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Melody          
Toch defines melody as a temporal succession of music tones.  Copland sees melody in the same way but makes a good case for the relationship between melody and the musical scale that defines an octave.  They are both right.  Melody is one tone following another.  They might well argue about where that tone originated – within a chromatic scale or diatonic scale or even outside of such conventions.
The first step in understanding a melody is to identify its “motive” or theme.  Often musicians use the French term “motif.”  A motif or motive or theme is generally considered to be the basic unit of a complete musical thought.  Think of a motif in the same way you think of a phrase in the English language.   

In the examples that follows, you need not be able to read music in order to identify each of the four motifs. Notice how they repeat and how each motif differs from the other. The first motive contains an ascending line of three tones terminated with a single descending tone. The second motive is an ascending line of three tones that begins a little higher than the first. The third motif is a descending line. The fourth motive rocks back and forth on the opening tone to close the composition. 

Click here to see the motive in the song Are You Sleeping Brother John?

Motifs will be introduced by composers and then augmented, stretched, embellished, diminished and otherwise altered to hold the interests of listeners. Well-written music introduces a motif, plays with it and then restates it to keep the listener oriented to the music. Much of a composer’s work is finding ways to vary the motif. 

Click here to see an example of how a composer varies a motif. 
The piece is an Irish Aire titled The South Wind.     

See how the second statement of the motif has the identical rhythmic pattern of the first, but uses different tones. 

Motifs have parts too and these are called “germs.” A germ is a basic unit within a motif. Musical germs are often recognized because they are repeated within a motive or shared either rhythmically or melodically among several motifs.

Click here to see a germ within Are You Sleeping Brother John?
Click here to see the recurrent germ within South Wind.
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Melodic Shape
Toch was the first person to describe melody as a “wave.”  He wrote that “with the combination of ascending and descending scale-segments, melody approaches its real nature:  the ‘wave’.”  There are nine general wave shapes in music:

The Wave  - A gentle undulation.  Gregorian chants are examples.  This shape produces tranquil melodies.

The Rising Wave – This form swoops up in a series of small waves.  It rises and drops back and then rises again.  After its grand climax this shape drops off.  Each successive crest of the wave is successively higher.

The Falling Wave – This form starts up and comes down in a series of successively small waves.

The Arch – The piece rises and falls gently with the peak or climax in the middle.  The arch may be a series of small waves leading to the peak in the middle.  In this case, the shape is known as the “ornamental arch”.

The Bowl – This is an inverted arch.  Instead of a peak in the middle, there is a pit in the middle of the piece.   Handel’s Joy to the World is an example.

The Rising Line – This form is a straight, linear rise to a high point.  Ravel’s Bolero is an example

The Falling Line– This form is a straight, linear decline to a low point.  The form is often found in scores written for the movies.  Think of an action scene that terminates in a static scene.  The music helps the listener make the transition from high energy to low energy.

The Horizontal Line – This form stays at one level through the music.  Hip-Hop and heavy metal music typically employ a horizontal line form often impressed into the recording by electronic techniques that eliminate all the natural dynamic range. 

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To hear samples from Said the Moon or Spring Tide on the Tump,
  Click on the images.