“By the time of his Fourth String Quartet, inversional symmetry had become as fundamental a premise of Bartók's harmonic language as it is of the twelve-tone music of Schoenberg, Berg, and Webern. Neither he nor they ever realized that this connection establishes a profound affinity between them in spite of the stylistic features that so obviously distinguish his music from theirs…Nowhere does he [Bartók] recognize the communality of his harmonic language with that of the twelve-tone composers that is implied in their shared premise of the harmonic equivalence of inversionally symmetrical pitch-class relations.”

—  George Perle

Pages 46-47
The Listening Composer

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George Perle11
American composer 1915–2009

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“If…[Alban] Berg departs so radically from tradition, through his substitution of a symmetrical partitioning of the octave for the asymmetrical partitionings of the major/minor system, he departs just as radically from the twelve-tone tradition that is represented in the music of Schoenberg and Webern, for whom the twelve-tone series was always an integral structure that could be transposed only as a unit, and for whom twelve-tone music always implied a constant and equivalent circulation of the totality of pitch classes.”

George Perle (1915–2009) American composer

Page 98
See: Common practice period, Twelve-tone technique
The Listening Composer

“Prokofiev was not alone among the leading composers of the twentieth century in changing his style repeatedly in the course of his career: Stravinsky, Schoenberg, Bartók, and others modified their musical language drastically at various stages of their creative lives. In Prokofiev’s case, he always maintained certain stylistic facets throughout the transformations of his musical language.”

Boris Berman (1948) Russian/American musician

Prokofiev’s piano sonatas : a guide for the listener and the performer (2008), Prokofiev: His Life and the Evolution of His Musical Language

“The pre-World War I works of Schoenberg, Berg, and Webern, "give a glimpse of a new universe of emancipated discourse, unfortunately quickly abandoned when Schoenberg returned to the classical musical shapes upon adopting the twelve-tone system."”

Elliott Carter (1908–2012) American composer

Elliott Carter (1977). The Writings of Elliott Carter, p.186. Bloomington: Indiana University Press.
Cited in Albright, Daniel (2004). Modernism and Music: An Anthology of Sources. University of Chicago Press. ISBN 0226012670.

“Collections of all twelve pitch classes can be differentiated from one another only by assigning an order to the pitch classes or by partitioning them into mutually exclusive sub-collections. The ordering principle is the basis of the twelve-tone system formulated by Schoenberg, the partitioning principle the basis of the system formulated around the same time by Hauer. In Schoenberg's compositional practice, however, the concept of a segmental pitch-class content is represented as well, as a basis for the association of paired inversionally related set forms. On the relation between Schoenberg and Hauer see Bryan R. Simms, "Who First Composed Twelve-Tone Music, Schoenberg or Hauer?" Journal of the Arnold Schoenberg Institute X/2”

George Perle (1915–2009) American composer

November 1987
Page 101, note 2
The Listening Composer

“The crucial and monumental development in the art music of our century has been the qualitative change in the foundational premises of our musical language--the change from a highly chromaticized tonality whose principle functions and operations are still based on a limited selection, the seven notes of the diatonic scale, from the universal set of twelve pitch classes to a scale that comprehends the total pitch-class content of that universal set. We can point to the moment of that change with some precision. It occurs most obviously in the music of Scriabin and the Vienna circle, Schoenberg, Webern, and Berg, in 1909-1910, and very soon afterwards, though less obviously, in the music of Bartok and Stravinsky. I think it is safe to say that nothing of comparable significance for music has ever occurred, because the closing of the circle of fifths gives us a symmetrical collection of all twelve pitch classes that eliminates the special structural function of the perfect fifth itself, which has been the basis of every real musical system that we have hitherto known.”

George Perle (1915–2009) American composer

Pages 42-43
The Listening Composer

Frank Wilczek photo

“The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time… As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion…. Harmony… can be considered a special kind of rhythm…. pure musical tones are produced when the vibrations are… periodic or… repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm—or, in mathematical language, if their periods are in proportion. Kepler… in the third book of Harmonice mundi… attempted to make other… related, connections between musical harmony and mathematical proportion.”

Frank Wilczek (1951) physicist

Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

Frank Wilczek photo

“The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time… As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion. …Harmony …can be considered a special kind of rhythm. …pure musical tones are produced when the vibrations are… periodic or… repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm—or, in mathematical language, if their periods are in proportion.”

Frank Wilczek (1951) physicist

Kepler... in the third book of Harmonice mundi... attempted to make other... related, connections between musical harmony and mathematical proportion.
Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

John Cage photo

“The composer (organizer of sound) will be faced not only with the entire field of sound but also with the entire field of time. The 'frame' or fraction of a second, following established film technique, will probably be the basic unit in the measurement of time. No rhythm will be beyond the composer's reach.
NEW METHODS WILL BE DISCOVERED, BEARING A DEFINITE RELATION TO SCHOENBERG'S TWELVE-TONE SYSTEM”

John Cage (1912–1992) American avant-garde composer

1930s
Source: 'The Future of Music: Credo' (1937); in: 'Silence: lectures and writings by Cage, John', Publisher Middletown, Conn. Wesleyan University Press, June 1961, 4/SILENCE

Letitia Elizabeth Landon photo

“Ah, deeply the Minstrel has felt all he sings,
Every passion he paints his own bosom has known;
No note of wild music is swept from the strings,
But first his own feelings have echoed the tone.”

Letitia Elizabeth Landon (1802–1838) English poet and novelist

(27th April 1822) The Poet
4th May 1822) Sappho see The Vow of the Peacock (1835
The London Literary Gazette, 1821-1822

Ernest Flagg photo

“A Greek architect of the great epoch would no more have thought of omitting the mark of the harmonic scale of proportion, on which the design was based, than would the composer of music think of omitting the harmonic scale of his composition.”

Ernest Flagg (1857–1947) American architect

Source: Small Houses: Their Economic Design and Construction (1922), Ch. II

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