4.2 KiB
Generators & Sequences
Sequences of values drive music: arpeggios, parameter sweeps, rhythmic patterns. Cagire has dedicated words for building sequences on the stack, transforming them, and collapsing them to single values.
Ranges
.. pushes an integer range onto the stack. Both endpoints are inclusive. If start exceeds end, it counts down:
1 5 .. ;; 1 2 3 4 5
5 1 .. ;; 5 4 3 2 1
0 7 .. ;; 0 1 2 3 4 5 6 7
., adds a step parameter. Works with floats:
0 1 0.25 ., ;; 0 0.25 0.5 0.75 1
0 10 2 ., ;; 0 2 4 6 8 10
1 0 0.5 ., ;; 1 0.5 0 (descending)
geom.. builds a geometric sequence. Takes start, ratio, and count:
1 2 4 geom.. ;; 1 2 4 8
100 0.5 4 geom.. ;; 100 50 25 12.5
Musical use -- build a harmonic series:
110 2 5 geom.. 5 rev note
That gives you 110, 220, 440, 880, 1760 (reversed), ready to feed into note or freq.
Computed Sequences
gen executes a quotation n times and collects all results. The quotation must push exactly one value per call:
{ 1 6 rand } 4 gen ;; 4 random values between 1 and 6
{ coin } 8 gen ;; 8 random 0s and 1s
Contrast with times, which executes for side effects and does not collect. times sets @i to the current index:
4 { @i } times ;; 0 1 2 3 (pushes @i each iteration)
4 { @i 60 + note sine s . } times ;; plays 4 notes, collects nothing
The distinction: gen is for building data. times is for doing things.
Euclidean Patterns
euclid distributes k hits evenly across n positions and pushes the hit indices:
3 8 euclid ;; 0 3 5
4 8 euclid ;; 0 2 4 6
5 8 euclid ;; 0 1 3 5 6
euclidrot adds a rotation parameter that shifts the pattern:
3 8 0 euclidrot ;; 0 3 5 (no rotation)
3 8 1 euclidrot ;; 1 4 6
3 8 2 euclidrot ;; 1 4 6
These give you raw indices as data on the stack. This is different from bjork and pbjork (covered in the Randomness tutorial), which execute a quotation on matching steps. euclid gives you numbers to work with; bjork triggers actions.
Use euclid indices to pick notes from a scale:
: pick ( ..vals n i -- val ) rot drop swap ;
c4 d4 e4 g4 a4 ;; pentatonic scale on the stack
3 8 euclid ;; get 3 hit positions
Transforming Sequences
Four words reshape values already on the stack. All take n (the count of items to operate on) from the top:
rev reverses order:
1 2 3 4 4 rev ;; 4 3 2 1
c4 e4 g4 3 rev ;; g4 e4 c4 (descending arpeggio)
shuffle randomizes order:
c4 e4 g4 b4 4 shuffle ;; random permutation each time
sort and rsort for ascending and descending:
3 1 4 1 5 5 sort ;; 1 1 3 4 5
3 1 4 1 5 5 rsort ;; 5 4 3 1 1
Reducing Sequences
sum and prod collapse n values into one:
1 2 3 4 4 sum ;; 10
1 2 3 4 4 prod ;; 24
Useful for computing averages or accumulating values:
{ 1 6 rand } 4 gen 4 sum ;; sum of 4 dice rolls
Replication
dupn (alias !) duplicates a value n times:
440 3 dupn ;; 440 440 440
c4 4 dupn ;; c4 c4 c4 c4
Build a drone chord -- same note, different octaves:
c3 note 0.5 gain sine s .
c3 note 12 + 0.5 gain sine s .
c3 note 24 + 0.3 gain sine s .
Or replicate a value for batch processing:
0.5 4 dupn 4 sum ;; 2.0
Combining Techniques
An arpeggio that shuffles every time the step plays:
c4 e4 g4 b4 4 shuffle
drop drop drop ;; keep only the first note
note sine s .
Parameter spread across voices -- four sines with geometrically spaced frequencies:
220 1.5 4 geom..
4 { @i 1 + pick note sine s . } times
Euclidean rhythm driving note selection from a generated sequence:
3 8 euclid ;; 3 hit indices
A chord built from a range, then sorted high to low:
60 67 .. 8 rsort
Rhythmic density control -- generate hits, keep only the loud ones:
{ 0.0 1.0 rand } 8 gen
The generator words produce raw material. The transform words shape it. Together they let you express complex musical ideas in a few words.