⬢ Euclidean fills — the world's oldest rhythms, from the arithmetic

Live 12's Euclidean generator (manual §11.3.5) on the groove grid: spread N
pulses as evenly as possible over the pattern, with adjustable steps (cycle
length) and rotation, tiled into the 16-step grid. E(3,8) tresillo, E(5,8)
cinquillo, E(4,16) four-on-the-floor — one control fills any groove or gate
lane (note lanes fill the root). Verified live: E(4,16)→[0,4,8,12],
E(3,8)→[0,3,6,8,11,14], E(5,16)→[0,4,7,10,13]. Self-check guards the
canonical patterns. Grimoire + integrated manual updated to match.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

GODSTRUMENT_MANUAL_SOURCE.md

@@ -538,7 +538,7 @@ Learn these seven gestures and the whole planet is under your hands:
 
 - **Press `T` — tracks, for making actual songs.** A conventional tracks-and-clips view for anyone who finds the cathedral overwhelming: every voice is a **track**, eight **bars** run across, and each cell cycles **● live** (the world plays that lane) → **A** → **B** → **C** (clip patterns on the groove grids — A and B come pre-seeded so it makes music immediately) → **silent**. Double-click any clip to edit its groove in the piano roll. Press **▶** and the arrangement loops on the godtime clock — the planet still plays *through* your song, because live lanes stay wired to the world. Arrangements **save with your patch**, play out over MIDI like everything else, and **export .mid** hands you a Standard MIDI File of the note lanes to drag into Ableton, Logic, anything. Not a DAW — a sketchpad where the world sits in on your session. The panel earns its keep like one, too: a **🎛 tracks button** sits bottom-right always; **drag the panel's top edge to resize** (remembered); the top bar **tabs between clips and grooves** — the grooves tab is a full-size pattern editor (pick a track, pick a letter, big piano roll or 16 steps; double-clicking any clip jumps you straight there); and **right-click any track name for that voice's full routing menu** — every cable, every level, patch and unpatch without leaving the panel.
 
-- **The Groove — one feel for the whole pattern.** The grooves tab carries Ableton's Groove Pool, reduced to the 16-step grid: **swing** lays the off-beats back, **humanize** is a touch of random timing so nothing is machine-stiff, **velocity** lets each hit breathe in loudness, and an **amount** master scales the lot — with one-click presets (*straight, swing 16, MPC 8-4, drunk*). Under the roll sit two expression lanes: **velocity** (how hard each step hits) and **chance** (how likely each step fires at all — drop a step to 40% and it plays four times in ten, so the loop varies itself). The feel and the per-step shaping **save with your patch**.
+- **The Groove — one feel for the whole pattern.** The grooves tab carries Ableton's Groove Pool, reduced to the 16-step grid: **swing** lays the off-beats back, **humanize** is a touch of random timing so nothing is machine-stiff, **velocity** lets each hit breathe in loudness, and an **amount** master scales the lot — with one-click presets (*straight, swing 16, MPC 8-4, drunk*). Under the roll sit two expression lanes: **velocity** (how hard each step hits) and **chance** (how likely each step fires at all — drop a step to 40% and it plays four times in ten, so the loop varies itself). The feel and the per-step shaping **save with your patch**. And any lane takes a **⬢ Euclidean fill** — say how many *pulses* to spread across the steps and they distribute themselves as evenly as possible (E(3,8) is the tresillo, E(5,8) the cinquillo, E(4,16) four-on-the-floor), with *steps* and *rotate* to taste: the oldest rhythms of the world fall straight out of the arithmetic.
 
 - **⤳ Follow actions — the song composes itself.** Give any clip (A/B/C) a **follow action** in the grooves tab — *play again, next, any, any other, stop* — with a **chance**, and once the arrangement is playing that clip can hand off to another at the bar line instead of just repeating. Set two clips to "any other" and they trade the lane back and forth; sprinkle a low-chance divert and the piece drifts. As Ableton's manual puts it, "structures that repeat but can also be surprising… never exactly repeat." A ⤳ marks any clip that can divert. Nothing changes for arrangements without follow actions — they loop exactly as written.
 
@@ -971,3 +971,4 @@ Every feed the world sends is one of eight temperaments; the shape dictates how
 - **The Groove** — Ableton's Groove Pool on the 16-step grid: `swing` (delays the off-beats), `humanize` (the manual's Random timing jitter), `velocity` (per-note deviation), and an `amount` master (0..130%). Presets: straight / swing 16 / mpc 8-4 / drunk. Applied globally in the clock + `seqTick`; travels with the patch.
 - **Per-step expression** — a `velocity` lane (how hard each step hits) and a `chance` lane (0..100% probability the step fires) under the piano roll, per voice. Drop a step's chance and the loop varies itself.
 - **⤳ Follow Actions** — each arranger clip (A/B/C) can hand off to another at the bar line by chance: again / next / any / any-other / stop. A live overlay diverts playback without rewriting the authored grid; arrangements with no follow actions loop exactly as written. Turns an 8-bar loop into a self-composing structure.
+- **⬢ Euclidean fills** — Live 12's Euclidean generator (§11.3.5): spread N `pulses` as evenly as possible over the pattern, with adjustable `steps` (cycle length) and `rotate`. E(3,8) tresillo, E(5,8) cinquillo, E(4,16) four-on-the-floor — the world's oldest rhythms falling straight out of the arithmetic. Fills any groove or gate lane.