Unspoken words for thought

Posts tagged ‘mathematics’


Ji Liu “DNA” Sonata for Solo Piano, 2012 HD- Awesome Find.

Description from YouTube:

Composer: Ji Liu
Piano: Ji Liu
Live from Wigmore Hall, Mar. 30th, 2012
This performance at Wigmore Hall was the World Première of this Piano Sonata.

Programme Note © Ji Liu 2012

“By the time I started the idea of writing this piece, I thought Sonata Form would be perfect for me to explore how the contrary elements can opposite and syncretize each other. Later, I was inspired by the philosophical ideas of “Yin Yang” from the ancient Chinese book “I Ching”, also known as the “Book of Changes”. It is one of the oldest of the Chinese classic texts and extant books of divination. Traditionally it was believed that the principles of the “I Ching” originated with the mythical Fu Xi. By the time of the legendary Yu 2194–2149 BC, the trigrams had supposedly been developed into 64 hexagrams, which were recorded in the scripture of Lián Shan (meaning “continuous mountains” in Chinese), which begins with the hexagram Bound (艮 gèn). This depicts a mountain mounting on another and is believed to be the origin of the scripture’s name. The text of the “I Ching” is a set of oracular statements represented by 64 sets of six lines each called hexagrams. Each hexagram is a figure composed of six stacked horizontal lines (爻yáo), each line is either Yang (an unbroken, or solid line), or Yin (broken, an open line with a gap in the center). With six such lines stacked from bottom to top there are 26 or 64 possible combinations, and thus 64 hexagrams represented. In Asian philosophy, the concept of “Yin Yang” is used to describe how polar opposites or seemingly contrary forces are interconnected and interdependent in the natural world, and how they give rise to each other in turn.

So within the Sonata Form, I thought by using the conflicts musical subjects, I could attempt to interpret the spirit of Yin Yang. From the title, the Sonata is designed on the structure of the DNA double helix which consists of two long polymers of simple units called nucleotides, with backbones made of sugars and phosphate groups joined by ester bonds. These two strands run in opposite directions to each other and are therefore anti-parallel. This interlaced structure reflects the Sonata not only structurally, but also harmonically and texturally. And this is the reason that other than the Classical Sonata structure of being 3 or 4 movements, I decided to renovate it to a single-movement Sonata which includes 3 parts. Here, apart from DNA’s original meaning of the Deoxyribonucleic acid, DNA also stands for D and A — and can be the name of the two notes, or the name of the two keys which create so-called a multi-tonality functioned system.

Mathematically, the Yin Yang plays an important role in the Sonata. Yin typifies the odd number, and Yang typifies the even number. So the Sonata has 2012 beats in total, the first part of the Sonata has 1236 beats (103 bars with a meter of 12/8) which represents Yin; the second part of the Sonata has 764 beats (72 bars with a meter of 9/8 and 14 bars with a meter of 7/8, in total 86 bars) which represents Yang; and the third part has 12 beats (1 bar with a meter of 12/8). Indeed, the first part plays a role as the exposition of the whole sonata, but itself is also established by the classical sonata form comprised by exposition, development, recapitulation and a small coda (1 bar). The Exposition is comprised by a rather chaotic and colossal first subject, a mysterious and yearning second subject and an ethereal codetta. The Development Section is quite straight forward with the conflicts between all the elements which we had before, here I use the one of Messiaen’s typical technique called “Agrandissements asymetriques”. This technique is basic on keeping some voice in the same tone level; some voices go upper and upper by semi-tones; and some voices go lower and lower by semi-tones. The sound of this passage does sound quite unsure and disorder. To me, It is like the planets in the universe moving with different route but in the same time, they are cooperated each other by a bigger society and force. The recapitulation uses quite the similar materials as the Exposition but leads a tremendous storm to the one-bar Coda which is also the starting point of the second part of the whole sonata. There is the Golden Section Ratio of the Sonata- the perfect proportion of the 0.618. This part is timeless, improvised and quite simple. After the echo like motive displays, the motive becomes more human voice. Then there is a passage of canon on the 17th interval. The third part of the Sonata is paralleled with the end of the second part using my creation of a composition technique called “Tempi Modulation”, which compressed the first part of the Sonata into one bar of 6/8 while the ending of the second part has 5 bars of 7/8; this third part also reflects all the materials which were displayed in the exposition. “

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