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
This video will explore each of these options in a systematic manner. It starts
by setting up three modules that form the core of the technique:
- 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
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.
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.
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
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.
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.