Herma (Xenakis)
Encyclopedia
Herma is a piece for solo piano
composed by Iannis Xenakis
in 1961. It is based on a formulation of the algebra
ic equation
s of Boolean algebra, and is also an example of what Xenakis called symbolic music.
Herma was the composer's first major work for piano. It was composed after a visit to Japan
in 1961, where Xenakis befriended pianist and composer Yuji Takahashi
. Xenakis completed the piece upon his return to Paris
and dedicated it to Takahashi, who premièred the piece on February 2, 1962. The pianist's impression of that concert was that the piece "made some excited and wonder, others feel painful" (Harley 2004, 26).
Boolean algebra is the main mathematical principle behind Herma (Chung 2003, 33). Xenakis defines several pitch sets and proceeds to apply various logical operations to them. The results are incorporated into music by using successions and combinations of various sets. Stochastic procedures are used to select the order and place of notes within each set (Harley 2004, 27).
The piece has been described by the pianist and critic Susan Bradshaw
as "[deserving] the label of the most difficult piano piece ever written", because of its extreme tempo.
Piano
The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...
composed by Iannis Xenakis
Iannis Xenakis
Iannis Xenakis was a Romanian-born Greek ethnic, naturalized French composer, music theorist, and architect-engineer. He is commonly recognized as one of the most important post-war avant-garde composers...
in 1961. It is based on a formulation of the algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
ic equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
s of Boolean algebra, and is also an example of what Xenakis called symbolic music.
Herma was the composer's first major work for piano. It was composed after a visit to Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
in 1961, where Xenakis befriended pianist and composer Yuji Takahashi
Yuji Takahashi
is a Japanese composer, performer, pianist and author.Studied under Roh Ogura and Minao Shibata at the Toho Gakuen School of Music. In 1960, he made his debut as a pianist by performing Bo Nilsson's Quantitaten. He lived in Europe from 1963 to 1966 where he worked with Iannis Xenakis. He gave the...
. Xenakis completed the piece upon his return to Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
and dedicated it to Takahashi, who premièred the piece on February 2, 1962. The pianist's impression of that concert was that the piece "made some excited and wonder, others feel painful" (Harley 2004, 26).
Boolean algebra is the main mathematical principle behind Herma (Chung 2003, 33). Xenakis defines several pitch sets and proceeds to apply various logical operations to them. The results are incorporated into music by using successions and combinations of various sets. Stochastic procedures are used to select the order and place of notes within each set (Harley 2004, 27).
The piece has been described by the pianist and critic Susan Bradshaw
Susan Bradshaw
Susan Bradshaw was a British pianist, teacher and writer. She was mainly associated with contemporary music, and especially with the work of Pierre Boulez, several of whose writings she translated...
as "[deserving] the label of the most difficult piano piece ever written", because of its extreme tempo.
Further reading
- Chung, Immin. 2003. Mathematical and Architectural Concepts Manifested in Iannis Xenakis's Piano Music, dissertation, University of Texas.
- Harley, James. 2004. Xenakis: His Life in Music, Routledge. ISBN 0415971454
- Hill, Peter. 1975. Xenakis and the Performer, Tempo 112 (1975), 17–22.
- Montague, Eugene. 1995. The Limits of Logic: Structure and Aesthetics in Xenakis's "Herma", M.A. thesis, University of Massachusetts. Study based on the thesis available online.
- Sevrette, Daniel. 1973. Étude statistique sur Herma. Dissertation, Schola Cantorum.
- Solomos, Makis. A propos des premières oeuvres (1953–69) de I. Xenakis. Thesis, University of Paris.
- Squibbs, Ron. 1996. An Analytical Approach to the Music of Iannis Xenakis. Dissertation, Yale University. Available online.
- Sward, Rosalie. 1981. An Examination of the Mathematical Systems used in Selected Compositions of Milton Babbitt and Iannis Xenakis. Dissertation, Northwestern University.
- Wannamaker, Robert. 2001. Structure and Perception in Herma by Iannis Xenakis. Music Theory Online, 7/3. (Available online.)