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American composer Conlon Nancarrow created an innovative series of canons for player piano. Using a mechanical means of performance enabled him to conceive of rhythm relationships too complex for a human performer. In Study No. 24 , the three voices are moving in a speed ratio of 14/15/16. The effect is similar to heterophony; but here the voices are split into different registers.

These twentieth century examples dramatize how canons build on identity. Though Webern and Nancarrow’s canons are each based on a single melodic line, the complexity of the canons disguise this internal consistency. The resulting textures take on a life of their own.

Preserving the harmony

In many different genres and styles of music, dynamic repetition of the harmonic progression is a primary way of transforming the material.

In a classical “theme and variations,” the variations are based on the harmonic progression of the theme. The following excerpts are from a set of variations for string quartet by Franz Schubert based on his song “Death and the Maiden.” The variations offer a sampling of the diversity that can be created from a single progression.

As in a theme and variations, the underlying harmonic progression is maintained in a traditional jazz improvisation: As the progression is repeated, each member of the ensemble takes turn creating a spontaneous melody on top of it.

Here is the progression underlying Miles Davis’ So What , followed by the piano solo.

In a classical theme and variations and traditional jazz, the piece will have one underlying progression that cycles repeatedly. In other works, there may be a greater assortment of harmonies and progressions.

In the following excerpt from Sheherezade: The Sea and Sinbad’s Ship , Nikolai Rimsky-Korsakov creates a rhapsodic, extended melody.

The “bead” of this elaborate melodic strand is a short motive that is transposed over and over. Later in the work, an intense passage builds on the identity of the harmony: The motive is at first absent, but the progression that supports it is played repeatedly. At the end of the excerpt, the motive returns forcefully in the low brass—fitting in perfectly on top of the already present harmonic progression.

The following excerpt is from the second movement of Stravinsky’s Symphony of Psalms . Beneath the women’s voices, the lower strings are playing the movement’s main theme.

In the third movement, Stravinsky alludes to this passage by replaying its harmonic progression in slow motion. The men’s vocal line is a variation of the second movement theme.

Thus, harmonic progression may be preserved, while the surface details are varied.

Preserving the rhythm

Finally, a rhythmic pattern may be maintained, while the melodies and harmonies used to express it are changed.

In Alban Berg’s opera Wozzeck , the title character staggers into a tavern after murdering his unfaithful wife. The music in the scene is based on a single rhythm, called by Berg a “mono-rhythm,” first introduced by the percussion.

The saloon pianist picks up the mono-rhythm and incorporates it into a raucous polka:

Wozzeck joins in, his vocal line also echoing the mono-rhythm:

When a neighbor Margret spots blood on Wozzeck’s hand, her words are carefully timed to the mono-rhythm.

In the gradually escalating confrontation, the two singers are accompanied by the mono-rhythm. Berg creates this entire scene from the mono-rhythm without ever playing it the same way twice.

Much of Bernard Herrmann’s music for Alfred Hitchcock’s thriller North by Northwest is focused on the following compact, agitated theme:

In the climactic scene, as Cary Grant and Eva Marie-Saint are escaping down the slopes of Mount Rushmore, Hermann creates a panoramic display of the theme. In the excerpt that follows, the winds, brass and percussion mimic the rhythm of the theme—but not the notes.

Thus, a theme may also be reduced to its rhythmic pattern, freeing it to assume many melodic and harmonic forms.


We have studied how dynamic repetition can revitalize a musical idea. We are now in a better position to assess what the variations by Paganini, Brahms, Lutoslawski and Rochberg had in common with Paganini’s original theme.

First of all, Paganini’s theme is built out of a single pattern.

Likewise, all of the variations feature an insistent pattern of their own.

Notice that this is not true of the Schumann example: Its opening pattern is not maintained so literally.

Second, Paganini’s theme is divided into two halves: In the first, the harmonic progression oscillates back and forth between two chords. In the second half, the harmonic progression “opens up” into a broader progression:

The variations all follow this harmonic plan. They also mimic the pacing of Paganini’s harmonies.

The Schumann follows neither the same harmonic plan nor the same pacing. It also lasts longer!

Each of the variations has other features in common with Paganini’s theme: Just enough of the theme’s identity is maintained to preserve its integrity. Meanwhile, the variations leave aspects of its identity behind. For instance, not all follow the theme’s contour: Brahms’ motive heads downwards, Rochberg’s remains rooted in the same place.

Building on identity requires that at least one aspect of the musical idea remain constant: We have observed how melody, harmony and rhythm may all be preserved, while the other features are altered.

In some musical styles and traditions, the means of transformation defines the genre : In jazz, the harmonic progression—such a “twelve-bar blues”—cycles as the ensemble members take turns improvising. In an Indian raga, the soloist improvises over the underlying rhythmic cycle, called a tala.

Thus far, we have considered the make-over of an entire musical idea. But composers can also take a hammer to their material and smash it in order to create new forms.

Questions & Answers

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s. Reply
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s. Reply
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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Prasenjit Reply
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Source:  OpenStax, Sound reasoning. OpenStax CNX. May 31, 2011 Download for free at http://cnx.org/content/col10214/1.21
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