Numerology Techniques #3 : Discrete Sequencing

Now we come to a compositional technique that is really the core of what Numerology is all about, something called "Discrete Sequencing". This is a technique that makes Numerology truly unique. Although there are a few other software programs that can emulate this approach, none can do it with the ease or flexibility you will see here. In addition, this lesson will introduce you to CV and Gate data streams, and show you how to view and modify connections between modules.

In our previous lesson, we used a pair of sequencing modules that generated MIDI Notes directly into AU synthesizer modules. In order to add variety to the composition, we set them up to run at slightly different lengths, so that their melodic patterns would continually move against each other.

Here, instead of using sequencers that generate MIDI notes, we will use sequencers that generate sub-components of notes, specifically, pitch intervals and gate values. This allows us to do some amazing things very easily:

• We can vary the rhythmic part of our melody independently of the pitched part.
  
  
• By using multiple Pitch Interval Sequencers, we can easily setup a chord progression, and maintain the ability to edit the melody and the progression independently.
  
  
• By manipulating the rate and length of multiple Pitch Interval Sequencers, we can setup complex melodic transpositions that remain easy to control and experiment with.

• An IntervalSeq module, for generating pitch intervals.
• A GateSeq, for generating rhythmic values.
• A NoteGen module, for creating notes based on inputs from the IntervalSeq and GateSeq.

Having separate sequencers for pitch and rhythmic values allows us to manipulate each independently of the other. This is a type of isorhythm. The example continues by adding a second IntervalSeq to create a chord progression, then shows how by modifying the secondary sequencer, we can explore a range of melodic composition options based on selective transposition. Finally, a third IntervalSeq is added so that we can combine three pitch sources: one for melody, one for selective transposition, and a third for chord changes.

Musically, there are plenty of precedents for chord progressions, but the selective transposition technique shown here is a bit harder to nail down. There are a couple of very similar musical processes to consider. The example you will hear in this video is somewhat similar to the fast-picked guitar parts used by King Crimson in their early-mid 80's albums, such as Discipline. As described by Eric Tamm in Robert Fripp : from King Crimson to Guitar Craft,

among the most impressive passages in their music are those where two, three, or all four musicians are playing rapid-fire ostinatos that interlock and counterpoint each other in a glittering pointillistic texture reminiscent of the gamelan orchestras of Indonesia.
(p. 139)

The gamelan-like texture readily lends itself to polymeter -- where the players share a common pulse or beat, but group their beats in measures of different lengths. Such is the premise of the instrumental piece "Discipline", for instance, where beat groupings of two, three, four, five and even seventeen jockey for the baffled listener's attention.
(p. 140)

Although this example in the Numerology video is just a single part, near the end a 1-second delay is added so that you can hear the part playing against the delayed version of itself. And, as demonstrated in the previous lesson, it is not big deal to create multiple parts like this that explore a variety of polymetrical situations similar to what Tamm describes.

Another reference comes from a more remote location, Paul F. Berliner's classic ethnographic text The Soul of Mbira:

musicians themselves observe that a single mbira can produce the effect of two or more instruments being played simultaneously. One explanation for the apparent complexity of the music lies in a phenomenon known as "inherent rhyths." Inherent rhythms are those melodic/rhythmic patterns not directly being played by the performer but arising from the tonal complex of the mbira music. They are the product of the psycho-acoustic fact that the ear does not necessarily follow the precise linear melodic patterns being played; it picks out pitches of a similar level and groups them in separate independent phrases. Compositions of the Baroque period in which there is a contrapuntal dialogue between the upper and lower voices, such as the Bach unaccompanied violin and cello suites, create this effect in Western music.
(p. 88)

Here Berliner describes a musical effect produced by musicians playing the traditional Shona mbira music of Zimbabwe. Despite only playing a single note on the instrument at any one time, by alternating notes from different pitch ranges (typically in patterns of 3), the effect produced is one of multiple simultaneous melodic lines. The Numerology example explored in this video does not quite exhibit the stratification of pitch ranges necessary to achieve this effect, but it is very close to it, and certainly that is a promising avenue for further exploration.

The example file for this lesson has the same modules and patterns as in the video, but uses Apple's DLS synth so it will run regardless of what AU's you have installed.