n-rg-rd

Nørgård

v0.1.1

A small library to generate Nørgård infinity sequences for Norns.

Thank you to Ezra Buchla for his lua Nørgård algorithm and Lawton Hall for his Nørgård SuperCollider algorithms.

---

Install

You can install this library and demos via Maiden. Be sure to refresh the Community lists, and look for nørgård.

Otherwise, if you're a developer, pull down the library from Github and checkout the API below.

---

Usage

Look at the demos to see how the library can be used. The library itself is lib/noergaard.lua just add that file to your scripts folder, wherever you chose (I prefer lib/). Then add the following to your script.

local noergaard = include("path/to/noergaard")

---

Demos

Along with the library are 3 demos showing how to use the library.

noergaard-simple

Generates Nørgård infinity series and played using the PolyPerc engine. There are no controls, it just starts and goes on... infinitely

noergaard-sequencer

A fairly simple sequencer that plays infinity sequence — uses PolyPerc engine and also outputs Midi notes (to device 1).

Page	Controller	Description	Values
All	E1	Change page
1	E2	BPM	20 - 300
1	E3	note length	1/256 - 4
2	E2	Midi root	C-2 - C8
2	E3	Scale type (see norns/musicutil.lua for full list); 0 = scale determined naturally by algorithm	0 - 46
3	E2	Step	1 – 12
3	E3	Sequence length; 0 = maximum (or 480)	0 - 320
4	E2	Loop at length	true (1) or false (0)
4	E3	Increment	1 - 8

noergaard-chords

Generate chords from infinity series intervals — uses PolyPerc engine and also outputs Midi notes (to device 1). Thanks to Devine Lu Linvega for the keyboard.

Page	Controller	Description	Values
All	E1	Change page
1	E2	BPM	20 - 300
1	E3	note length	1/256 - 4
2	E2	Midi root	C-2 - C8
2	E3	Chord type (see norns/musicutil.lua for full list); 0 = build chord from sequence notes using amount determined by Chord length	0 - 26
3	E2	Step	1 – 12
3	E3	Sequence length; 0 = maximum (or 480)	0 - 320
4	E2	Loop at length	true (1) or false (0)
4	E3	Chord length; only applies when Chord type is set to Noergaard	2 - 9

---

API

Noergaard.compute(t, step)

Nørgård algorithm to compute intervals. Thank you @zebra! https://llllllll.co/t/35657/9

Parameters

t a table containing at least 2 values

step (optional, default=1) new interval step

Returns

nothing; new value is appended to the table in-place

Noergaard.integer(index)

Returns integer in infinity series by index. https://www.lawtonhall.com/blog/2019/9/9/per-nrgrds-infinity-series

Parameters

index index of infinity series to calculate

Returns

Nørgård number

Noergaard.compute_subset(start_index, end_index)

Populates intervals table with Nørgård integers within a given range. https://www.lawtonhall.com/blog/2019/9/9/per-nrgrds-infinity-series

Parameters

start_index starting index of infinity series

end_index ending index of infinity series

Noergaard.step()

Adds interval to table, based on "start" and "step" params.

Noergaard.get_step()

Gets step increment.

Returns

Step interval

Noergaard.get_interval(index)

Gets interval.

Parameters

index (optional) interval index; no index returns last added interval

Returns

Interval

Noergaard.get_midi_note(index)

Gets Midi note number.

Parameters

index (optional) note index; no index returns last added note

Returns

Midi note number

Noergaard.get_midi_note_scale(scale_type, index)

Gets Midi note number, snapped to given scale.

Parameters

scale_type String defining scale type (eg, "major", "aeolian" or "neapolitan major"), see "musicutil" class for full list.

index (optional) note index; no index returns last added note

Returns

Midi note number

Noergaard.get_midi_root()

Gets Midi root note as name + octave e.g. "C4".

Returns

Midi root note

Noergaard.get_note_name(index)

Gets Midi note name e.g. "C".

Parameters

index (optional) note index; no index returns last added note

Returns

Midi note name

Noergaard.get_note_freq(index)

Gets note as frequency name e.g. C4 => "261.63".

Parameters

index (optional) note index; no index returns last added note

Returns

Note frequency

Noergaard.get_note_freq_scale(scale_type, index)

Gets note as frequency name e.g. C4 => "261.63", mapped to given scale

Parameters

scale_type String defining scale type (eg, "major", "aeolian" or "neapolitan major"), see "musicutil" class for full list.

index (optional) note index; no index returns last added note

Returns

Note frequency

Noergaard.set_octave(index)

Sets octave to lock Midi notes to.

Parameters

index (optional) Midi octave value -2 to 8; no index sets octave to "Natural".

Noergaard.get_octave()

Gets octave as string.

Returns

Octave value

---

Params

params:set("noergaard_start", num)

Sets seed starting value, setting/changing this will reset the interval values table; default = 0

params:get("noergaard_start")

Returns seed starting value

Range

0 – 12

params:set("noergaard_step", num)

Sets seed step value, setting/changing this will reset the interval values table; default = 1

params:get("noergaard_step")

Returns seed step value

Range

1 – 12

params:set("noergaard_midi_root", num)

Sets root (starting) note for all Midi subsequent notes.

params:get("noergaard_midi_root")

Returns Midi root (starting) note as number

Range

0 – 128

params:set("noergaard_octave", num)

Sets octave for notes returned any value above 0 locks the returned notes to that octave; default = 0 (or Natural)

params:get("noergaard_octave")

Range

• 0: Natural, i.e. what the algorithm would naturally generate
• 1: -2
• 2: -1
• 3: 0
• 4: 1
• 5: 2
• 6: 3
• 7: 4
• 8: 5
• 9: 6
• 10: 7
• 11: 8

params:set("noergaard_len", num)

Sets a specific maximum number for intervals, a value of 0 means no defined length, but the maximum is 480; default = 0

params:get("noergaard_len")

Range

0 – 480

---

References

• Per Nørgård
• A guide to Per Nørgård's music
• Per Nørgård's infinity sequence
• Composition Toolkit Blog - Generative Techniques
• Per Nørgård's Infinity Series