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Here is how the music sounds when the two pianos begin in alignment.

A little while later, the second pianist shifts the basic pattern slightly out of alignment.

Later still, the second pianist shifts the pattern further and further out of alignment.

The farther out of alignment the two pianos get, the harder it is to recognize the underlying pattern. But ask yourselfthe following: Did the pianos change speed? Did the length of the pattern cycle change? Did the pianos play in a newregister or at a different volume? When you think about it, you will be able to sense the steadfastness of the basic pattern.

Here is one more example of the pianos out of alignment.

Now, listen to this extended excerpt from Piano Phase . When you listen to the excerpt, you will notice that, when the second pianist shifts alignment, thereis a brief "blurry" transition passage; then, the new alignment is established. The 3-minute excerpt will take youthrough the first three changes of alignment.

Reich's method uses very minimal means to achieve the goal of varied repetition. He manages to create gradual varietywithout changing the register, loudness or density of the pattern. Furthermore, unlike the other examples, Reich isvery patient in his presentation: He allows each stage of the process to persist, repeating over and over again,before shifting to the next. As a result, Reich's piece is more meditative and hypnotic than the other works; it hasmore in common with the stable repetition of pop music. However, Reich is still stretching his material bymaximizing the miminum: Eventually, the work explores every possible superposition of the basic pattern with itself.

Composers are often divided up by era and style: Bach , Chopin , Stravinsky and Reich would rarely be grouped together. However, beneath their unique personalities andstyles, these composers are all striving to create musical intelligibility through varied repetition . In the examples above, each has found a different way to achieve this underlying goal.

Varied repetition is not only a guiding principle in Western art-music. In a jazz work, a pattern such as the famous"twelve-bar blues," will provide an underlying consistency on top of which the band will create ever-changing, spontaneousimprovisations. In an Indian raga, an underlying rhythmic pattern, called a tala , creates the framework for elaborate improvisations. Music sustains itself, evolves andspans the globe because of the richness of possibilities created by varied repetition .

Repetition and recognition

Listening to explicit, literal repetition is like eating a simple carbohydrate: It is easily digested and quicklyabsorbed. That is why popular music has so much literal repetition: Its success depends on making an immediateimpact. On the other hand, listening to transformed repetition is like eating a complexcarbohydrate: It takes longer to digest. More of our attention is engaged: What changed? By howmuch? How fast did it happen? How long will it persist in the new form? Observations lead to interpretation: Why did itchange? What are the consequences of what happened?

More and more, nutritionists are emphasizing that complex carbohydrates are healthier for our bodies. Similarly,transformed repetition may be healthier for our musical minds: It demands greater concentration, more astute observations andmore careful reasoning--in short, more active listening. Learning to recognize and evaluate transformedrepetition is a crucial aspect of music appreciation.


Because music is an abstract, non-verbal time-art, repetition lies at the heart of how music makes sense. In pop music, therepetition tends to be more literal, while in classical music, it is often varied and transformed. As much as composers are oftensearching for new sounds and instrumental combinations, they are also inventing new means of building repetition.

Musical repetition offers powerful and suggestive models for how we understand the world and ourselves. The composer MarioDavidovsky, one of America's great living composers, has said that he listens to music not with knowledge but rather for knowledge, for guidance in understanding and grappling with life. Through itsimaginative and ever-changing use of repetition, music constantly presents us with new ways to recognize the unities and consistencies underlying our experience.

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Michael's sound reasoning. OpenStax CNX. Jan 29, 2007 Download for free at http://cnx.org/content/col10400/1.1
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