457 lines
9.8 KiB
Markdown
457 lines
9.8 KiB
Markdown
# Notes & Harmony
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This tutorial covers everything pitch-related: notes, intervals, chords, voicings, transposition, scales, and diatonic harmony. Each section builds on the previous one.
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## Notes
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A note name followed by an octave number compiles to a MIDI integer:
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```forth
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c4 note sine snd .
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```
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That plays middle C (MIDI 60). `a4` is concert A (69), `e3` is 52. Sharps use `s` or `#`, flats use `b`:
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```forth
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fs4 note 0.5 decay saw snd .
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```
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```forth
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eb4 note 0.8 decay tri snd .
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```
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`fs4` and `f#4` both mean F sharp 4 (MIDI 66). `bb3` is B flat 3 (58). Octave range is -1 to 9.
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Notes are just integers. They work anywhere an integer works — you can do arithmetic on them, store them in variables, pass them to any word that expects a number.
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## Intervals
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An interval duplicates the top of the stack and adds semitones. Stack two intervals to build a chord by hand:
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```forth
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c4 M3 P5 note 1.5 decay sine snd .
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```
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That builds a C major triad from scratch: C4 (60), then a major third above (64), then a perfect fifth above the root (67). Three notes on the stack, all played together.
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```forth
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a3 m3 P5 note 1.2 decay saw snd .
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```
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A minor triad: A3, C4, E4.
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**Simple intervals** (within one octave):
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| Interval | Semitones | Name |
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|----------|-----------|------|
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| `P1` / `unison` | 0 | Perfect unison |
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| `m2` | 1 | Minor 2nd |
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| `M2` | 2 | Major 2nd |
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| `m3` | 3 | Minor 3rd |
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| `M3` | 4 | Major 3rd |
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| `P4` | 5 | Perfect 4th |
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| `aug4` / `dim5` / `tritone` | 6 | Tritone |
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| `P5` | 7 | Perfect 5th |
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| `m6` | 8 | Minor 6th |
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| `M6` | 9 | Major 6th |
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| `m7` | 10 | Minor 7th |
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| `M7` | 11 | Major 7th |
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| `P8` | 12 | Octave |
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**Compound intervals** (beyond one octave):
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| Interval | Semitones |
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|----------|-----------|
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| `m9` | 13 |
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| `M9` | 14 |
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| `m10` | 15 |
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| `M10` | 16 |
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| `P11` | 17 |
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| `aug11` | 18 |
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| `P12` | 19 |
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| `m13` | 20 |
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| `M13` | 21 |
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| `m14` | 22 |
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| `M14` | 23 |
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| `P15` | 24 |
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Custom voicings with wide intervals:
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```forth
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c3 P5 P8 M10 note 1.5 decay sine snd .
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```
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C3, G3, C4, E4 — an open-voiced C major spread across two octaves.
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## Chords
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Chord words replace a root note with all the chord tones. They're shortcuts for what intervals do manually:
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```forth
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c4 maj note 1.5 decay sine snd .
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```
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That's the same C major triad, but in one word instead of `M3 P5`. A few more:
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```forth
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d3 min7 note 1.5 decay saw snd .
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```
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```forth
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e3 dom9 note 1.2 decay saw snd .
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```
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```forth
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a3 sus2 note 1.5 decay tri snd .
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```
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Common triads:
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| Word | Intervals |
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|------|-----------|
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| `maj` | 0 4 7 |
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| `m` | 0 3 7 |
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| `dim` | 0 3 6 |
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| `aug` | 0 4 8 |
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| `sus2` | 0 2 7 |
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| `sus4` | 0 5 7 |
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| `pwr` | 0 7 |
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Common seventh chords:
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| Word | Intervals |
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|------|-----------|
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| `maj7` | 0 4 7 11 |
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| `min7` | 0 3 7 10 |
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| `dom7` | 0 4 7 10 |
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| `dim7` | 0 3 6 9 |
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| `m7b5` | 0 3 6 10 |
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| `minmaj7` | 0 3 7 11 |
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| `aug7` | 0 4 8 10 |
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| `augmaj7` | 0 4 8 11 |
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| `7sus4` | 0 5 7 10 |
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Extended, add, altered, and other chord types are listed in the Reference section at the end.
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## Voicings
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Four words reshape chord voicings without changing the harmony.
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`inv` moves the bottom note up an octave (inversion):
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```forth
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c4 maj inv note 1.5 decay sine snd .
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```
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The root C goes up, giving E4 G4 C5 — first inversion. Apply it twice for second inversion:
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```forth
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c4 maj inv inv note 1.5 decay sine snd .
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```
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G4 C5 E5. `dinv` does the opposite — moves the top note down an octave:
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```forth
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c4 maj dinv note 1.5 decay sine snd .
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```
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G3 C4 E4. The fifth drops below the root.
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`drop2` and `drop3` are jazz voicing techniques for four-note chords. `drop2` takes the second-from-top note and drops it an octave:
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```forth
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c4 maj7 drop2 note 1.2 decay saw snd .
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```
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From C4 E4 G4 B4, the G drops to G3: G3 C4 E4 B4. `drop3` drops the third-from-top:
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```forth
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c4 maj7 drop3 note 1.2 decay saw snd .
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```
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E drops to E3: E3 C4 G4 B4. These create wider, more open voicings common in jazz guitar and piano.
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## Transposition
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`tp` shifts every note on the stack by N semitones:
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```forth
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c4 maj 3 tp note 1.5 decay sine snd .
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```
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C major transposed up 3 semitones becomes Eb major. Works with any number of notes:
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```forth
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c4 min7 -2 tp note 1.5 decay saw snd .
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```
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Shifts the whole chord down 2 semitones (Bb minor 7).
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`oct` shifts a single note by octaves:
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```forth
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c4 1 oct note 0.3 decay sine snd .
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```
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C5 (one octave up). Useful for bass lines:
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```forth
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0 2 4 5 7 5 4 2 8 cycle minor note
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-2 oct 0.8 gain sine snd .
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```
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## Scales
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Scale words convert a degree index into a MIDI note. By default the root is C4 (MIDI 60):
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```forth
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0 major note 0.5 decay sine snd .
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```
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Degree 0 of the major scale: C4. Degrees wrap with octave transposition — degree 7 gives C5 (72), degree -1 gives B3 (59).
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Walk through a scale with `cycle`:
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```forth
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0 1 2 3 4 5 6 7 8 cycle minor note 0.5 decay sine snd .
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```
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Random notes from a scale:
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```forth
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0 7 rand pentatonic note 0.8 decay saw snd .
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```
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### Setting the key
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By default scales are rooted at C4. Use `key!` to change the tonal center:
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```forth
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g3 key! 0 major note 0.5 decay sine snd .
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```
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Now degree 0 is G3 (55) instead of C4. The key persists across steps until changed again:
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```forth
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a3 key! 0 3 5 7 3 cycle minor note 0.8 decay tri snd .
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```
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A minor melody starting from A3.
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**Common modes:**
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| Word | Pattern |
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|------|---------|
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| `major` | 0 2 4 5 7 9 11 |
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| `minor` | 0 2 3 5 7 8 10 |
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| `dorian` | 0 2 3 5 7 9 10 |
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| `phrygian` | 0 1 3 5 7 8 10 |
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| `lydian` | 0 2 4 6 7 9 11 |
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| `mixolydian` | 0 2 4 5 7 9 10 |
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| `pentatonic` | 0 2 4 7 9 |
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| `minpent` | 0 3 5 7 10 |
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| `blues` | 0 3 5 6 7 10 |
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| `harmonicminor` | 0 2 3 5 7 8 11 |
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| `melodicminor` | 0 2 3 5 7 9 11 |
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Jazz, symmetric, and modal variant scales are listed in the Reference section.
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## Diatonic Harmony
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`triad` and `seventh` build chords from scale degrees. Instead of specifying a chord type, you get whatever chord the scale produces at that degree:
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```forth
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0 major triad note 1.5 decay sine snd .
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```
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Degree 0 of the major scale, stacked in thirds: C E G — a major triad. The scale determines the chord quality automatically. Degree 1 gives D F A (minor), degree 4 gives G B D (major):
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```forth
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4 major triad note 1.5 decay sine snd .
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```
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`seventh` adds a fourth note:
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```forth
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0 major seventh note 1.2 decay saw snd .
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```
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C E G B — Cmaj7. Degree 1 gives Dm7, degree 4 gives G7 (dominant). The diatonic context determines everything.
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Combine with `key!` to play diatonic chords in any key:
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```forth
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g3 key! 0 major triad note 1.5 decay sine snd .
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```
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G major triad rooted at G3.
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A I-vi-IV-V chord progression using `pcycle`:
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```forth
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( 0 major seventh ) ( 5 major seventh )
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( 3 major seventh ) ( 4 major seventh ) 4 pcycle
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note 1.2 decay saw snd .
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```
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Combine with voicings for smoother voice leading:
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```forth
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( 0 major seventh ) ( 5 major seventh inv )
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( 3 major seventh ) ( 4 major seventh drop2 ) 4 pcycle
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note 1.5 decay saw snd .
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```
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Arpeggiate diatonic chords using `at` + `cycle` (see the *Timing with at* tutorial):
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```forth
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0 0.25 0.5 0.75 at sine snd [ 0 major seventh ] cycle note 0.5 decay .
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```
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## Frequency Conversion
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`mtof` converts a MIDI note to frequency in Hz. `ftom` does the reverse:
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```forth
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c4 mtof freq sine snd .
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```
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Useful when a synth parameter expects Hz rather than MIDI.
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## Reference
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### All Chords
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**Triads:**
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| Word | Intervals |
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|------|-----------|
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| `maj` | 0 4 7 |
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| `m` | 0 3 7 |
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| `dim` | 0 3 6 |
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| `aug` | 0 4 8 |
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| `sus2` | 0 2 7 |
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| `sus4` | 0 5 7 |
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| `pwr` | 0 7 |
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**Seventh chords:**
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| Word | Intervals |
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|------|-----------|
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| `maj7` | 0 4 7 11 |
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| `min7` | 0 3 7 10 |
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| `dom7` | 0 4 7 10 |
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| `dim7` | 0 3 6 9 |
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| `m7b5` | 0 3 6 10 |
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| `minmaj7` | 0 3 7 11 |
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| `aug7` | 0 4 8 10 |
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| `augmaj7` | 0 4 8 11 |
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| `7sus4` | 0 5 7 10 |
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**Sixth chords:**
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| Word | Intervals |
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|------|-----------|
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| `maj6` | 0 4 7 9 |
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| `min6` | 0 3 7 9 |
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| `maj69` | 0 4 7 9 14 |
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| `min69` | 0 3 7 9 14 |
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**Extended chords:**
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| Word | Intervals |
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|------|-----------|
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| `dom9` | 0 4 7 10 14 |
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| `maj9` | 0 4 7 11 14 |
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| `min9` | 0 3 7 10 14 |
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| `9sus4` | 0 5 7 10 14 |
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| `dom11` | 0 4 7 10 14 17 |
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| `maj11` | 0 4 7 11 14 17 |
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| `min11` | 0 3 7 10 14 17 |
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| `dom13` | 0 4 7 10 14 21 |
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| `maj13` | 0 4 7 11 14 21 |
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| `min13` | 0 3 7 10 14 21 |
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**Add chords:**
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| Word | Intervals |
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|------|-----------|
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| `add9` | 0 4 7 14 |
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| `add11` | 0 4 7 17 |
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| `madd9` | 0 3 7 14 |
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**Altered dominants:**
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| Word | Intervals |
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|------|-----------|
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| `dom7b9` | 0 4 7 10 13 |
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| `dom7s9` | 0 4 7 10 15 |
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| `dom7b5` | 0 4 6 10 |
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| `dom7s5` | 0 4 8 10 |
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| `dom7s11` | 0 4 7 10 18 |
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### All Scales
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**Modes:**
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| Word | Pattern |
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|------|---------|
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| `major` | 0 2 4 5 7 9 11 |
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| `minor` / `aeolian` | 0 2 3 5 7 8 10 |
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| `dorian` | 0 2 3 5 7 9 10 |
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| `phrygian` | 0 1 3 5 7 8 10 |
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| `lydian` | 0 2 4 6 7 9 11 |
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| `mixolydian` | 0 2 4 5 7 9 10 |
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| `locrian` | 0 1 3 5 6 8 10 |
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**Pentatonic and blues:**
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| Word | Pattern |
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|------|---------|
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| `pentatonic` | 0 2 4 7 9 |
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| `minpent` | 0 3 5 7 10 |
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| `blues` | 0 3 5 6 7 10 |
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**Harmonic and melodic minor:**
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| Word | Pattern |
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|------|---------|
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| `harmonicminor` | 0 2 3 5 7 8 11 |
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| `melodicminor` | 0 2 3 5 7 9 11 |
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**Chromatic and whole tone:**
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| Word | Pattern |
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|------|---------|
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| `chromatic` | 0 1 2 3 4 5 6 7 8 9 10 11 |
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| `wholetone` | 0 2 4 6 8 10 |
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**Jazz / Bebop:**
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| Word | Pattern |
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|------|---------|
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| `bebop` | 0 2 4 5 7 9 10 11 |
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| `bebopmaj` | 0 2 4 5 7 8 9 11 |
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| `bebopmin` | 0 2 3 5 7 8 9 10 |
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| `altered` | 0 1 3 4 6 8 10 |
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| `lyddom` | 0 2 4 6 7 9 10 |
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**Symmetric:**
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| Word | Pattern |
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|------|---------|
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| `halfwhole` | 0 1 3 4 6 7 9 10 |
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| `wholehalf` | 0 2 3 5 6 8 9 11 |
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| `augmented` | 0 3 4 7 8 11 |
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| `tritone` | 0 1 4 6 7 10 |
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| `prometheus` | 0 2 4 6 9 10 |
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**Modal variants (from melodic minor):**
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| Word | Pattern |
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|------|---------|
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| `dorianb2` | 0 1 3 5 7 9 10 |
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| `lydianaug` | 0 2 4 6 8 9 11 |
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| `mixb6` | 0 2 4 5 7 8 10 |
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| `locrian2` | 0 2 3 5 6 8 10 |
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