predictability. Just as the traumas of the family trickle in psychogenealogical rivets to create the pool of psychic pain of the present, so to we risk articulating the many pains of that gap-toothed behemoth, whose flat smile guides fingers in the lock-loops of other times. To play the piano without understanding the unique instrument/performer assemblage we create at the first moment of haptic contact is to re-articulate the trauma of the piano, to compulsively relive the hands of others. The normal curve found in the works of Beethoven, Scarlatti, Mozart and Schubert is one manifestation of the sins of the father.

What are offered below are not solutions to a problem but methodologies for distancing; that we might revisit that beginner's mind, and with that experience to return with the wisdom of absence to revisit our old, black-bodied friend and love him all the more. The techniques below may be useful for keyboard improvisers looking for a dexterous freshness or players of notation who wish their heart to grow fonder – and there are probably many other uses...

1. Re-mapping The Keyboard

One possible way of changing the relationship between the performer and instrument in ways which may prevent the re-articulation of habits accrued through pedagogy and the topology of the instrument is through reassigning the sounding notes of each key.

For this reason, a patch for pure data was created which randomizes the relationship between piano key and sounding result, by swapping notes around. This idea owes a debt to Johannes Kreidler's pioneering work in this field. The patch can be downloaded here.

Interface for keyboard re-mapper program.

Pd-still-screen

To use it, a MIDI keyboard should be run through through a computer running the pure data patch and the patch should output to a MIDI device that makes sound. In the patch, several options have been created for randomizing the keyboard.

There are two main options for randomization: one in which the pitch-classes are randomized, keeping notes one octave apart in the same pitch class; the other in which the entire keyboard is randomized irrespective of pitch classes.

The first option allows two further options – one in which all notes in a pitch class occur in an order running from low to high, and another in which they are randomized.

The second option allows for several degrees of randomization, ranging from extremely local-level two note randomizations, up to the entire keyboard being swapped around.

The patch also allows for the randomization of Type 0 MIDI files of piano music.

It is hoped that this tool will allow composers and performers to interact in a different way with the piano keyboard, by subverting the normal relations between hand and key position and sounding pitch.

2. Re-sizing The Keyboard

In one of the infographics shown at the top of the page, images of keyboards were created in which the size of each key was proportional to its usage in Beethoven's piano sonatas. A further continuation of this project will be the use of this technique to create playable, 3D printed models of piano keyboards. Transforming these diagrams into real piano keyboards could fundamentally warp the topology of the piano in such a way that, if a human were to interact with it, a lot of inbuilt pedagogic aspects and relationships between the sculptural placement of the hand on the key and sounding result would no longer be functional.

Although this project is in its early stages, it could be a useful pedagogical tool, a keyboard that could be frequently replaced could not only allow for the creation of special keyboards for the practising of physiological exercises, but its flexible surface could prevent the calcification of technique through pedagogy. These piano keyboards would be designed in such a way that they can be placed over the top of, or replace an existing piano keyboard, thus creating a new interface for interacting with the instrument. Below is a 3D model of the 2D infographic of the first sonata, shown in the diagrams above.

Fig. 13 Draft 3D Model of piano keys proportionally sized according to note usage in Beethoven's 1st Sonata.
Fig-13-keyboard

As can be seen from the analyses of other composers, it seems as if quite a lot of 17th and 18th century piano music tends towards the normal curve. A 3D printed keyboard provides a possible way of combating this by creating keyboards that compensate for this bias by increasing the size of certain keys and decreasing others in inverse relationship to their usage, thus flattening out the normal curve. Below is a diagram showing the differences between a conventional piano keyboard, our version of Beethoven's first sonata, and a keyboard which has an inverse weighting. This inversion allows for a new, more linear way of interacting with the keyboard that bypasses the built-in topological and pedagogic biases that cause key usage to approximate a normal distribution.

Comparison of keyboards created using sizes based on Beethoven's first sonata, an equally weighted piano keyboard, and the inverse data of Beethoven's first sonata.
Beeth-So-1

3. Combination

In the future it is hoped that the MIDI randomizer and the proportionally sized keyboard can be brought together to radically alter the piano's topology and allow composition and performance to move away from the normal distribution.

4. Composition

Some Analogue Heat Maps For Leo Svirsky

These pieces are arranged on the page in the order they were written.

If playing all of these pieces in the same concert, the order should be adjusted to

IV – II – III – I

to prevent any residues left over on the keys from the previous pieces affecting the colour changes.

An Analogue Heat Map For Leo Svirsky I

Attach one strip of litmus paper to every key on the piano.

Dip all of your fingers in lemon juice or another acidic liquid.

Improvise using only the keys of the piano.

If your fingers dry out whilst playing, re-dip them in the acidic liquid.

When the litmus paper on a note has changed colour that note cannot be played again.

The piece finishes when the litmus paper on every key has changed colour.

When you have finished wipe down the piano to prevent liquid-damage.

An Analogue Heat Map For Leo Svirsky II

Attach one strip of irreversible thermochromic paper to every key on the piano.

Improvise using only the keys of the piano.

Each note should be held down until the colour of the paper has changed.

When the thermochromic paper on a note has changed colour that note cannot be played again.

The piece finishes when the thermochromic paper on every key has changed colour.

When you have finished wipe down the piano to prevent liquid-damage.

An Analogue Heat Map For Leo Svirsky III

Attach one strip of irreversible hydrochromic paper to every key on the piano.

Dip all of your fingers in water.

Improvise using only the keys of the piano.

If your fingers dry out whilst playing, re-dip them in the water.

When the hydrochromic paper on a note has changed colour that note cannot be played again.

The piece finishes when the hydrochromic paper on every key has changed colour.

When you have finished wipe down the piano to prevent liquid-damage.

An Analogue Heat Map For Leo Svirsky IV

Cover every key on the piano with black fingerprinting powder.

Improvise using only the keys of the piano.

When your fingerprint appears on a key, that note cannot be played again.

The piece finishes when your fingerprint is on every key on the piano.

When you have finished wipe down the piano.


David Pocknee 29 May 2014

Reference List

Beethoven, L v., (1958) Sonatas For Piano Pianoforte Vol. I ed. Craxton, H. London: Associated Board

Beethoven, L v., (1958) Sonatas For Piano Pianoforte Vol. II ed. Craxton, H. London: Associated Board

Beethoven, L v., (1958) Sonatas For Piano Pianoforte Vol. III ed. Craxton, H. London: Associated Board

Bilson, M (1997), liner notes to The Complete Piano Sonatas On Period Instruments Thun, Switzerland

Coldicott, A. L. (1991) Piano Music The Beethoven Companion ed. Cooper, B., London: Thames & Hudson p. 239-248

Melville, D. (1971a) Beethoven's Pianos The Beethoven Companion London: Faber & Faber p. 41 – 67

Melville, D. (1971b) Beethoven's Piano The Musical Times Vol. 112, No. 1542 (August, 1971) p. 757

Melville, D. (1972) Beethoven's Pianos The Musical Times, Vol. 113, No. 1550 (April, 1972), p. 361-362

Newsome, W. S. (1970) Beetoven's Piano Versus His Piano Ideals Journal of the American Musicological Society, Vol 23, No. 3 (Autumn 1970) p. 484-504

Newman, W. S. (1971) Beethoven's Pianos The Musical Times, Vol. 112, No. 1546 (December 1971), p. 1171

Sadie, S. (1971) Angles on Beethoven The Musical Times Vol. 112, No. 1540 (June 1971), p. 554-557

Tovey, D. (1958) Preface in Beethoven, L v., (1958) Sonatas For Piano Pianoforte Vol. I ed. Craxton, H. London: Associated Board p. 5-8