''Herma'' (from Greek ἕρμα "a stringing together, a foundation") is a piece for solo

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

composed by

Iannis Xenakis Giannis Klearchou Xenakis (also spelled for professional purposes as Yannis or Iannis Xenakis; , ; 29 May 1922 – 4 February 2001) was a Romanian-born Greek-French avant-garde composer, music theorist, architect, performance director and enginee ...

in 1961. About ten minutes long, it is based on a formulation of the

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

equation In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for ...

s of

Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denot ...

, and is also an example of what Xenakis called symbolic music.

Composition

''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

Yūji Takahashi is a composer, pianist, critic, conductor, and author. Biography Yuji Takahashi 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 ''Quantitäten''. ...

. 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". Boolean algebra is the main mathematical principle behind ''Herma''. Xenakis defines several

pitch set A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collec ...

s and proceeds to apply various

logical operations In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the ...

to them. The results are incorporated into music by using successions and combinations of various sets.

Stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...

procedures are used to select the order and place of notes within each set. The piece has been described by the pianist and critic

Susan Bradshaw Susan Bradshaw (Monmouth, 8 September 1931 – London, 30 January 2005) was a British pianist, teacher, writer, and composer. She was mainly associated with contemporary music, and especially with the work of Pierre Boulez, several of whose writi ...

as " eservingthe label of the most difficult piano piece ever written", because of its extreme tempo.

References

Sources * * * *

'' 112:17–22. * Montague, Eugene. 1995. "The Limits of Logic: Structure and Aesthetics in Xenakis's ''Herma''". M.A. thesis. Amherst: University of Massachusetts Amherst
Study based on the thesis available online.
* Sevrette, Daniel. 1973. "Étude statistique sur Herma". Dissertation, Schola Cantorum. * Solomos, Makis. "À propos des premières œuvres (1953–69) de I. Xenakis". Thesis, University of Paris. * Squibbs, Ron. 1996. "An Analytical Approach to the Music of Iannis Xenakis". Dissertation. New Haven: Yale University. * Sward, Rosalie. 1981. "An Examination of the Mathematical Systems used in Selected Compositions of

Milton Babbitt Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He was a Pulitzer Prize and MacArthur Fellowship recipient, recognized for his serial and electronic music. Biography ...

and Iannis Xenakis". Dissertation. Evanston: Northwestern University. * Wannamaker, Robert. 2001
"Structure and Perception in Herma by Iannis Xenakis"
''

Music Theory Online The Society for Music Theory (SMT) is an American organization devoted to the promotion, development and engagement of music theory as a scholarly and pedagogical discipline. Founded in 1977 by a group of distinguished theorists, among them Alle ...

'' 7/3.

External links

* , Anton Gerzenberg, 2019 Festival of the

Accademia Musicale Chigiana The Accademia Musicale Chigiana (''English'': Chigiana Musical Academy) is a music institute in Siena, Italy. It was founded by Count Guido Chigi-Saracini in 1932 as an international centre for advanced musical studies. It organises Master Class ...

, Siena * , artin von der Heydt, 2009 {{Authority control Compositions by Iannis Xenakis Compositions for solo piano 1961 compositions Music dedicated to ensembles or performers

Composition

References

Further reading

External links