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

piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

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

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

equation In mathematics, an equation is a 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 example, in ...

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 variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in e ...

, 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''. H ...

. 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 collect ...

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. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary co ...

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

Stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...

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 is particularly noted for his Serialism, serial and electronic music. Biography Babbitt was born in Philadelphia t ...

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

Music Theory Online ''Music Theory Online'' is a quarterly peer-reviewed open access academic journal covering music theory and musical analysis, analysis. It was established in 1993 and is published by the Society for Music Theory. The initial issues were designat ...

'' 7/3.

External links

* , Anton Gerzenberg, 2019 Festival of the Accademia Musicale Chigiana, 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