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Paul Hindemith
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Paul Hindemith (/ˈpaʊl ˈhɪndəmɪt/ POWL HIN-də-mit; German: [ˌpaʊ̯l ˈhɪndəmɪt] ⓘ; 16 November 1895 – 28 December 1963) was a German and American composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advocate of the Neue Sachlichkeit (New Objectivity) style of music in the 1920s, with compositions such as Kammermusik, including works with viola and viola d'amore as solo instruments in a neo-Bachian spirit. Other notable compositions include his song cycle Das Marienleben (1923), his oratorio Das Unaufhörliche (1931),[1] Der Schwanendreher for viola and orchestra (1935), the opera Mathis der Maler (1938) and the symphony Mathis der Maler (1934), the Symphonic Metamorphosis of Themes by Carl Maria von Weber (1943), and the oratorio When Lilacs Last in the Dooryard Bloom'd (1946), a requiem based on Walt Whitman's poem. Hindemith and his wife emigrated to Switzerland and the United States ahead of World War II, after worsening difficulties with the Nazi German regime. In his later years, he conducted and recorded much of his own music.
Key Information
Most of Hindemith's compositions are anchored by a foundational tone, and use musical forms and counterpoint and cadences typical of the Baroque and Classical traditions. His harmonic language is more modern, freely using all 12 notes of the chromatic scale within his tonal framework, as detailed in his three-volume treatise, The Craft of Musical Composition.
Life and career
[edit]Paul Hindemith was born in Hanau, near Frankfurt, the eldest child of the painter and decorator Robert Hindemith from Lower Silesia and his wife Marie (née Warnecke).[2] He was taught the violin as a child. He entered Frankfurt's Dr. Hoch's Konservatorium, where he studied violin with Adolf Rebner, as well as conducting and composition with Arnold Mendelssohn and Bernhard Sekles. At first he supported himself by playing in dance bands and musical-comedy groups. He became deputy leader of the Frankfurt Opera Orchestra in 1914 and was promoted to concertmaster in 1916.[3] He played second violin in the Rebner String Quartet from 1914.
After his father's 1915 death in World War I, Hindemith was conscripted into the Imperial German Army in September 1917 and sent to a regiment in Alsace in January 1918.[4] There he was assigned to play bass drum in the regiment band, and also formed a string quartet. In May 1918 he was deployed to the front in Flanders, where he served as a sentry; his diary has him "surviving grenade attacks only by good luck", according to New Grove Dictionary.[4] After the armistice he returned to Frankfurt and the Rebner Quartet.[4]
In 1921, Hindemith founded the Amar Quartet, playing viola, and extensively toured Europe with an emphasis on contemporary music. His younger brother Rudolf was the original cellist.[5]
As a composer, he became a major advocate of the Neue Sachlichkeit (New Objectivity) style of music in the 1920s, with compositions such as Kammermusik. Reminiscent of Bach's Brandenburg Concertos, they include works with viola and viola d'amore as solo instruments in a neo-Bachian spirit.[6] In 1922, some of his pieces were played in the International Society for Contemporary Music festival at Salzburg, which first brought him to the attention of an international audience. The next year, he composed the song cycle Das Marienleben (The Life of Mary) and began to work as an organizer of the Donaueschingen Festival, where he programmed works by several avant-garde composers, including Anton Webern and Arnold Schoenberg. In 1927 he was appointed Professor at the Berliner Hochschule für Musik in Berlin.[7] Hindemith wrote the music for Hans Richter's 1928 avant-garde film Ghosts Before Breakfast (Vormittagsspuk) and also acted in the film; the score and original film were later burned by the Nazis.[8] In 1929, Hindemith played the solo part in the premiere of William Walton's viola concerto, after Lionel Tertis, for whom it was written, turned it down.
On 15 May 1924, Hindemith married the actress and singer Gertrud (Johanna Gertrude) Rottenberg (1900–1967).[2] The marriage was childless.[9]
The Nazis' relationship to Hindemith's music was complicated. Some condemned his music as "degenerate" (largely based on his early, sexually charged operas such as Sancta Susanna). In December 1934, during a speech at the Berlin Sports Palace, Germany's Minister of Propaganda Joseph Goebbels publicly denounced Hindemith as an "atonal noisemaker".[10] The Nazis banned his music in October 1936, and he was subsequently included in the 1938 Entartete Musik (Degenerate Music) exhibition in Düsseldorf.[11] Other officials working in Nazi Germany, though, thought that he might provide Germany with an example of a modern German composer, as, by this time, he was writing music based in tonality, with frequent references to folk music. The conductor Wilhelm Furtwängler's defence of Hindemith, published in 1934, takes this line.[12] The controversy around his work continued throughout the thirties, with Hindemith falling in and out of favour with the Nazis.
During the 1930s, Hindemith visited Cairo and also Ankara several times. He accepted an invitation from the Turkish government to oversee the creation of a music school in Ankara in 1935, after Goebbels had pressured him to request an indefinite leave of absence from the Berlin Academy.[11] In Turkey, he was the leading figure of a new music pedagogy in the era of president Kemal Atatürk. His deputy was Eduard Zuckmayer. Hindemith led the reorganization of Turkish music education and the early efforts to establish the Turkish State Opera and Ballet. He did not stay in Turkey as long as many other émigrés, but he greatly influenced Turkish musical life; the Ankara State Conservatory owes much to his efforts. Young Turkish musicians regarded Hindemith as a "real master", and he was appreciated and greatly respected.[10]

Toward the end of the 1930s, Hindemith made several tours of America as a viola and viola d'amore soloist.
He emigrated to Switzerland in 1938, partly because his wife was of part-Jewish ancestry; "it was primarily Hindemith's conflict with the artistic policies of the Third Reich, however, that determined his decision to leave."[13]
At the same time that he was codifying his musical language, Hindemith's teaching and compositions began to be affected by his theories, according to critics such as Ernest Ansermet.[14] Arriving in the U.S. in 1940, he taught primarily at Yale University,[15] where he founded the Yale Collegium Musicum.[6] At Yale, he required his students to study composition and theory from his pedagogical work, The Craft of Musical Composition, among other educational texts. Because of his commitments outside the university, the number of composers who studied under Hindemith was small. According to Luther Noss's A History of the Yale School of Music 1855–1970, Hindemith taught for a little over ten years, teaching 400 students, of whom 46 earned degrees, mostly in music theory.[16] He had such notable students as Lukas Foss, Graham George, Andrew Hill, Norman Dello Joio, Mel Powell, Yehudi Wyner, Harold Shapero, Hans Otte, Ruth Schönthal, Samuel Adler, Leonard Sarason, Fenno Heath, Mitch Leigh, and George Roy Hill. Hindemith also taught at the University at Buffalo, Cornell University, and Wells College.[17] During this time he gave the Charles Eliot Norton Lectures at Harvard, from which the book A Composer's World (1952) was extracted.[18] Hindemith had a long friendship with Erich Katz, whose compositions were influenced by him.[19] Also among Hindemith's students were the future rocket scientist Wernher von Braun[20] and the composers Franz Reizenstein, Harald Genzmer, Oskar Sala, Arnold Cooke,[21] Robert Strassburg,[22] and dozens of other notables.

Hindemith became a U.S. citizen in 1946, but returned to Europe in 1953, living in Zürich and teaching at the university there until he retired from teaching in 1957.[6][11] Toward the end of his life he began to conduct more and made numerous recordings, mostly of his own music.[11]
In 1954, an anonymous critic for Opera magazine, having attended a performance of Hindemith's Neues vom Tage, wrote: "Mr Hindemith is no virtuoso conductor, but he does possess an extraordinary knack of making performers understand how his own music is supposed to go."[23]
Hindemith received the Wihuri Sibelius Prize in 1955.[24] He was awarded the Balzan Prize in 1962 "for the wealth, extent and variety of his work, which is among the most valid in contemporary music, and which contains masterpieces of opera, symphonic and chamber music."[24][25]
Despite a prolonged decline in his physical health, Hindemith composed almost until his death. He died in Frankfurt from pancreatitis, aged 68. He and his wife were buried in the cemetery in La Chiésaz, Vaud, Switzerland.[2]
Music
[edit]Hindemith is among the most significant German composers of his time. His early works are in a late romantic idiom, and he later produced expressionist works, rather in the style of the early Schoenberg, before developing a leaner, contrapuntally complex style in the 1920s. This style has been described as neoclassical,[26] but is quite different from the works by Igor Stravinsky labeled with that term, owing more to the contrapuntal language of Johann Sebastian Bach and Max Reger than the Classical clarity of Mozart.[citation needed]
The new style can be heard in the series of works called Kammermusik (Chamber Music) from 1922 to 1927. Each of these pieces is written for a different small instrumental ensemble, many of them very unusual. Kammermusik No. 6, for example, is a concerto for the viola d'amore, an instrument that has not been in wide use since the baroque period, but which Hindemith himself played. He continued to write for unusual groups of instruments throughout his life, producing (for example) a trio for viola, heckelphone and piano (1928), seven trios for three trautoniums (1930), a sonata for double bass, and a concerto for trumpet, bassoon, and strings (both in 1949).
In the 1930s Hindemith began to write less for chamber music groups, and more for large orchestral forces. He wrote his opera Mathis der Maler, based on the life of the painter Matthias Grünewald, in 1933–1935. This opera is rarely staged, though a well-known production by the New York City Opera in 1995 was an exception.[27] In 2021, Naxos released a 2012 Theater an der Wien production on DVD.[28] The opera combines the neoclassicism of Hindemith's earlier works with folk song. As a preliminary stage of composing the opera, Hindemith wrote a purely instrumental symphony also called Mathis der Maler, which is one of his most frequently performed works. In the opera, some portions of the symphony appear as instrumental interludes; others are elaborated in vocal scenes.
Hindemith wrote Gebrauchsmusik (Music for Use)—compositions intended to have a social or political purpose and sometimes written to be played by amateurs. The concept was inspired by Bertolt Brecht. An example of this is Hindemith's Trauermusik (Funeral Music), written in January 1936. He was preparing the London premiere of his viola concerto Der Schwanendreher when he heard news of the death of George V. He quickly wrote Trauermusik for solo viola and string orchestra in tribute to the late king, and the premiere was given that same evening, the day after the king's death.[29] Other examples of Hindemith's Gebrauchsmusik include:
- the Plöner Musiktage (1932), a series of pieces written for a day of community music-making in the city of Plön, culminating in an evening concert by grammar-school students and teachers.
- a Scherzo for viola and cello (1934), written in several hours during a series of recording sessions as a "filler" for an unexpected blank side of a 78 rpm album, and recorded immediately upon its completion.
- Wir bauen eine Stadt ("We're Building a City"), an opera for eight-year-olds (1930).
Hindemith's most popular work, both on record and in the concert hall, is probably the Symphonic Metamorphosis of Themes by Carl Maria von Weber, written in 1943. It takes melodies from various works by Carl Maria von Weber, mainly piano duets, but also one from the overture to his incidental music for Turandot (Op. 37/J. 75), and transforms and adapts them so that each movement of the piece is based on one theme.
In 1951, Hindemith completed his Symphony in B-flat. Scored for concert band, it was written for the U.S. Army Band "Pershing's Own". Hindemith premiered it with that band on 5 April of that year.[30] Its second performance took place under the baton of Hugh McMillan, conducting the Boulder Symphonic Band at the University of Colorado. The piece is representative of Hindemith's late works, exhibiting strong contrapuntal lines throughout, and is a cornerstone of the band repertoire. He recorded it in stereo with members of the Philharmonia Orchestra for EMI in 1956.
Musical system
[edit]
Most of Hindemith's music employs a unique system that is tonal but non-diatonic, often notated without a traditional key signature. Like most tonal music, it is centred on a tonic and modulates from one tonal centre to another, but it "attempts ... the free use of all the twelve tones of the chromatic scale",[31] rather than relying on a diatonic scale as a restricted subset of these notes. He even rewrote some of his music after developing this system. One of the core features of Hindemith's system is a ranking of all musical intervals of the 12-tone equally tempered scale, from the most consonant to the most dissonant. He classifies chords in six categories, on the basis of dissonance, whether they contain a tritone, and whether they clearly suggest a root or tonal centre. His philosophy also encompassed melody—he strove for melodies that do not clearly outline major or minor triads.[32]
In the late 1930s Hindemith wrote an instructional treatise in three volumes, The Craft of Musical Composition, which lays out this system in great detail. He also advocated this system as a means of understanding and analyzing the harmonic structure of other music, claiming that it has a broader reach than the traditional Roman numeral approach to chords (an approach strongly tied to diatonic scales). In the final chapter of Book 1, Hindemith seeks to illustrate the wide-ranging relevance and applicability of his system, analyzing musical examples from the medieval to the contemporary. These analyses include the early Gregorian melody Dies irae, compositions by Guillaume de Machaut, J. S. Bach, Richard Wagner, Igor Stravinsky, Arnold Schoenberg, and a composition of his own.[33]
Hindemith's 1942 piano work Ludus Tonalis contains twelve fugues, in the manner of Johann Sebastian Bach, using traditional devices like inversion, diminution, augmentation, retrogradation, stretto, etc. Each fugue is connected by an interlude to the next, during which the music moves from the key of the last to its successor. The order of the keys follows Hindemith's ranking of musical intervals around the tonal center of C.[34]
Another traditional aspect of classical music that Hindemith retains is the idea of dissonance resolving to consonance. Much of Hindemith's music begins in consonant territory, progresses into dissonant tension, and resolves in full, consonant chords and cadences.[35] This is especially apparent in his Concert Music for Strings and Brass (1930).
Awards and honors
[edit]

- Howland Memorial Prize (1940), awarded by Yale University[2][36]
- Elected to American Academy of Arts and Sciences (1940)[37]
- Bach Prize of the Free and Hanseatic City of Hamburg (1951)[2][38]
- Order Pour le Mérite (1952)[38][39]
- Wihuri Sibelius Prize (1955)[2][38]
- Goethe Plaque of the City of Frankfurt (1955)[40]
- Elected to the American Philosophical Society (1962)[41]
- Balzan Prize (1963)[2][38]
- 5157 Hindemith (1973), asteroid discovered and named for him[42]
Honorary doctorates
[edit]- Philadelphia Academy of Music (1945)[36]
- Columbia University (1948)[36]
- Goethe University Frankfurt (1949)[2][38]
- FU Berlin (1950)[2][38]
- Oxford University (1954)[2][38]
Compositions
[edit]Pedagogical writings
[edit]Hindemith's complete set of instructional books, in possible educational order:
- Elementary Training for Musicians. London: Schott; New York: Associated Music Publishers, 1946. ISBN 978-0-901938-16-9
- A Concentrated Course in Traditional Harmony
- Book 1: With Emphasis on Exercises and a Minimum of Rules, revised edition. New York: Schott, 1968. ISBN 978-0-901938-42-8
- Book 2: Exercises for Advanced Students, translated by Arthur Mendel. New York: Schott, 1964. ISBN 978-0-901938-43-5
- Book 1: Theoretical Part, translated by Arthur Mendel. London: Schott; New York: Associated Music Publishers, 1942. ISBN 978-0-901938-30-5
- Book 2: Exercises in Two-Part Writing, translated by Otto Ortmann. London: Schott; New York: Associated Music Publishers, 1941. ISBN 978-0-901938-41-1
- Book 3: Exercises in Three-Part Writing, translated by John Colman. London: Schott; New York: Associated Music Publishers, 2024. ISBN 978-3-7957-1605-9
Notable students
[edit]Recordings
[edit]Hindemith was a prolific composer.[43] He conducted some of his own music in a series of recordings for EMI with the Philharmonia Orchestra and for Deutsche Grammophon with the Berlin Philharmonic Orchestra, which have been digitally remastered and released on CD.[44][45] The Violin Concerto was also recorded by Decca/London, with the composer conducting the London Symphony Orchestra and David Oistrakh as soloist. Everest Records issued a recording of Hindemith's postwar When Lilacs Last in the Dooryard Bloom'd ("A Requiem for Those We Love") on LP, conducted by Hindemith. A stereo recording of Hindemith conducting the requiem with the New York Philharmonic Orchestra, with Louise Parker and George London as soloists, was made for Columbia Records in 1963 and later issued on CD. He also appeared on television as a guest conductor of the Chicago Symphony Orchestra's nationally syndicated "Music from Chicago" series; the performances have been released by VAI on home video. A complete collection of Hindemith's orchestral music was recorded by German and Australian orchestras, all conducted by Werner Andreas Albert and released on the CPO label.
Hindemithon Festival
[edit]An annual festival of Hindemith's music has been held at William Paterson University in Wayne, New Jersey, from 2003 through at least 2017. It features student, staff, and professional musicians performing a range of Hindemith's works.[46]
See also
[edit]References
[edit]Notes
[edit]- ^ "Hindemith (Das) Unaufhörliche" Gramaphone
- ^ a b c d e f g h i j Maurer Zenck, Claudia (2018). "Paul Hindemith". In Maurer Zenck, Claudia; Petersen, Peter; Fetthauer, Sophie (eds.). Lexikon verfolgter Musiker und Musikerinnen der NS-Zeit. Hamburg: Universität Hamburg. Retrieved 8 August 2020.
- ^ Mootz, William (19 February 1950). "Hindemith To Conduct Sinfonietta Here Next Week". The Courier-Journal. Louisville, KY. p. 69. Retrieved 24 May 2020 – via Newspapers.com.
- ^ a b c Schubert, Giselher (2001). "Hindemith, Paul". Grove Music Online. Oxford: Oxford University Press. doi:10.1093/gmo/9781561592630.article.13053. ISBN 978-1-56159-263-0. (subscription, Wikilibrary access, or UK public library membership required)
- ^ Potter, Tully (2003). Hindemith as Interpreter: The Amar-Hindemith Quartet (Liner notes). Arbiter Records. 139. Retrieved 7 April 2023.
- ^ a b c "Paul Hindemith — People — Royal Opera House". www.roh.org.uk. Retrieved 22 August 2018.
- ^ A Dictionary of Twentieth Century World Biography. United Kingdom: Book Club Associates, 1992, p. 267.
- ^ Wilke, Tobias (2010). Medien der Unmittelbarkeit (in German). Munich: Wilhelm Fink. p. 63. ISBN 978-3-7705-4923-8.
- ^ "Marriage: Paul Hindemith". www.hindemith.info.
- ^ a b Reisman, Arnold, ed. (2006). "Chapter 5: The Creators". Turkey's Modernization: Refugees from Nazism and Atatürk's Vision. New Academia Publishing. pp. 88–90. ISBN 978-0-9777908-8-3. Retrieved 5 April 2023.
- ^ a b c d "Music and the Holocaust: Paul Hindemith". holocaustmusic.ort.org. ORT. Retrieved 22 August 2018.
- ^ Furtwängler 1934.
- ^ Steinberg, Michael (1998). The Concerto: A Listener's Guide. Oxford University Press. p. 205. ISBN 978-0-19-802634-1. Retrieved 23 March 2013.
- ^ Ansermet 1961, note to p. 42 added on an errata slip.
- ^ "Yale Plans to honor Composer Paul Hindemith". The Bridgeport Post. Bridgeport, CT. 25 October 1964. p. 46. Retrieved 24 May 2020 – via Newspapers.com.
- ^ Forte, Allen; Hindemith, Paul (21 January 1998). "Paul Hindemith's Contribution to Music Theory in the United States". Journal of Music Theory. 42 (1): 6. JSTOR 843851.
- ^ "Courses as an Instructor: Paul Hindemith". www.hindemith.info.
- ^ Hindemith, Paul (1952). A Composer's World: Horizons and Limitations. Cambridge: Harvard University Press.
- ^ Davenport 1970, p. 43.
- ^ Ward, Bob (2005). Dr. Space: The Life of Wernher von Braun. Naval Institute Press. p. 11. ISBN 978-1-591-14926-2.
- ^ Lessing, Kolja (2002). Notes to Franz Reizenstein: Solo Sonatas. EDA Records.
- ^ Pfitzinger, Scott (2017). Composer Genealogies: A Compendium of Composers, Their Teachers, and Their Students. Rowman & Littlefield. p. 522. ISBN 978-1-4422-7225-5 – via Google Books.
- ^ Opera (June 1954): 348.
- ^ a b "Paul Hindemith, modern music pioneer, succumbs at age 68". Intelligencer Journal. Lancaster, Pennsylvania. 30 December 1963. p. 9. Retrieved 24 May 2020 – via Newspapers.com.
- ^ "Paul Hindemith: 1962 Balzan Prize for Music". Retrieved 22 August 2018.
- ^ Taylor 1997, p. 261.
- ^ Holland 1995.
- ^ Naxos
- ^ Steinberg, Michael (1998). The Concerto: A Listener's Guide. Oxford University Press. p. 212. ISBN 978-0-19-802634-1. Retrieved 23 March 2013.
- ^ "Biography". Hindemith Foundation. Archived from the original on 13 April 2001.
- ^ Searle, Humphrey (1955). Twentieth Century Counterpoint (2nd ed.). London: Ernest Benn. p. 55.
- ^ "Principles and Categories". www.hindemith.info. Hindemith Foundation. Retrieved 30 March 2023.
- ^ Hindemith, Paul. Unterweisung im Tonsatz. 3 vols. Mainz: B. Schott's Söhne, 1937–1970. First two volumes in English, as The Craft of Musical Composition, translated by Arthur Mendel and Otto Ortmann. New York: Associated Music Publishers; London: Schott & Co., 1941–1942.
- ^ Tippett, Michael (1995). Tippett on Music, p.77. Oxford University. ISBN 9780198165422.
- ^ Kemp, Ian (1970). Hindemith. Oxford Studies of Composers 6. London: Oxford University Press. p. 19. ISBN 0193141183.
- ^ a b c "Influence in America". www.hindemith.info.
- ^ "Paul Hindemith". American Academy of Arts & Sciences. Retrieved 16 November 2022.
- ^ a b c d e f g "Schott Music". en.schott-music.com.
- ^ "Pour le Mérite: Paul Hindemith" (PDF). www.orden-pourlemerite.de. Archived from the original (PDF) on 19 July 2021. Retrieved 7 August 2020.
- ^ "Hessian Biography". www.lagis-hessen.de.
- ^ "APS Member History". American Philosophical Society. Retrieved 30 March 2023.
- ^ "(5157) Hindemith". IAU Minor Planet Center. Retrieved 5 April 2023.
- ^ Allison, John (4 December 2013). "Paul Hindemith: The 20th century's most neglected composer". The Telegraph. Archived from the original on 12 January 2022.
- ^ "Review: Hindemith Conducts Hindemith". Gramophone: 40. 20 April 1987.
- ^ "Hindemith Conducts Hindemith: The Complete Recordings on Deutsche Grammophon". Amazon. Retrieved 7 October 2012.
- ^ "Midday Artists Series". William Paterson University. Spring 2017. Retrieved 1 April 2023.
Sources
[edit]- Ansermet, Ernest. 1961. Les fondements de la musique dans la conscience humaine. 2 v. Neuchâtel: La Baconnière.
- Briner, Andres. 1971. Paul Hindemith. Zürich: Atlantis-Verlag; Mainz: Schott.
- Davenport, LaNoue. 1970. "Erich Katz: A Profile". The American Recorder (Spring): 43–44. Retrieved 2 November 2011.
- Eaglefield-Hull, Arthur (ed.). 1924. A Dictionary of Modern Music and Musicians. London: Dent.
- Furtwängler, Wilhelm. 1934. "Der Fall Hindemith". Deutsche Allgemeine Zeitung 73, no. 551 (Sunday, 25 November): 1. Reprinted in Berta Geissmar, Musik im Schatten der Politik. Zürich: Atlantis, 1945. Reprinted in Wilhelm Furtwängler, Ton und Wort: Aufsätze und Vorträge 1918 bis 1954, 91–96. Wiesbaden: F.A. Brockhaus, 1954; reissued Zürich: Atlantis Musikbuch-Verlag, 1994. ISBN 978-3-254-00199-3. English version as "The Hindemith Case", in Wilhelm Furtwängler, Furtwängler on Music, edited and translated by Ronald Taylor, 117–20. Aldershot, Hants.: Scolar Press, 1991. ISBN 978-0-85967-816-2.
- Hindemith, Paul. 1937–1970. Unterweisung im Tonsatz. 3 vols. Mainz: B. Schott's Söhne. First two volumes in English, as The Craft of Musical Composition, translated by Arthur Mendel and Otto Ortmann. New York: Associated Music Publishers; London: Schott & Co., 1941–1942.
- Hindemith, Paul. 1952. A Composer's World: Horizons and Limitations. Cambridge: Harvard University Press.
- Holland, Bernard. 1995. "Music Review; City Opera Gamely Flirts with Danger". The New York Times, 9 September.
- Kater, Michael H. 1997. The Twisted Muse: Musicians and Their Music in the Third Reich. New York and Oxford: Oxford University Press.
- Kater, Michael H. 2000. Composers of the Nazi Era: Eight Portraits. New York and Oxford: Oxford University Press. Ch. 2, pp. 31-56, is titled "Paul Hindemith: The Reluctant Emigré".
- Kemp, Ian. 1970. Hindemith. Oxford Studies of Composers (6). London, New York: Oxford University Press.
- Neumeyer, David. 1986. The Music of Paul Hindemith. New Haven: Yale University Press.
- Noss, Luther. 1989. Paul Hindemith in the United States. Urbana: University of Illinois Press.
- Preussner, Eberhard. 1984. Paul Hindemith: ein Lebensbild. Innsbruck: Edition Helbling.
- Skelton, Geoffrey. 1975. Paul Hindemith: The Man Behind the Music: A Biography. London: Gollancz. New York: Crescendo Publishing.
- Taylor, Ronald. 1997. Berlin and Its Culture: A Historical Portrait. Yale University Press. ISBN 978-0-300-07200-6.
- Taylor-Jay, Claire. 2004. The Artist-Operas of Pfitzner, Krenek and Hindemith: Politics and the Ideology of the Artist. Aldershot: Ashgate.
Further reading
[edit]- Fried, Alexander (19 February 1939). "Paul Hindemith Brings Fresh Air to Symphony". The San Francisco Examiner. San Francisco. p. 50. Retrieved 24 May 2020 – via Newspapers.com.
- Schwarze, Richard (21 November 1981). "Hindemith: He was simply a musician who produced 'music as a tree bears fruit' ... Well, not really". The Journal Herald. Dayton, Ohio. p. 27. Retrieved 23 May 2020 – via Newspapers.com.
- Desbruslais, Simon. 2019. The Music and Music Theory of Paul Hindemith Archived 6 August 2020 at the Wayback Machine. Woodbridge: Boydell Press. ISBN 978-1-78327-210-5.
- Gregor, Neil. 2025. The Symphony Concert in Nazi Germany. Chicago: University of Chicago Press. ISBN 978-0226839103.
- Luttmann, Stephen. 2013. Paul Hindemith: A Research and Information Guide. New York: Routledge. ISBN 978-1-135-84841-5.
- Petropoulos, Jonathan. 2014. Artists Under Hitler: Collaboration and Survival in Nazi Germany. New Haven and London: Yale University Press. Ch. 5, pp. 88–113, is titled "Paul Hindemith".
- Skelton, Geoffrey, ed. and trans. 1995. Selected Letters of Paul Hindemith. New Haven, Connecticut: Yale University Press.
- Winkler, Heinz-Jürgen (2004). "Fascinated by Early Music: Paul Hindemith and Emanuel Winternitz". Music in Art: International Journal for Music Iconography. 29 (1–2): 14–19. ISSN 1522-7464.
External links
[edit]- Paul Hindemith Oral History collection at Oral History of American Music
- Free scores by Paul Hindemith on IMSLP at the International Music Score Library Project (IMSLP)
- Hindemith Foundation
- Schott Music Publisher page
- An Inner Emigration, notes on Hindemith and Der Schwanendreher by Ron Drummond
- Paul Hindemith in conversation with Seymour Raven (7 April 1963)
- Publications by and about Paul Hindemith in the catalogue Helveticat of the Swiss National Library
- Newspaper clippings about Paul Hindemith in the 20th Century Press Archives of the ZBW
- "Hindemith Kabinett im Kuhhirtenturm". Museumsufer Frankfurt. Retrieved 21 December 2022.
Paul Hindemith
View on GrokipediaPaul Hindemith (16 November 1895 – 28 December 1963) was a German composer, violist, conductor, violinist, teacher, and music theorist whose prolific output and theoretical innovations shaped twentieth-century music.[1][2]
Born in Hanau near Frankfurt, Hindemith received early training at the Hoch Conservatory and served as concertmaster of the Frankfurt Opera orchestra from 1915 to 1923, interrupted by military service.[1] During the Weimar Republic, he dominated German musical life, composing expressionist operas, neoclassical Kammermusik concertos, and chamber works that emphasized functional, accessible "Gebrauchsmusik" for practical performance.[2][1]
His music drew Nazi criticism as degenerate despite initial recognition from figures like Goebbels; by 1936, his works were banned, and the 1934 "Hindemith Affair" involving the blocked premiere of his opera Mathis der Maler exemplified regime interference, prompting emigration to Switzerland in 1938 and the United States in 1940.[3][1] In America, he naturalized as a citizen in 1946 and taught composition at Yale University from 1940 to 1953, where he required students to study his pedagogical text The Craft of Musical Composition, which systematized tonality through hierarchical series of intervals.[2][3]
Hindemith's defining achievements include sonatas for nearly every orchestral instrument, the symphony Mathis der Maler (1934), Symphonic Metamorphosis of Themes by Carl Maria von Weber (1943), and ballets like The Four Temperaments (1940), blending contrapuntal rigor with tonal functionality amid modernist experimentation.[1][2] Returning to Switzerland in 1953, he continued composing until illness led to his death in Frankfurt.[2]
Early Life
Childhood and Family Influences
Paul Hindemith was born on November 16, 1895, in Hanau, a town near Frankfurt, Germany, as the eldest of three children to Robert Rudolf Hindemith, a painter and decorator of modest means, and Marie Sophie Warnecke, whose family background traced to farmers and shepherds in Lower Saxony.[4][2] The family endured chronic financial instability, with Robert's insecure income from trade work and occasional painting leading to frequent relocations within the region and periods of severe poverty that marked Hindemith's early years.[4][2] Robert Hindemith, originating from a line of Polish shopkeepers and craftsmen, adopted a draconian and harsh parenting style aimed at enforcing social advancement for his children through rigorous discipline and practical skills, viewing music not initially as an artistic pursuit but as a viable profession to combat the family's economic hardships.[5][6] He systematically trained his children in instruments—assigning Paul the violin, younger brother Rudolf the cello, and sister Toni the piano—forming them into the "Frankfurt Children's Trio" for paid performances across Silesia and local venues, which provided essential income and instilled early professional habits in Paul from around age 11.[4][7] This paternal insistence on music as a survival mechanism, rather than pure vocation, exposed Paul to relentless practice and public playing amid a joyless home environment, fostering his technical proficiency while straining family relations; Robert's death in 1915 during World War I on the French front further underscored the era's disruptions.[5][8] Marie Sophie played a supportive but less directive role, helping manage the household amid relocations, including a three-year period when young Paul resided with his grandfather to alleviate family burdens, though her influence appears secondary to Robert's domineering approach in shaping his musical trajectory.[4] The siblings' collaborative trio performances honed Paul's ensemble skills and adaptability, contributing to his self-reliant development as a versatile string player before formal conservatory entry, while the overarching poverty compelled an pragmatic orientation toward music as craft over idealism.[7][2]Initial Musical Training
Hindemith commenced violin studies in childhood under his father's insistence, who enforced daily practice amid the family's poverty in Hanau.[4] His initial private instruction included lessons with Eugene Reinhardt and Anna Hegner, the latter of whom recognized his aptitude and facilitated his advancement.[9] [10] At approximately age 12 or 13, around 1908, Hindemith entered the Dr. Hoch's Konservatorium in Frankfurt am Main, where he pursued violin training under Adolf Rebner, the institution's violin professor and concertmaster of the Frankfurt Opera orchestra.[11] [7] Rebner's mentorship proved pivotal, granting Hindemith a scholarship that waived tuition fees due to his demonstrated talent and rapid progress.[4] During his conservatory years, from roughly 1908 to 1915, Hindemith supplemented violin studies with exposure to other instruments, including piano and clarinet, and began formal composition lessons in 1912 with Bernhard Sekles.[3] To support himself financially, he performed in local theater orchestras as early as age 13, honing practical ensemble skills alongside academic training.[2] By 1915, at age 20, he had advanced to concertmaster of the Frankfurt Opera orchestra, reflecting the intensity and precocity of his formative education.[3]Weimar-Era Career
Rise as Performer and Innovator
Following World War I, Hindemith advanced his performing career in Frankfurt, serving as concertmaster of the Opera Orchestra until his resignation in 1923 to prioritize chamber music activities.[12] [13] In 1922, he founded the Amar Quartet, in which he played viola alongside violinist Licco Amar, his brother Rudolf on cello (alternating with others), and a second violinist; the ensemble toured extensively across Europe from 1922 to 1929, specializing in premieres of contemporary chamber works by composers including Hindemith himself, Schoenberg, and Stravinsky.[12] [2] The quartet's performances elevated Hindemith's status as a virtuoso violist, renowned for technical precision and advocacy for modernist repertoire.[2] As an innovator, Hindemith gained prominence through provocative compositions premiered at the Donaueschingen Festival, such as his String Quartet Op. 16 in 1921, which showcased his shift toward dissonant, expressionist idioms.[12] The following year, Kammermusik No. 1, Op. 24 No. 1, debuted at the same venue on July 28, 1922, incorporating unconventional elements like wailing sirens and a foxtrot finale to challenge bourgeois audiences and bourgeois musical conventions.[12] This work initiated a series of seven Kammermusik pieces composed between 1922 and 1927, blending neo-Baroque concerto forms with modern instrumentation—including accordion, slide whistle, and jazz rhythms—while emphasizing functional polyphony over romantic expressivity.[2] [12] Hindemith's involvement extended to organizing new music events; in 1923, he joined the Donaueschingen Festival's committee, promoting experimental genres such as mechanical music, radio compositions, and film scores alongside traditional forms.[12] His 1922 Suite for piano exemplified machine-like rhythms, reflecting broader Weimar-era fascination with technology and anti-romantic austerity.[2] These efforts positioned Hindemith as a central figure in the Neue Sachlichkeit movement, prioritizing craftsmanship and utility in music over subjective emotion.[2] By the mid-1920s, his reputation as both performer and composer solidified, culminating in the 1926 premiere of his opera Cardillac in Dresden, which further demonstrated his synthesis of dramatic narrative with contrapuntal rigor.[12]Development of Gebrauchsmusik
Hindemith emerged as the principal advocate of Gebrauchsmusik, or utility music, in the mid-1920s amid the Weimar Republic's cultural experimentation, promoting compositions designed for practical use by amateur musicians in community or domestic settings rather than elite concert halls.[14] This approach contrasted with the technical demands of late Romantic and early modernist works, prioritizing accessibility, social engagement, and functional simplicity to foster widespread musical participation.[14] Influenced by the Neue Sachlichkeit movement's emphasis on objective, utilitarian art, Hindemith viewed Gebrauchsmusik as a means to democratize music-making, drawing parallels to historical precedents like Johann Sebastian Bach's community-oriented church compositions.[15] His promotion intensified through festivals and writings, including participation in the Baden-Baden events from 1926, where he explored influences from jazz, popular forms, and mechanical instruments to create adaptable repertoire.[15] In a 1929 article, Hindemith formalized the concept as Gebrauchsmusik and Gemeinschaftsmusik, advocating for pieces that enabled non-professional performers—such as workers, students, or families—to engage actively, often under the umbrella of Hausmusik for home-based ensemble playing inspired by 15th- to 18th-century traditions.[16] He argued that such utilitarian works held greater value than virtuoso concert music, serving socio-political purposes like community building and education.[16] Key manifestations included the cantata Frau Musica, Op. 45 (1928–1929), with its foreword emphasizing performative utility, and the children's operetta Wir bauen eine Stadt (1930–1931), composed for young amateurs to promote collaborative creation.[16] The Plöner Musiktag of June 1932 exemplified this ethos, featuring a full day of Hindemith-orchestrated community performances in Plön, involving schoolchildren and locals in newly written pieces for mixed amateur ensembles.[16] Though Hindemith later rejected the term Gebrauchsmusik for its reductive connotations, these efforts influenced subsequent community music initiatives, such as Carl Orff's Schulwerk, by establishing music as a participatory social tool.[16]Nazi Period and Exile
Engagement and Conflicts with the Regime
Hindemith initially sought to maintain his career under the Nazi regime after Adolf Hitler's appointment as Chancellor on January 30, 1933, by composing works aligned with themes of German cultural heritage, such as the opera Mathis der Maler (1933–1934), which drew on the life of Matthias Grünewald and emphasized national artistic traditions in a tonal style intended to appeal to regime preferences for accessible, monumental music.[17] The opera's narrative, portraying an artist's defiance of corrupt authority during the Peasants' War, carried allegorical undertones critiquing contemporary political interference in art, though Hindemith avoided overt confrontation.[3] Conflicts escalated when Berlin State Opera director Wilhelm Furtwängler scheduled the opera's premiere for the 1934–1935 season, prompting Nazi officials to ban it due to Hindemith's modernist associations and the perceived subversive content.[18] Furtwängler responded by conducting the extracted Mathis der Maler Symphony on March 16, 1934, with the Berlin Philharmonic, and publicly defended Hindemith in his November 25, 1934, article "Der Fall Hindemith" in the Deutsche Allgemeine Zeitung, arguing that suppressing a German composer's work undermined national culture and advocating for artistic autonomy.[19] [20] This stance drew sharp rebuke from Joseph Goebbels and other Nazi leaders, who labeled Hindemith's music "degenerate" and culturally Bolshevist; Furtwängler temporarily resigned from key positions, including presidency of the Reichsmusikkammer, on December 5, 1934, amid the uproar.[3] [21] Hindemith's position worsened due to his marriage to Gertrud Rottenberg, who had partial Jewish ancestry, rendering him suspect under racial policies despite his own Aryan background; this factor amplified Nazi scrutiny beyond his compositional style, which they viewed as elitist and atonal-influenced.[22] By October 1936, his works were officially banned from performance and publication, with limited exceptions for pre-existing commitments, following lists of "degenerate music" compiled by regime cultural enforcers.[3] Hindemith reduced public activities, resigning from the Prussian Academy of Arts in 1934 after internal pressures, and privately expressed contempt for Nazi ideology while teaching sporadically at the Berlin Hochschule für Musik until 1935.[2] These mounting restrictions, coupled with the regime's inconsistent tolerance—evident in sporadic allowances for his music despite bans—ultimately compelled his disengagement from German institutions.[23]Flight to Switzerland and Emigration to America
As pressures mounted under the Nazi regime, Paul Hindemith's compositions were officially banned in October 1936 for exhibiting traits associated with "cultural Bolshevism," though selective performances were permitted as part of inconsistent Nazi cultural policies.[3] His works were further stigmatized as "degenerate" and included in the Entartete Musik exhibition in Düsseldorf in April 1938, which displayed confiscated modern art and music to deride perceived cultural decay.[3] [8] These measures, combined with the vulnerability arising from his wife Gertrud's partial Jewish ancestry, prompted Hindemith to seek safety abroad.[3] [1] In August 1938, Paul and Gertrud Hindemith departed Berlin for Switzerland, establishing residence in the canton of Valais (Wallis), where Hindemith expressed initial optimism about the relocation in correspondence.[8] [24] Earlier that year, on May 28, the Zurich Opera premiered his opera Mathis der Maler, derived from the symphony of the same name, marking a significant artistic statement amid his growing estrangement from Germany; the work's themes of individual conscience resisting authoritarian conformity had failed to reconcile him with regime expectations despite earlier attempts at accommodation.[19] In Switzerland, Hindemith maintained productivity, accepting commissions and guest engagements, but the looming threat of war and unresolved professional isolation necessitated further relocation.[24] By early 1940, with World War II underway and Nazi influence extending toward neutral Switzerland, Hindemith secured a teaching position in the United States and departed on February 4, 1940, arriving to begin his American phase. This emigration, following a roughly 18-month stay in Switzerland, positioned him among European artists fleeing totalitarianism, though unlike some contemporaries, Hindemith's move was pragmatic rather than ideologically driven opposition, as he had navigated early Nazi overtures before conflicts proved insurmountable.[25][17] Upon arrival, he initially taught at institutions including the Berkshire Music Center, leveraging his reputation to rebuild amid wartime disruptions.[25]American Period
Professorship at Yale University
Paul Hindemith joined the Yale School of Music faculty in 1940 as professor of theory and composition, having emigrated from Europe amid political pressures.[26] He held this position until 1953, resigning to focus on conducting engagements in Europe.[27] Hindemith's teaching centered on music theory and composition, with an emphasis on practical musicianship including sightsinging from plainchant notation and analysis of contrapuntal structures.[28] He instructed approximately 400 students through regular classes and public lectures, many of whom were non-degree participants drawn to his expertise in both contemporary and historical repertoires.[25] In 1943, Hindemith founded and directed the Yale Collegium Musicum, an ensemble committed to authentic performances of music from the 12th to 18th centuries.[29] The group conducted 12 concerts under his leadership through 1953, integrating student performers with community musicians and promoting the early music revival in the United States.[29] This initiative, alongside his theoretical instruction, enhanced Yale's graduate programs and established the school as a leading conservatory for compositional training.[27]Theoretical Writings and Compositions
During his American period, particularly while teaching at Yale University from 1940 to 1953, Paul Hindemith published English translations of his seminal theoretical treatise Unterweisung im Tonsatz as The Craft of Musical Composition. Volume 1, the theoretical part translated by Arthur Mendel, appeared in 1942 and presented a hierarchical system of tonal functions based on interval degrees derived from acoustic series, prioritizing consonance through natural overtones while accommodating chromaticism without abandoning tonality.[30] Volume 2, translated by Otto Ortmann and focused on practical exercises in two- and three-part writing, was issued in 1941 to guide students in applying these principles.[31] These texts reflected Hindemith's rejection of pure atonality in favor of a structured tonal language grounded in empirical acoustics and contrapuntal discipline. Hindemith further articulated his philosophical stance on music in A Composer's World: Horizons and Limitations, derived from his Charles Eliot Norton Lectures at Harvard University in 1949–1950 and published in 1952. The book delineates the composer's creative boundaries, advocating for music's organic development from innate human capacities rather than abstract mathematical constructs like serialism, which Hindemith critiqued as overly restrictive and disconnected from auditory intuition.[32] He emphasized composition as a craft serving functional and expressive purposes, aligning with his earlier advocacy for Gebrauchsmusik but adapted to neoclassical clarity. Hindemith's compositions from this era directly embodied his theoretical framework, most prominently Ludus Tonalis for solo piano, composed from August to October 1942. This work comprises a prelude, twelve fugues (one each in major and minor modes ordered by his interval scale), corresponding interludes, and a postludium inverting the prelude, serving as a practical demonstration of tonal organization, counterpoint, and keyboard technique within his system.[33] He also produced a series of sonatas for nearly every orchestral instrument, including flute (1936, revised), viola, and tuba, which utilized quartal harmonies and melodic lines governed by his consonance rankings to exploit each instrument's idiomatic qualities.[34] Larger works like the Symphony in B-flat (1941) and Symphonic Metamorphosis on Themes by Carl Maria von Weber (1943) integrated these elements into symphonic forms, balancing contrapuntal rigor with thematic transformation.Later Years in Europe
Return to Teaching in Zurich
In 1951, Paul Hindemith accepted an appointment as the first professor of musicology at the University of Zurich's newly established Department of Musicology, initially dividing his time between this role and his position at Yale University.[35][36] Following the award of this professorship, he resigned from Yale in 1953 and relocated permanently to Switzerland, settling in Zurich where he continued teaching music theory, composition, and music education until 1957.[2][12] This move marked his full return to Europe after over a decade in the United States, driven by a desire to focus on conducting and European musical activities amid declining compositional influence.[25] Hindemith's teaching at Zurich emphasized practical engagement over theoretical abstraction, involving students and colleagues in active music-making such as sightreading Mahler's Kindertotenlieder for harmonic analysis or performing Carlo Gesualdo's madrigals post-lecture.[35] His unconventional methods created intense, nerve-wracking sessions, as recalled by student Andres Briner, who described a challenging exam requiring on-the-spot performance and critique.[35] This hands-on approach reflected Hindemith's lifelong commitment to Gebrauchsmusik—functional music for performers—prioritizing technical mastery and ensemble work to foster direct comprehension of compositional structures.[35] By 1957, Hindemith withdrew from his Zurich duties, citing the strains of balancing teaching with growing conducting commitments across Europe.[35] His tenure, though brief, contributed to the institutionalization of musicology at the university, leaving a legacy preserved in archives donated to UZH, which document his multifaceted pedagogical impact.[35]Final Works and Death
In 1953, Hindemith returned to Europe after nearly two decades in the United States, settling in Zürich, Switzerland, where he accepted a professorship at the university and continued his pedagogical and compositional activities.[37][38] He retired from teaching in 1957 but remained active as a conductor and composer, producing works that reflected his deepening critique of contemporary modernist trends, including serialism, in favor of tonal structures rooted in his theoretical principles.[38] Among his significant late compositions was the opera Die Harmonie der Welt (1957), which explored themes of cosmic order through the life of astronomer Johannes Kepler, premiered in Munich and exemplifying Hindemith's synthesis of historical forms with contrapuntal rigor.[39] His output in these years emphasized clarity and accessibility, often drawing on Baroque influences, though production slowed amid health issues and travel, including conducting engagements across Europe and a final visit to the United States shortly before his death.[40] Hindemith received the Wihuri Sibelius Prize in 1955 and the Balzan Prize in 1962 for his contributions to music.[41] His health deteriorated in 1963 following a fever and strokes, leading to hospitalization in Frankfurt am Main, West Germany, where he died on December 28 from acute pancreatitis at age 68.[42][43][44] He was buried alongside his wife, Gertrud, in the cemetery at La Chiésaz, Vaud, Switzerland.Musical Language and Theory
Stylistic Evolution from Expressionism to Neoclassicism
Hindemith's compositional style in the immediate post-World War I period drew heavily from German Expressionism, featuring jagged dissonances, angular rhythms, and heightened emotional intensity reminiscent of Arnold Schoenberg's early atonal phase.[45] Key works from 1919 to 1921, such as the one-act operas Mörder, Hoffnung der Frauen (premiered June 1921 in Stuttgart) and Das Nusch-Nuschi (premiered 1921), exemplified this approach through sparse orchestration, speech-like vocal lines, and harmonic tension derived from clustered intervals rather than traditional resolution.[46] These pieces prioritized subjective psychological states over structural coherence, aligning with the era's avant-garde rejection of pre-war Romanticism.[16] By 1922, Hindemith began transitioning away from pure Expressionism toward a more objective, contrapuntally driven aesthetic influenced by the Neue Sachlichkeit (New Objectivity) movement, which emphasized utility and craftsmanship in art amid Weimar Germany's cultural reorientation.[37] This shift manifested in his Kammermusik series (Op. 36, Nos. 1–7, composed 1922–1927), concerto-like chamber works for small ensembles that revived Baroque forms such as the concerto grosso while incorporating motoric rhythms and reduced dissonance for greater accessibility.[47] For instance, Kammermusik No. 1 (1922) for flute and strings deploys intricate fugal writing and clear tonal centers, marking a deliberate pivot from atonal experimentation to functional polyphony rooted in Johann Sebastian Bach's models.[37] The neoclassical phase solidified in the late 1920s, characterized by disciplined counterpoint, modal inflections, and a harmonic language favoring quartal stacks over tertian progressions, yet anchored in diatonic frameworks to ensure structural integrity.[48] Works like the String Quartet No. 3 (1927) demonstrate this evolution through layered imitative textures and rhythmic vitality, eschewing Expressionist subjectivity for an ethos of Gebrauchsmusik (music for use) that served amateur performers and educational purposes.[49] Hindemith later codified this style in theoretical texts, arguing that music's validity stemmed from its relational logic rather than emotional excess, a principle causal to his enduring emphasis on craft over ideology.[50] This progression not only reflected personal maturation but also paralleled broader European reactions against modernism's fragmentation, prioritizing empirical sonic balance verifiable through performance.[48]Interval-Based Harmonic System
Paul Hindemith developed his interval-based harmonic system primarily in the 1937 treatise Unterweisung im Tonsatz, later translated and expanded as The Craft of Musical Composition in two volumes (1941 and 1945), grounding harmony in acoustic principles derived from the natural overtone series rather than conventional functional tonality.[51] This approach rejected the diatonic bias of earlier theories, treating the full chromatic scale as fundamental and evaluating intervals based on their inherent tension, determined by the degree to which the partials (overtones) of two tones coincide or clash when sounded together.[51] Hindemith posited that musical coherence arises from combining tones with minimal overall tension relative to a perceived root, prioritizing empirical auditory perception over arbitrary rules.[52] Central to the system are two analytical series for each tone, used to assess melodic and harmonic relationships. Series I ranks the intervals from a given fundamental (e.g., C) in order of decreasing consonance, reflecting the harmonic series' influence: starting with the octave (C'), then perfect fifth (G), major third (E), minor sixth (A♭), perfect fourth (F), minor third (E♭), major sixth (A), major second (D), minor seventh (B♭), major seventh (B), minor second (D♭), and tritone (F♯) as the most dissonant.[51] Series II evaluates the reverse perspective, measuring each tone's tension against the fundamental, enabling bidirectional analysis for vertical sonorities.[51] Chords are classified by identifying the root as the tone experiencing the lowest aggregate tension from all others, with progressions designed to create controlled fluctuations in tension levels, mimicking natural acoustic stability.[52]| Degree of Dissonance | Interval Example (from C) |
|---|---|
| 1 (least) | Octave (C') |
| 2 | Perfect fifth (G) |
| 3 | Major third (E) |
| 4 | Minor sixth (A♭) |
| 5 | Perfect fourth (F) |
| 6 | Minor third (E♭) |
| 7 | Major sixth (A) |
| 8 | Major second (D) |
| 9 | Minor seventh (B♭) |
| 10 | Major seventh (B) |
| 11 | Minor second (D♭) |
| 12 (most) | Tritone (F♯) |

