Kaii Lee had combined several piano/keyboard method books and her life long music learning books to create this sequential music theory study for this website. This page is about the understanding of Compositional Methods and the uses of the tools in the Contemporary ways. By clicking on the other colored links at the bottom of this page, the other music theory topics can be found easily.
For more information, please contact Kaii directly: info@kafm.net
Atonality | Bitonality | Polytonality | Melody Inversion | Retrograde | Retrograde Inversion | Quartal Harmony | Serialism | Twelve Tone Row
The following compositional tools, each has a very different way to address the harmonic and/or melodic function in musical compositions.
An Atonality composition is created with no specific tonality, key, or mode, and is very different than the traditional compositions that always have a focused harmonic and melodic structure. The Atonality idea started roughly in the early 20th century. See the following example from Arnold Schoenberg's "Klavierstück, Op. 11", composed when he was experimenting with Atonality.
| Klavierstück, Op. 11, #1, by Arnold Schoenberg (1909) |
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Bitonality is the use of two different tonal centers at the same time in a musical composition. A famous Russian composer, Igor Stravinsky, employeed this tool in his "The Rite of Spring." It tool was also used by Bela Bartok, as he called it the "duality of key" featured in A minor and C? minor in his folk song. Here is an example of a piano work, "Saudades do Brazil", by Darius Milhaud. The left-hand part was written in the key of G major, while the right-hand part was written in the key of B major.
| "Copacabana" from "Saudades do Brazil", by Darius Milhaud, (1922) |
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Polytonality is a way to combine several tonalities into one music composition. Polytonality also requires the presentation of simultaneous key-centers. As early as Wolfgang Amadeus Mozart, this type arrangement had been used in music compositions. See the following example from Mozart's "Ein musikalischer Spass", K.522, "A Musical Joke", composed in 1787.
| "Ein Musikalischer Spass", K.522, "A Musical Joke", by Wolfgang Amadeus Mozart, (1787) |
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Many other composers have used polytonality in their compositions as well, such as "Symphony No. 2", by Samuel Barber (1944), "House of Cards", an American TV series, theme song by Jeff Beal (2013), "Symphony No. 2", by Phillip Glass (1994), "Planet of Apes", the movie theme song by Jerry Goldsmith (1968), "The Planets: Neptune", by Gustav Holst (1914-1917), "Variations on "America", by Charles Ives (1909-1910), "The Untouchables", theme song by Ennio Morricone (1987), "Petrushka" and "Rite of Spring", by Igor Stravinsky (1911 and 1913), and even the theme song from "Star Wars", by John Williams (1977).
A Melodic Inversion is an "upside-down" rearrangement of the musical elements in an interval, a chord, a melody, or a group of lines of music. By using this tool, composers create new melodies. The following graph shows the rearrangement result of intervals.
| Original | Inversion | Original | Inversion |
|---|---|---|---|
| Perfect | Perfect | Unison | Octave |
| Major | Minor | Second | Seventh |
| Augmented | Diminished | Third | Sixth |
| Fourth | Fifth |
One of the most famous piano works by Sergei Rachmaninoff, "Rhapsody on a Theme of Paganini", has a standout variation that was the result of a Melodic Inversion. See the Paganini melody here and the Rachmaninoff in the following score.
| "Caprices for Solo Violin", Op.1, #24, Theme, by Niccolo Paganini |
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| "Rhapsody on a Theme of Paganini", Op.43, Var.18, by Sergei Rachmaninoff |
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Retrograde is another tool used in music where a melody or musical phrase is performed backward. It means reversing the order of notes from their original sequence, such as A-B-C-D-E becomes E-D-C-B-A. Here is an example from Johann Sebastien Bach's "The Musical Offering", BWV 1079, that all the notes between the two-part canon are precisely in the form of retrograde.
| "Das Musikalische Opfer", "The Music Offering", BWV1079, by Johann Sebastian Bach |
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Retrograde Inversion is one more way to manipulate a melody. It literally means "backward-upside-down" in music compositions. This type of technique was popular in the Serialism and the Twelve-Tone music. Usually, a main melody, Prime, is identified first, then the inversion of that melody, followed by the Retrograde, and lastly, the Retrograde Inversion. See the following graph for a comparison.
| Prime - Retrograde - Inversion - Retrograde Inversion |
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Quartal Harmony is referring to harmony that is created by intervals of perfect fourths. It’s been used by classical composers such as Stravinsky, Debussy and Bartók. Music composed with chords built on fourths don’t have the same predictability as more traditional harmony. The following sample starts with Quartal Harmony and soon to have a whole-tone scale as the main melody. It is the beginning of "The Cage", by Charles Ives, composed in 1906.
| "The Cage", by Charles Ives, 1906 |
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Serialism is a compositional technique in which a fixed series of notes, especially the twelve notes of the chromatic scale, are used to generate the harmonic and melodic basis of a piece and are subject to change only in specific ways. The first fully serial movements appeared in works by Arnold Schoenberg, roughly since World War I. In most of the western classical and popular music, composers use major scales, minor scales or possibly modes to create their music. In Serialism, these do not exist. Serialism is based on a “series” of notes that determines the development of the composition; therefore, they sound very different. Igor Stravinsky was another 20th century composer who adopted the Serialism into his work. The following sample is taken from the end of the first movement of "Movements for Piano and Orchestra", by Stravinsky, 1958-1959. Look at the time signatures and all the accidentals.
| "Movements for Piano and Orchestra", by Igor Stravinsky, 1958-1959 |
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The Twelve-Tone technique, also known as dodecaphony, twelve-tone serialism, andtwelve-note composition, is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. However, the most famous composer who used Twelve-Tone technique in his music since the early 1900s was Arnold Schoenberg. With the Twelve-tone technique, all of the twelve notes of the chromatic scale are used in a fixed order, which is then used in different ways that all of the notes generally given more-or-less equal importance. Here is a sample of Josef Matthias Hauer's Twelve-Tone music from 1919.
| "Anthematic", by Josef Matthias Hauer, 1919 |
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Thank you for reading!
Music Theory that every musician could use and should know The Basics
Math in Music
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Time Signatures Intervals Modulations Homophonic Style Polyphonic Style Diatonic & Chromatic Steps Transposition Contrapuntal Techniques Key Signatures Triads & Inversions Binary Form Primary Triads Augmented Sixth Chords Ternary Form Secondary Triads Traditional Compositional Tools Dance Suites Scales Seventh Chords Contemporary Compositional Tools Prelude & Fugue Secondary Dominant Musical Signs Sonata Form Cadences Rondo Form Modes Chord Progressions Musical Terms Theme & Variations Figured Bass & Basso Continuo Serialism
For more information, please contact Ms. Lee at: info@kafm.net
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