6.8 KiB
Notes & Harmony
Cagire speaks music theory. Notes, intervals, chords, and scales are all first-class words that compile to stack operations on MIDI values. This tutorial covers every pitch-related feature.
MIDI Notes
Write a note name followed by an octave number. It compiles to a MIDI integer:
c4 ;; 60 (middle C)
a4 ;; 69 (concert A)
e3 ;; 52
Sharps use s or #. Flats use b:
fs4 ;; 66 (F sharp 4)
f#4 ;; 66 (same thing)
bb3 ;; 58 (B flat 3)
eb4 ;; 63
Octave range is -1 to 9. The formula is (octave + 1) * 12 + base + modifier, where C=0, D=2, E=4, F=5, G=7, A=9, B=11.
Note literals push a single integer onto the stack, just like writing 60 directly. They work everywhere an integer works:
c4 note sine s . ;; play middle C as a sine
a4 note 0.5 gain modal s . ;; concert A, quieter
Intervals
An interval duplicates the top of the stack and adds semitones. This lets you build chords by stacking:
c4 M3 P5 ;; stack: 60 64 67 (C major triad)
c4 m3 P5 ;; stack: 60 63 67 (C minor triad)
a3 P5 ;; stack: 57 64 (A plus a fifth)
Simple intervals (within one octave):
| Interval | Semitones | Name |
|---|---|---|
P1 / unison |
0 | Perfect unison |
m2 |
1 | Minor 2nd |
M2 |
2 | Major 2nd |
m3 |
3 | Minor 3rd |
M3 |
4 | Major 3rd |
P4 |
5 | Perfect 4th |
aug4 / dim5 / tritone |
6 | Tritone |
P5 |
7 | Perfect 5th |
m6 |
8 | Minor 6th |
M6 |
9 | Major 6th |
m7 |
10 | Minor 7th |
M7 |
11 | Major 7th |
P8 |
12 | Octave |
Compound intervals (beyond one octave):
| Interval | Semitones |
|---|---|
m9 |
13 |
M9 |
14 |
m10 |
15 |
M10 |
16 |
P11 |
17 |
aug11 |
18 |
P12 |
19 |
m13 |
20 |
M13 |
21 |
m14 |
22 |
M14 |
23 |
P15 |
24 |
Chords
Chord words take a root note and push all the chord tones. They eat the root and replace it with the full voicing:
c4 maj ;; stack: 60 64 67
c4 min7 ;; stack: 60 63 67 70
c4 dom9 ;; stack: 60 64 67 70 74
Triads:
| Word | Intervals | Example (C4) |
|---|---|---|
maj |
0 4 7 | 60 64 67 |
m |
0 3 7 | 60 63 67 |
dim |
0 3 6 | 60 63 66 |
aug |
0 4 8 | 60 64 68 |
sus2 |
0 2 7 | 60 62 67 |
sus4 |
0 5 7 | 60 65 67 |
Seventh chords:
| Word | Intervals | Example (C4) |
|---|---|---|
maj7 |
0 4 7 11 | 60 64 67 71 |
min7 |
0 3 7 10 | 60 63 67 70 |
dom7 |
0 4 7 10 | 60 64 67 70 |
dim7 |
0 3 6 9 | 60 63 66 69 |
m7b5 |
0 3 6 10 | 60 63 66 70 |
minmaj7 |
0 3 7 11 | 60 63 67 71 |
aug7 |
0 4 8 10 | 60 64 68 70 |
Sixth chords:
| Word | Intervals | Example (C4) |
|---|---|---|
maj6 |
0 4 7 9 | 60 64 67 69 |
min6 |
0 3 7 9 | 60 63 67 69 |
Extended chords:
| Word | Intervals | Example (C4) |
|---|---|---|
dom9 |
0 4 7 10 14 | 60 64 67 70 74 |
maj9 |
0 4 7 11 14 | 60 64 67 71 74 |
min9 |
0 3 7 10 14 | 60 63 67 70 74 |
dom11 |
0 4 7 10 14 17 | 60 64 67 70 74 77 |
min11 |
0 3 7 10 14 17 | 60 63 67 70 74 77 |
dom13 |
0 4 7 10 14 21 | 60 64 67 70 74 81 |
Add chords:
| Word | Intervals | Example (C4) |
|---|---|---|
add9 |
0 4 7 14 | 60 64 67 74 |
add11 |
0 4 7 17 | 60 64 67 77 |
madd9 |
0 3 7 14 | 60 63 67 74 |
Altered dominants:
| Word | Intervals | Example (C4) |
|---|---|---|
dom7b9 |
0 4 7 10 13 | 60 64 67 70 73 |
dom7s9 |
0 4 7 10 15 | 60 64 67 70 75 |
dom7b5 |
0 4 6 10 | 60 64 66 70 |
dom7s5 |
0 4 8 10 | 60 64 68 70 |
Chord tones are varargs -- they eat the entire stack. So a chord word should come right after the root note:
c4 maj note sine s . ;; plays all 3 notes as one chord
Scales
Scale words convert a degree index into a MIDI note. The base note is C4 (MIDI 60). Degrees wrap around with octave transposition:
0 major ;; 60 (C4 -- degree 0)
4 major ;; 67 (G4 -- degree 4)
7 major ;; 72 (C5 -- degree 7, wraps to next octave)
-1 major ;; 59 (B3 -- negative degrees go down)
Use scales with cycle or rand to walk through pitches:
0 1 2 3 4 5 6 7 8 cycle minor note sine s .
Standard modes:
| Word | Pattern (semitones) |
|---|---|
major |
0 2 4 5 7 9 11 |
minor |
0 2 3 5 7 8 10 |
dorian |
0 2 3 5 7 9 10 |
phrygian |
0 1 3 5 7 8 10 |
lydian |
0 2 4 6 7 9 11 |
mixolydian |
0 2 4 5 7 9 10 |
aeolian |
0 2 3 5 7 8 10 |
locrian |
0 1 3 5 6 8 10 |
Pentatonic and blues:
| Word | Pattern |
|---|---|
pentatonic |
0 2 4 7 9 |
minpent |
0 3 5 7 10 |
blues |
0 3 5 6 7 10 |
Chromatic and whole tone:
| Word | Pattern |
|---|---|
chromatic |
0 1 2 3 4 5 6 7 8 9 10 11 |
wholetone |
0 2 4 6 8 10 |
Harmonic and melodic minor:
| Word | Pattern |
|---|---|
harmonicminor |
0 2 3 5 7 8 11 |
melodicminor |
0 2 3 5 7 9 11 |
Jazz / Bebop:
| Word | Pattern |
|---|---|
bebop |
0 2 4 5 7 9 10 11 |
bebopmaj |
0 2 4 5 7 8 9 11 |
bebopmin |
0 2 3 5 7 8 9 10 |
altered |
0 1 3 4 6 8 10 |
lyddom |
0 2 4 6 7 9 10 |
Symmetric:
| Word | Pattern |
|---|---|
halfwhole |
0 1 3 4 6 7 9 10 |
wholehalf |
0 2 3 5 6 8 9 11 |
augmented |
0 3 4 7 8 11 |
tritone |
0 1 4 6 7 10 |
prometheus |
0 2 4 6 9 10 |
Modal variants (from melodic minor):
| Word | Pattern |
|---|---|
dorianb2 |
0 1 3 5 7 9 10 |
lydianaug |
0 2 4 6 8 9 11 |
mixb6 |
0 2 4 5 7 8 10 |
locrian2 |
0 2 3 5 6 8 10 |
Octave Shifting
oct transposes a note by octaves:
c4 1 oct ;; 72 (C5)
c4 -1 oct ;; 48 (C3)
c4 2 oct ;; 84 (C6)
Stack effect: (note shift -- transposed). The shift is multiplied by 12 and added to the note.
Frequency Conversion
mtof converts a MIDI note to frequency in Hz. ftom does the reverse:
69 mtof ;; 440.0 (A4)
60 mtof ;; 261.63 (C4)
440 ftom ;; 69.0
Useful when a synth parameter expects Hz rather than MIDI:
c4 mtof freq sine s .
Putting It Together
A chord progression cycling every pattern iteration:
{ c3 maj7 } { f3 maj7 } { g3 dom7 } { c3 maj7 } 4 pcycle
note sine s .
Arpeggiate a chord across the step's time divisions:
c4 min7 arp note 0.5 decay sine s .
Random notes from a scale:
0 7 rand minor note sine s .
A bass line walking scale degrees:
0 2 4 5 7 5 4 2 8 cycle minor note
-2 oct 0.8 gain sine s .
Chord voicings with random inversion:
e3 min9
{ } { 1 oct } 2 choose
note modal s .
Stacked intervals for custom voicings:
c3 P5 P8 M10 ;; C3, G3, C4, E4
note sine s .