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Editions 75
Tilework for Piano [free audio download] PDF Print E-mail
Music - Compact discs

For one interested in one-dimensional tiling, some mathematical curiosities can be found in most of these “seven pieces of tilework”, but Tilework for Piano has actually stimulated some serious research in mathematics, or at least in mathematical games. I pointed out in a 2003 article that the piece demonstrates the simplest tiling of a line with the different voices all playing three notes in different tempos. The tempos, from bass to treble, are 7 to 5 to 4 to 2 to 1, and this is the only solution with five voices. This observation was repeated in a long article about my music by Jean-Paul Delahaye (Pour la Science, May 2004) and people have been programming their computers ever since to find “perfect tilings” with more than five voices or more than four notes.

I am particularly pleased to have this recording of John McAlpine, because he has played much of my piano music over the years, and he understands it particularly well. He has performed this piece many times, but this early live concert interpretation, with its extreme dynamic contrasts, has a brashness that I appreciate as much as the refinements that came later. The recording was made by Peter Mohr at a concert of the Cologne Society for New Music in May 2004. 

Tom Johnson, Paris September 2010  

Tilework for Piano, played by John McAlpine 

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Counting Keys (released in 2009) PDF Print E-mail
Music - Compact discs

A new disc of Edition Wandelweiser Records with four pieces by Tom Johnson: Counting Keys, Organ and Silence for Piano, Tilework for Piano and Block Design for Piano. Played by John McAlpine.  Reference EWR 0901. 12€.

Liner notes by John McAlpine:

Counting Keys  Most composers who use mathematics to construct music do not intend it to be heard. Tom Johnson does. When he performed his piano cycle "Counting Keys" in Cologne in 1986 he began each piece by counting out its structure in numbers so that the audience could follow the logic of the music.

A particularly appreciative member of that audience was John Cage. One might wonder what the famous advocate of indeterminacy could find interesting in this exactly determined, highly predictable music, until one considers his favourite definition of art as the imitation of nature in her manner of operation. Much of what we see in nature, whether flowers, sea-shells, ice-crystals or patterns of growth and decay, is determined by mathematical processes.

The first piece in "Counting Keys" begins with a single high note. This is repeated followed by a 2-note cluster played twice, the whole being repeated followed by a 3-note cluster played three times, the process being repeated chromatically down the keyboard ending in the lowest register with a 12-note cluster played twelve times. The keys are literally counted. The effect is like an avalanche, beginning with a snowflake and ending in a pile of rubble at the foot of a mountain.

Over the years, the mathematics of Tom Johnson's music has become increasingly complex. "Organ and Silence", completed in 2000, is a cycle of 28 pieces for organ answering the challenge of composing music consisting more of silence than of sound. It is also a compendium of the compositional techniques he had developed up till then, from simple procedures like subtraction or permutation to the more sophisticated operations he refers to as automata and self-similar melodies. A consequence of the many long pauses it contains is the slowing down of the mathematical processes, making them much easier to hear. "Organ and Silence for Piano" is a reworking of eight of these pieces for piano made by the composer and myself in 2002.

"Tilework for Piano" is one of a series of pieces for solo instruments utilising the mathematics of arranging tiles in a single line along a wall to produce interlocking repeated patterns. In musical terms, if each tile is a note, motive or, as in "Tilework for Piano", chord, this means creating counterpoint with one voice. Imagine a row of 15 coloured tiles without gaps. There are 5 different colours; 3 of each. The same-coloured tiles are arranged in 5 equally-spaced interlocking triplets, each triplet having a different spacing. There is only one way to do this and this provides the basic structure of "Tilework for Piano". The triplets are first presented singly. Then every combination of 2 triplets is presented twice, every combination of 3 triplets  three times and so on, until finally all 5 triplets together are presented five times.

The mathematical term "block design" comes from combination theory and refers to the distribution of a fixed number of elements into blocks of a fixed size according to specific combinatory preconditions. In "Block Design for Piano" the blocks are a sequence of 330 different ascending 6-note arpeggios. Their notes are taken from a fixed 12-note chord in such a way that every combination of four particular notes occurs 10 times in 10 different arpeggios. The 330 arpeggios are presented in 30 groups of eleven. Unlike most of Tom Johnson's compositions, the mathematical logic is not easily discernable. In an introductory text he sent me shortly after completing the piece, he commented on the difficulty of predicting the course of the music and wrote: "As I listen, I can imagine that I am hearing something derived from nature." Indeed, like the waves washing up on a beach, no two them identical yet all following the same unfathomable laws, this music has the inevitability and timelessness of the processes of nature.
 
Tom Johnson has written extensively about his compositional techniques. His writings can be found at Editions75.com.

John McAlpine

 

 

 
FREE CD "Seven Pieces of Tilework" PDF Print E-mail
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When I prepared the Seven Pieces of Tilework  with the sound engineer Daniel Deshays, we thought it would be a CD, but now that the CD market has all but disappeared, it seems best just to place this music on the web site, where it can be heard by everyone without payment. In classical music, composers and performers never earned very much money from record sales anyway. The records were made mostly just to promote the ideas, and to stimulate the real profits generated by real musical experiences – live performances, and this continues to be the case. Our hope is that some performers will want to order the scores, that some broadcasters and concert producers will want to present them, and most of all, that listeners of all types will learn to appreciate music constructed as “tilework.” 

“Tilework” has to do with fitting together little tiles so as to fill lines and loops. One can think of this as making mosaics in one dimension, but it is also very much like stringing beads onto necklaces in various patterns. In musical terms, the Tilework series is a collection of compositions in which individual rhythms fit together into musical sequences without simultaneities, so that a single melodic instrument can play two or more voices at once. I gradually found so many ways of doing this that I ended up with a piece for each instrument of the orchestra. The year of 2002 was devoted almost exclusively to such pieces, published early in 2003. I am still waiting to hear good performances of Tilework for Oboe, Tilework for Horn, Tilework for Trumpet and some of the others, but by now excellent interpreters have made excellent recordings, and they all benefit by coming together.

Tom Johnson, Paris September 2010  


Tilework for Flute, played by Michael Schmid  

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Tilework for Clarinet, played by Cristo Barrios 

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Tilework for Saxophone, played by Laurent Estoppey 

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Tilework for Tuba, played by Arnaud Boukhitine 

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Tilework for Percussion, played by Adam Weisman 

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Tilework for Piano, played by John McAlpine 

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Tilework for Double Bass, played by Jean-Daniel Hégé 

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More content and download links will be added very soon.

 

 
NEW: Tilework for Oboe [free audio download] PDF Print E-mail
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Tilework for Oboe is subtitled “Three Crossings.” In each movement some music starts at the left side of the staff, some other music starts at the right side of the staff, and with each successive staff they advance toward one another and eventually cross through one another. Quite a few oboists have tried this score, but I think Marika Lombardi is the first one who can play it without mistakes. I was delighted when she said she would record it in a studio, along with some baroque repertoire, which she also plays very well. 

Tom Johnson, Paris, Februrary 2012  

Listen to Tilework for Oboe, played by Marika Lombardi 

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Listen also to 7 more pieces of the Tilework series.

 

 
Tilework for Double Bass [free audio download] PDF Print E-mail
Music - Compact discs

Having played my solo Failing quite a few times, Jean-Daniel Hégé wanted to work also on Tilework for Double Bass, but like other bass players, he found that knowing the first piece didn’t help at all in learning the second, and he couldn’t figure out how to interpret the tak-tak percussive element. I assumed that this would be played by tapping the bow on the bridge somehow, but this proved to be an unsatisfying solution for him. In discussing this problem, Hégé remembered that ever since childhood he knows how to make a loud click with his tongue, a sound I immediately loved, and that no one but Hégé will ever really be able to do. This problem solved, we made this recording on November 28, 2008, again with Daniel Deshays. 

Tom Johnson, Paris September 2010  

Listen to Tilework for Double Bass, played by Jean-Daniel Hégé 

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