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Measuring harmonic distance and locating harmonic goals is the most advanced and difficult aspect of listening to classical music. It’s easy to “feel at sea”: Just as it’s hard to orient yourself in the middle of the Atlantic, it’s hard to locate oneself harmonically: There are no visual signposts, no verbal explanations; everything has to be apprehended by ear. Each tonal work is at liberty to go its own way: There is no obligation to modulate to certain keys or travel a certain distance around the circle of fifths . Some pieces may limit themselves to neighboring keys; others may range more broadly. It’s necessary to follow each work on its own terms.

There is a lot to be gained by measuring harmonic distance : Tonal music creates suspense and excitement by moving away from the tonic to some extreme point and then finding a way back. Where the harmony ends up can have great structural and expressive significance. So, while this is one of the most challenging aspects of hearing harmony , it is also one of the most meaningful and rewarding.

Tonal works frequently begin by modulating to closely related keys and then gradually move farther away, before tracing their eventual return. Composers frequently reinforce their harmonic odyssey with perceptual cues. One of the most common is the introduction of a new theme. Often the theme will be of a contrasting character, adding a change in tone or spirit to the change in key.

Wolfgang Amadeus Mozart’s Symphony No. 41, “Jupiter,” opens with an assertive, martial theme.

Mozart marks the first main goal of modulation , the key of the dominant, with a new, gentler theme.

Ludwig van Beethoven’s Symphony No. 5 has one of the famous main themes in all of classical music.

Beethoven heralds his first goal of modulation — the relative Major, E-flat Major — with a new theme: The aggressiveness of the opening is supplanted by greater lyricism. Notice, though, that there is as a subtle reminder of where the music has come from: The rhythmic motto of the opening is embedded in the accompaniment, eventually coming to the fore at the end of the excerpt.

In many works, greater harmonic distance is associated with greater thematic transformation : The main material is generally most complete, stable and secure in the home key. The farther you stray from home, the more irregular the material becomes.

In. the Finale of Mozart’s Symphony No. 40 in g-minor, the violins initially present the main theme, with the winds playing a subsidiary role.

Throughout the movement, as Mozart gradually advances from the tonic, he moves farther and farther away from the original orchestration. At the start of this excerpt, the head motive of the theme is traded between the strings and winds. Eventually, the music makes it halfway around the circle of fifths — an extraordinary harmonic distance ! Mozart reinforces the remoteness of the key with an orchestration that is likewise very displaced from the original: The violins are silent. Instead, the cellos and the winds — who played only a supporting role at the outset — are now featured: The theme’s orchestration has turned itself inside out!

The Finale of Ludwig van Beethoven’s Piano Sonata in A-flat Major, opus 110 opens with a rising theme.

The texture gradually thickens and the music begins to modulate . As the music moves farther away from the tonic, anomalies begin to occur — including, very unusually, a refrain of the somber melody of an earlier movement. Finally at the most remote key, the harmony stops dead in its tracks. After resting here for a remarkably long time, another surprising thing occurs: the Finale’s theme reenters — upside down!

Thus, Beethoven sculpts a topography where greater distance from the tonic equals greater transformation . Even if you can’t recognize by ear that the music has moved from A-flat Major all the way to G-Major, Beethoven’s perceptual cues alert you that you have reached somewhere wild and strange.

Beethoven concludes with a triumphant return to the original key, with the theme turned right side up again and fully harmonized:

Scientists have demonstrated that long-term pitch memory can easily be disoriented : Therefore, supporting pitch memory with perceptual cues is very important for following large-scale harmonic structure . The main theme of Haydn’s Symphony No. 102 in B-flat Major is introduced by the strings:

At the end of a long modulating section, Haydn returns to the main theme. Is it in its original key? Haydn leaves a clue...

Instead of the strings, the flute is playing the theme: This is Haydn’s hint that the key is different. The prevention of closure at the end of the excerpt is a reminder that the main tonic has not been reached yet.

A little later, the theme returns—this time will all of the trappings of home.

When you’re driving, you count on standard highway signs to make quick and safe decisions. Classical works do not use perceptual cues so consistently; instead, each piece bears the stamp of individuality, not only in its themes but also in its formal unfolding and structural markers. You have to learn the road signs for each piece separately. These types of variables and nuances are why listening to classical music takes careful attention and repeated listening. With experience, you will be better able to recognize perceptual cues and interpret their significance.

It makes intuitive sense that harmonic distance and thematic transformation and contrast are often linked: The farther you get from home, the less recognizable your environment becomes. Listening for perceptual cues will help you apprehend the difference between the closest and most distant harmonic goals in a modulating work.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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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.
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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?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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?
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s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
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Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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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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