Melody and Counterpoint

Melody is most often associated with a musical ‘surface’; the portion of a composition that we might hum or whistle. While a thorough discussion of what constitutes a ‘good’ melody is well beyond our objectives here, there are two elements present in all melody: pitch and rhythm. We basically need to manipulate these two elements so they work together to produce the desired melody.

Basic Melody Creation

In general, any Track component can create basic ‘melody’ by assigning a ‘General Composition’ algorithm(s) to its ‘Pitch’ and ‘Duration’ composition variables. A melody produced in this way may or may not ‘hold together’ as a coherent entity depending on the algorithm chosen and your particular musical tastes or objectives.

Luckily, ArtSong provides several techniques you can use to improve the coherence of a melody.

First of all, any of the rhythm controlling techniques demonstrated in Advanced Topics 1 Rhythm and Meter, such as algorithmically generated rhythms, rhythm strings (sequences of duration values), or a rhythm algorithm, can be applied to improve rhythmic coherence of the melody. Rhythm will not be discussed again here.

Controlling the ‘pitch’ coherence of a melodic line is the principal objective of the techniques presented in this topic.

Improve Voice Leading

Voice leading refers to how ‘smoothly’ the individual melody notes connect. Conventional melodies often use stepwise motion between notes with more frequent small interval skips, and very infrequent larger interval skips. Modern ‘melodies’ can often contain numerous large-interval skips.

You can exert control over the size of intervals between adjacent pitches by using the ‘Change Limit %’ function for the ‘Pitch’ composition variable (Track Properties Editor)

The ‘Change Limit %’ variable governs the maximum difference allowed between adjacent variable values, expressed as a % of total range.

When the value is set to ‘100%” (default) any value within the range is possible each time a value is generated. Reducing the ‘Change Limit%’ value creates a temporary ‘value range’ around the previously generated value.

For a 2-octave initial pitch range, a setting of about 30% will limit the maximum interval between adjacent melody notes to about a fifth (2 octaves * 12 chromatic half-steps per octave * 0.3 = (approximately) 7 chromatic half-steps)

Control Melody Contour

Melody contour refers to the ‘pitch-time’ path the melody follows. ArtSong provides several different algorithms that can be used to create specific melody contours.

Envelope Algorithm

Use the Envelope algorithm (‘Control’ tab of Algorithms Palette) to create pitch contours.

• Draw an Envelope Component Event.
• Double-click in the ‘Pitch’ column to add a pitch envelope to any particular track. (or use the Add Button.
• Set the ‘Segment’ Lengths for each of the 3 envelope stages.
• Set the ‘Start%’ and ‘Range%’ for each of the 4 transition points.
• The generated pitches will follow the designated contour within the boundaries set by the range limits.
  

Contour Algorithm

Add the Melody Contour algorithm (‘Melody / Harmony’ tab of Algorithms Palette) to create pitch contours.

• Draw in a Contour Event
• Add ‘Primary Contour’ (first button on left): the center line represents the Starting Pitch Value as set in Tracks Property Editor. Each line above and below the center line represents one octave.
• Click and drag the mouse to add the primary contour.

Use the Options menu to set the resolution of the curve.

[Normal resolution provides 8 measures (4/4) of eighth note resolution, High provides 8 measures of sixteenth note resolution, Low provides 8 measures of quarter note resolution]

All contours will have a ‘Primary’ Contour. Additional options are also available.

[optional] Add secondary contour (select second button). Where a secondary contour exists and the primary contour is above the secondary (shown in yellow above) the melody oscillates between the two curves. Where a secondary contour exists and the primary contour is drawn below the secondary (shown in red above) the melody still oscillates between the two curves but additional passes through the mid-point. Use the secondary contour to create some melody effects.

The remaining buttons are used to erase portions of the secondary contour or to perform invert and retrograde operations on the curves themselves.

Fourier Algorithm

The Fourier Algorithm, located on the ‘General’ tab of Algorithms Palette, can also be used to create pitch contours.

This algorithm works by summing a weighted set of sine waves having a designated frequency and phase relationship.

CounterPoint

Multiple melodies sounding simultaneously is referred to as counterpoint. A principal concern in composing counterpoint is the independence of the individual melodies. Moving the melodies in contrary motion (when one melody’s pitch rises the other melody’s pitch falls) is used to preserve independence.

ArtSong’s ChaosMapper and ImageMapper algorithms can be used to create contrary motion between different tracks.

CounterPoint with ChaosMapper Algorithm

We have already encountered the ChaosMapper in Tutorial 3; please refer to the tutorial for additional information on how this algorithm converts movement along a chaotic function attractor to musical parameter values.

• We can create contrary pitch motion in two melody lines by using a ‘normal’ pitch mapping for one and the ‘inverse’ mapping for the other.
• The figure above demonstrates mapping the ‘X’ position to Track 1 pitch and its inverse to Track 2 pitch. This mapping ensures that when the pitch in Track 1 rises the pitch in Track 2 falls.

CounterPoint with ImageMapper Algorithm

The Image Mapper algorithm (below) provides a richer set of possibilities.

Like the Chaos Mapper algorithms there are also two versions of the Image Mapper algorithm. One that uses Iterated Function System (IFS) attractors and another that uses Quadratic function attractors. In addition there is also a version that traces a hand-drawn Free Form trajectory over the image.

1. The Image Mapper algorithm however uses the x, y position along the function attractor to select a point in an image.
2. It is the color at that point in the underlying image that gets mapped to the indicated composition variable. The Image Mapper algorithm allows you to map any pure color (Red, Green, or Blue) or combination of colors (RedGreen, RedBlue, RedGreenBlue, etc) or their Inverses (1 – R, 1 – RG, 1 – RGB, etc.) to the composition variables.
3. The figureabove demonstrates mapping the ‘RB’ color component to Track 1 pitch and its inverse ‘1-RB’ to Track 2 pitch. Again, this mapping ensures that when the pitch in Track 1 rises the pitch in Track 2 falls.

Of course this same technique can be used in many other ways, e.g. to create notes that increase duration as the pitch rises set both the ‘Pitch’ and ‘Duration’ composition values to the same mapping.