poly length sequences - thebox.myzen.co.uk

By Mike Cook - Ex, Manchester Metropolitan University Department Of Mathematics And Physics (Retired)

Poly Length SequencesFor Polyrhythms and Polymelodies

BEAM - 2012 - June 22nd

Tuesday, 4 June 2013

The starting point

✤ A tool in music will often define the way it is used, more so than it might be originally thought.

✤ Let’s define a new tool, with no preconceptions of how to use it and see where that leads.


The Hexome

✤ A Hexome, is similar to its cousin the Monome.

✤ It is an interface rather than an instrument.

✤ Whereas the Monome has a cartesian arrangement of lights and switches, the Hexome distributes these controls and indicators on a hexagonal grid.


Hexome sequencer - radar sweep

✤ One form of sequencer that can be made using a Hexome is the radar sweep sequencer. Here cells are stepped through at a constant speed like a radar display.

✤ Not all the cells on the instrument are used.

✤ Each step involves 3 or 5 cells alternatively.


Hexome sequencer - orbit sweep

✤ Another form of sequencer that can be made using a Hexome is the orbit sweep sequencer. Here concentric circles of cells are stepped through at a constant speed. Like planets orbiting the sun.

✤ Because the concentric circles are of differing length a poly sequence is established.


Orbit Sweep

✤ The total number of steps in a complete sequence is the lowest common multiple of the number of cells in all the rings

✤ This gives rise to some interesting patterns


What was happening

✤ Each cell was stepped through in turn✤ A cell when selected produced a note when the cell was reached ✤ Each ring produced the same pitch of note✤ Inner rings had lower pitch notes than outer rings✤ Note shifting applied equally to all rings✤ Notes were shifted by thirds


Analysis

✤ Concentric rings have:-✤ 6 cells✤ 12 cells✤ 18 cells✤ 24 cells✤ So successive rings have✤ Rn = Rn-1 + 6 cells in it✤ Where Rn is the number of cells in ring number


Analysis


Connected space

✤ Each cell is surrounded by 6 other cells.✤ So the Hexome can be considered to map into 6 connected space

geometry.


N - Connected space

✤ This concept can be expanded to any arbitrary number N

✤ Where the number of points in successive rings would be:-✤ Rm = n + Rm-1 + Rm-2 ....... R1✤ Where m is the ring number and n is the connected space

✤ However, note that it is only possible to draw 6 connected space in two dimensions. Other connected spaces are only theoretical.

✤ But this does not prevent us from using the concept when exploring orbital sequences.


Exploring connected space

Rm = n + Rm-1 + Rm-2 ....... R1

✤ Tri - 3 Connected space. Sequence length 180✤ Quad - 4 Connected space. Sequence length 240✤ Pent - 5 Connected space. Sequence length 300✤ Hex - 6 Connected space. Sequence length 1080✤ Sept - 7 Connected space. Sequence length 41160✤ Oct - 8 Connected space. Sequence length 1920

With n = 6 - that is 6 concentric rings


Poly3 tool for exploring

✤ Pent - 5 Connected space. Sequence length 300


Non linear connected space

✤ Any ring can have any number of cells✤ Maximum sequence length with prime numbers in each ring✤ With 7 rings and < 32 cells per ring sequence length can be✤ 5,870,865 Steps long!

✤ This can be done with Poly3

http://www.thebox.myzen.co.uk/Mac_Apps/Processing.html


Just one more thing.

✤ What if the notes in a sequence were not fixed by the ring number?✤ Enter the RFID sequencer, with connected space stepping modes


RFID Sequencer


RFID Sequencer

✤ Only the first 8 cells in a sequence are accessible


By Mike Cook - Ex, Manchester Metropolitan University Department Of Mathematics And Physics (Retired)

Poly Length SequencesFor Polyrhythms and Polymelodies

Thank you


poly length sequences - thebox.myzen.co.uk

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