On Melodic (and other types of) Contour

The term ‘contour’ can have a lot of meanings in music-at various levels of specificity. To some, it can refer vaguely to variations in intensity or energy (which can be accounted for by numerous factors including dynamics, texture, or rhythm). In fact, the way that anything that changes over time or space could be described in terms of contour in some way. (We could discuss the contour of a Porsche or Corvette from front to back, or the contour of a sports fan’s emotions over the course of a championship game played by his or her favorite team.)

For our purposes, we’ll need a way of communicating specifically about contour, and for that reason, we’ll use the contour segment (hereafter referred to as “cseg”) to describe contours and contour relationships.1 For this reading, we’ll discuss simple pitch contours. Pitch contours describe the general and relative up-ness and down-ness of melodic pitches. Take, for instance, the short subject of J.S. Bach’s Fugue in E major from the Well-Tempered Clavier, book 2.

Example 1: J. S. Bach, Fugue no. 9 in E major (WTC 2)

This opening of this theme has a contour that we can describe with cseg <0 1 3 2 1>. Each number in this ordered series refers to the relative height of each pitch. The lowest pitch in the theme gets the number zero, and all of the other pitches are numbered in relation to it in order from the next lowest to the highest. In other words,

E is the lowest note, which gets the number ‘0.’ F# is the 2nd to the lowest note, so it gets the number ‘1’ each time it sounds. G# is the next one higher, so it gets the number ‘2.’ A, being the highest, gets the number ‘3’

Naturally, the order of the pitches in the music gives the motive its shape, and it is for this reason that ordering is expressed in the contour segment.

1 The cseg model is discussed in Marvin, Elizabeth W. and Paul Laprade. 1987. “Relating Musical Contours: Extensions of a Theory for Contour,” Journal of Music Theory 31: 225 –67.

It is important to remember that contour segments are not interval-specific. That is, two melodies with very different intervals can have exactly the same melodic contour as long as they have the same basic shape (i.e., the same general up-and-down profile). Example 2 shows a melody with an equivalent contour but very different intervals.

Example 2: Another possible realization of contour segment <0 1 3 2 1>

cseg <0 1 3 2 1>

See how the first melodic tone is still the lowest, the next melodic tone is still the second from the lowest, etc? This is basically how csegs work. Below are some more contour segments from fairly well known melodies.

Example 3a: Eine kleine Nachtmusik (melody only)

cseg <1 0 1 0 1 0 1 2 3>

Example 3b Haydn Sonata no. 60 (parsed into smaller, relevant contour motives)

cseg < 3 1 2 0> <3 1 2 0> <0 1 3 2>

Example 3c Schoenberg Drei Klavierstuk, op. 11 no. 1

cseg < 5 3 2 4 1 0>

Note that in Example 3c, the cseg does not acknowledge the repetition of the note ‘F4.’ Contour segments usually do not acknowledge immediate repetitions of elements, as their function is only to describe general shape.

Cseg Families

An interesting thing about contour relationships is that segments easily form families. In fact, some composers have a lot of fun developing motives by using contour segments from the same family. A family of contour segments involves the prime (original), retrograde (backwards), inversion (upside-down), and retrograde inversion (upside-down and backwards). Lets take a relatively simple contour to demonstrate.

Example 4a: the family of contour segments about cseg <3 0 1 2>

P (prime): cseg <3 0 2 1>R (retrograde): cseg <1 2 0 3>I (inversion): cseg <0 3 1 2>RI (retrograde-inversion): cseg <2 1 3 0>

Example 4b: some possible realizations of this contour family

Clearly, the retrograde contour is determined by simply reversing the prime contour. The inversion, however, needs a little explanation. To invert a contour, we reverse the extremes so that the lowest number is the highest and the highest is the lowest. It follows that the 2nd-from-lowest becomes the 2nd-from-highest, and the 2nd-from- highest becomes the second-from-lowest. For this reason, the ‘3’ in Example 4b becomes ‘0’ in the inversion, while the ‘0’ becomes ‘3,’ the ‘1’ becomes ‘2’ and the ‘2’

becomes ‘1.’ Perhaps a more intuitive way to describe this would be that in Example 4b, the original cseg <3 0 1 2> starts with a large downward leap and is followed by movement upward that begins to fill in the gap left by the large leap. The inverted contour begins with an upward leap, and is followed by movement downward, producing cseg <0 3 2 1>. The retrograde inversion is simply the backwards form of the inversion.2

Perhaps the neatest thing about melodic contours is that they’re audible (that is, perceiving relative pitch height isn’t too difficult). Furthermore, it’s often easy to hear the relatedness of contour segments that are in the same family. You should practice making cseg families with the following ‘Prime’ csegs. Be sure to determine the R, I, and RI forms of each one. (Note: it may be possible for two cseg forms in a family to be indentical.)

cseg <1 3 0 2> cseg <3 1 2 0> cseg <4 2 0 3 1> cseg <1 2 0 4 3> cseg <0 1 2>

Melodic Contour AnalysisStefan Wolpe’s Solo Piece for Trumpet, mvt. II

Please take the time to listen to, sight-sing, or play through the second movement of Wolpe’s Solo Piece for Trumpet. This piece features many melodic gestures that invite comparison, even though the intervallic content of those gestures often are not equivalent. Consider, for instance the end of line 2 and the beginning of line 4, as shown in Examples 5a and 5b. Both of these gestures express the same melodic contour.

Example 5a: end of line 2

cseg <4 3 1 2 5 0>

Example 5b: beginning of line 4

2 FYI: While it’s often convenient to think of RI-forms as retrogrades of inversions, it’s also equally informative (and correct) to think of them as inversions of retrogrades.

cseg <4 3 1 2 5 0>

Equivalent csegs sound across line 3, as shown in Example 6a. The first occurrence is really part of a slightly longer gesture, comprising the 32nd notes on B3 that precedes it and the C4 that follows. However, the idea expressed by cseg <1 0 2 3> within this gesture clearly takes center stage for the rest of the line. Cseg <1 0 2 3>) is also expressed toward the end of line 4 by the notes Ab4, G4, A4, and C5, as well as in the first four notes of line 2 (C4, G3, Db4, and Bb4). Example 6b illustrates.

Example 6a: cseg <1 0 2 3> across line 3

cseg <1 0 2 3> <1 0 2 3> <1 0 2 3>

Example 6b: cseg <1 0 2 3> at the end of line 4

cseg < 1 0 2 3>

The last four notes of the opening gesture of this movement present cseg <0 2 3 1>. Example 7a illustrates. The retrograde of this motive (cseg <1 3 2 0>) sounds toward the end of line 4 with A5 and C5, and continues onward onto line 5 with B4 and F#4. The retrograde inversion of this motive (cseg <2 0 1 3>) sounds immediately afterward with F4, D4, E4, and A4. Examples 7b and 7c illustrate.

Example 7a: cseg <0 2 3 1> in the opening gesture

cseg <0 2 3 1>

Example 7b: cseg <1 3 2 0> (retrograde of cseg <0 2 3 1 >) crossing lines 4 and 5

cseg <1 3 2 0>

Example 7c: cseg <2 0 1 3> (retrograde inversion of cseg <0 2 3 1>)

cseg < 2 0 1 3>

Finally, an important subset of cseg <0 2 3 1> from the opening gesture involves its final three pitches: Ab4, Db5, and G4. They form cseg <1 2 0>, which sounds at the end of line 2 (Gb4, Db5, B3), at the end of the first gesture of line 3 (G4, D5, C4), and at the end of the first gesture of line 4 (Ab4, Db5, Gb4). Please consult the score or simply listen to the movement, and you’ll observe these occurrences readily enough.