tonnetz

tonnetz turns the keyboard into a walk across the neo-Riemannian Tonnetz.

The Tonnetz is the lattice of triads that neo-Riemannian theory uses to read late Romantic harmony, Wagner and Liszt drifting between chords a single tone apart rather than moving by functional progressions. Triads step along it by three transforms:

• p (parallel) keeps the root and flips the quality: C major to C minor and back.
• l (leittonwechsel) exchanges a triad with the one a major third away: C major to E minor and back.
• r (relative) exchanges a triad with its relative: C major to A minor and back.

Every keypress steps the sequence: a note-on first applies the next letter of the cycling sequence, then sounds the triad it arrives at. The starting triad itself is never heard; your first note is already one step in. Each triad tone is voiced at the key inside lo..=hi nearest your played key (ties break downward, and a pitch class with no key in the range is skipped), all at your velocity; include-played=true sounds the key you actually pressed as well.

The walk is deterministic, no seed: the same keypresses always trace the same path. The emitted set is remembered per note, so note-offs, retriggers, and scene switches release exactly the triad that is sounding.

Parameters

Parameter	Type	Default	Range
start	note name	required	"c", "f#", "bb", or "0".."11"
minor	boolean	false	true, false
sequence	string	"rl"	letters p, l, r, case-insensitive
lo	key number	48	0..=127
hi	key number	79	0..=127, at least lo
include-played	boolean	false	true, false

start takes a note name, a letter a..g with an optional # or b ("c", "f#", "bb", case does not matter), or a pitch class written "0".."11". With minor it names the triad the walk begins from. sequence is read left to right and cycles forever.

Example

The drift scene from examples/harmony.kdl:

miditool.kdl

input "Roland"
output virtual="miditool Out"

tonnetz start="c" minor=false sequence="rl" lo=48 hi=79
velocity-curve gamma=1.2 ceiling=96

"rl" alternates relative and leading-tone exchange, so from C major each keypress slides one station through A minor, F major, D minor, B flat major, and on around the diatonic circle of thirds.

Try this

The hexatonic drift:

tonnetz start="c" sequence="pl"

Alternating parallel and leittonwechsel traces one of Cohn’s hexatonic cycles: from C major the keypresses land on C minor, A flat major, A flat minor, E major, E minor, C major, then around again. Six notes close the loop, and the whole ride never leaves six pitch classes. Add include-played=true and your own key cuts through the cycle as a free voice against the drifting triads.