Herma (from Greek ἕρμα "a stringing together, a foundation") is a piece for solo piano composed by Iannis Xenakis in 1961. It is based on a formulation of the algebraic equations 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 (Matthews 1972,[page needed]).
- Chung, Immin. 2003. "Mathematical and Architectural Concepts Manifested in Iannis Xenakis's Piano Music".[full citation needed] dissertation. Austin: University of Texas.
- Harley, James. 2004. Xenakis: His Life in Music. New York: Routledge. ISBN 0-415-97145-4.
- Hill, Peter. 1975. "Xenakis and the Performer". Tempo 112:17–22.
- Matthews, Denis (editor). 1972. Keyboard music.[full citation needed]: Penguin Books. ISBN 0-14-021250-7.
- Montague, Eugene. 1995. "The Limits of Logic: Structure and Aesthetics in Xenakis's Herma". M.A. thesis.[full citation needed] University of Massachusetts. Study based on the thesis available online.
- Sevrette, Daniel. 1973. "Étude statistique sur Herma".[full citation needed]Dissertation, Schola Cantorum. (French)
- Solomos, Makis. A propos des premières oeuvres (1953–69) de I. Xenakis.[full citation needed]Thesis, University of Paris. (French)
- Squibbs, Ron. 1996. "An Analytical Approach to the Music of Iannis Xenakis".[full citation needed]Dissertation. New Haven: Yale University. Available online.[dead link]
- Sward, Rosalie. 1981. "An Examination of the Mathematical Systems used in Selected Compositions of Milton Babbitt and Iannis Xenakis".[full citation needed]Dissertation. Evanston: Northwestern University.
- Wannamaker, Robert. 2001. "Structure and Perception in Herma by Iannis Xenakis". Music Theory Online 7/3. (Available online.)