diff --git a/packages/core/euclid.mjs b/packages/core/euclid.mjs
index 49f96384b..eba3f3303 100644
--- a/packages/core/euclid.mjs
+++ b/packages/core/euclid.mjs
@@ -59,6 +59,11 @@ export const bjorklund = function (ons, steps) {
  * really useful for computer/algorithmic music because they can
  * describe a large number of rhythms with a couple of numbers.
  *
+ * A negative number of pulses inverts the pattern
+ * so pulses happen in the gaps of the normal euclidean rhythm.
+ *
+ * A negative number of steps changes it into `euclidLegato`.
+ *
  * @memberof Pattern
  * @name euclid
  * @tags temporal
@@ -137,8 +142,38 @@ const _euclidRot = function (pulses, steps, rotation) {
   return b;
 };
 
+const _euclidLegato = function (pulses, steps, rotation, pat) {
+  var bin_pat = _euclidRot(pulses, steps, 0);
+  // Because the `gapless` algorithm logic assumes the first entry in bin_pat is a 1,
+  // we rotate the pattern so the first onset is at the start.
+  const firstOnset = bin_pat.indexOf(1);
+  bin_pat = rotate(bin_pat, firstOnset);
+  steps = Math.abs(steps);
+  const gapless = bin_pat
+    .join('')
+    .split('1')
+    .slice(1)
+    .map((s) => [s.length + 1, true]);
+  return pat.struct(timeCat(...gapless).late(Fraction(rotation + firstOnset).div(steps)));
+};
+
+const _euclid = function (pulses, steps, rotation, pat) {
+  if (steps === 0 || pulses === 0) {
+    return silence;
+  }
+  const cycles = Math.ceil(Math.abs(pulses) / Math.abs(steps));
+  const totalSteps = cycles * steps;
+  if (totalSteps < 0) {
+    return _euclidLegato(pulses, -totalSteps, rotation, pat.fast(cycles)).slow(cycles);
+  }
+  return pat
+    .fast(cycles)
+    .struct(_euclidRot(pulses, totalSteps, rotation))
+    .slow(cycles);
+};
+
 export const euclid = register('euclid', function (pulses, steps, pat) {
-  return pat.struct(_euclidRot(pulses, steps, 0));
+  return _euclid(pulses, steps, 0, pat);
 });
 
 export const bjork = register('bjork', function (euc, pat) {
@@ -146,16 +181,18 @@ export const bjork = register('bjork', function (euc, pat) {
     euc = [euc];
   }
   const [pulses, steps = pulses, rot = 0] = euc;
-  return pat.struct(_euclidRot(pulses, steps, rot));
+  return _euclid(pulses, steps, rot, pat);
 });
 
 export const { euclidrot, euclidRot } = register(['euclidrot', 'euclidRot'], function (pulses, steps, rotation, pat) {
-  return pat.struct(_euclidRot(pulses, steps, rotation));
+  return _euclid(pulses, steps, rotation, pat);
 });
 
 /**
  * Similar to `euclid`, but each pulse is held until the next pulse,
  * so there will be no gaps.
+ *
+ * A negative number of steps changes it into `euclid`.
  * @name euclidLegato
  * @memberof Pattern
  * @tags temporal
@@ -167,27 +204,16 @@ export const { euclidrot, euclidRot } = register(['euclidrot', 'euclidRot'], fun
  * note("c3").euclidLegato(3,8)
  */
 
-const _euclidLegato = function (pulses, steps, rotation, pat) {
-  if (pulses < 1) {
-    return silence;
-  }
-  const bin_pat = _euclidRot(pulses, steps, 0);
-  const gapless = bin_pat
-    .join('')
-    .split('1')
-    .slice(1)
-    .map((s) => [s.length + 1, true]);
-  return pat.struct(timeCat(...gapless)).late(Fraction(rotation).div(steps));
-};
-
 export const euclidLegato = register(['euclidLegato'], function (pulses, steps, pat) {
-  return _euclidLegato(pulses, steps, 0, pat);
+  return _euclid(pulses, -steps, 0, pat);
 });
 
 /**
  * Similar to `euclid`, but each pulse is held until the next pulse,
  * so there will be no gaps, and has an additional parameter for 'rotating'
- * the resulting sequence
+ * the resulting sequence.
+ *
+ * A negative number of steps changes it into `euclidRot`.
  * @name euclidLegatoRot
  * @memberof Pattern
  * @tags temporal
@@ -198,7 +224,7 @@ export const euclidLegato = register(['euclidLegato'], function (pulses, steps,
  * note("c3").euclidLegatoRot(3,5,2)
  */
 export const euclidLegatoRot = register(['euclidLegatoRot'], function (pulses, steps, rotation, pat) {
-  return _euclidLegato(pulses, steps, rotation, pat);
+  return _euclid(pulses, -steps, rotation, pat);
 });
 
 /**
diff --git a/packages/core/test/euclid.test.js b/packages/core/test/euclid.test.js
index 6169abd71..a5fc23857 100644
--- a/packages/core/test/euclid.test.js
+++ b/packages/core/test/euclid.test.js
@@ -29,6 +29,44 @@ describe('euclid', () => {
         .map((a) => a.showWhole(true)),
     ).toStrictEqual(['0/1 → 1/8: a', '1/4 → 3/8: a', '3/8 → 1/2: a', '5/8 → 3/4: a', '3/4 → 7/8: a']);
   });
+  it('Can create euclidLegato using negative steps', () => {
+    expect(
+      fastcat('a')
+        .euclid(3, -8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    ).toStrictEqual(
+      fastcat('a')
+        .euclidLegato(3, 8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    );
+    expect(
+      fastcat('a')
+        .euclid(5, -8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    ).toStrictEqual(
+      fastcat('a')
+        .euclidLegato(5, 8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    );
+  });
+  it('stretches over multiple cycles if pulses is greater than steps', () => {
+    expect(
+      fastcat('a')
+        .euclid(5, 4)
+        .fast(2)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    ).toStrictEqual(['0/1 → 1/8: a', '1/4 → 3/8: a', '3/8 → 1/2: a', '5/8 → 3/4: a', '3/4 → 7/8: a']);
+  });
 });
 
 describe('euclidRot', () => {
@@ -67,6 +105,45 @@ describe('euclidLegato', () => {
         .map((a) => a.showWhole(true)),
     ).toStrictEqual(['0/1 → 1/4: a', '1/4 → 3/8: a', '3/8 → 5/8: a', '5/8 → 3/4: a', '3/4 → 1/1: a']);
   });
+  it('Can create euclid using negative steps', () => {
+    expect(
+      fastcat('a')
+        .euclidLegato(3, -8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    ).toStrictEqual(
+      fastcat('a')
+        .euclid(3, 8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    );
+    expect(
+      fastcat('a')
+        .euclidLegato(5, -8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    ).toStrictEqual(
+      fastcat('a')
+        .euclid(5, 8)
+        .firstCycle()
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    );
+  });
+  it('stretches over multiple cycles if pulses is greater than steps', () => {
+    expect(
+      fastcat('a')
+        .euclidLegato(5, 4)
+        .fast(2)
+        .firstCycle()
+        .filter((hap) => hap.hasOnset())
+        .sort((a, b) => a.part.begin.sub(b.part.begin))
+        .map((a) => a.showWhole(true)),
+    ).toStrictEqual(['0/1 → 1/4: a', '1/4 → 3/8: a', '3/8 → 5/8: a', '5/8 → 3/4: a', '3/4 → 1/1: a']);
+  });
 });
 
 describe('euclidLegatoRot', () => {
diff --git a/packages/mini/test/mini.test.mjs b/packages/mini/test/mini.test.mjs
index c38997308..c84819e87 100644
--- a/packages/mini/test/mini.test.mjs
+++ b/packages/mini/test/mini.test.mjs
@@ -84,6 +84,22 @@ describe('mini', () => {
   it('supports patterning euclidean rhythms', () => {
     expect(minS('[a(<3 5>, <8 16>)]*2')).toEqual(minS('a(3,8) a(5,16)'));
   });
+  it('supports inverted euclidean rhythms', () => {
+    expect(minS('a(-3, 8)')).toEqual(['a: 1/8 - 1/4', 'a: 1/4 - 3/8', 'a: 1/2 - 5/8', 'a: 5/8 - 3/4', 'a: 7/8 - 1']);
+  });
+  it('supports euclidean legato rhythms', () => {
+    expect(minS('a(3, -8)')).toEqual(['a: 0 - 3/8', 'a: 3/8 - 3/4', 'a: 3/4 - 1']);
+  });
+  it('supports inverted euclidean legato rhythms', () => {
+    expect(minS('a(-3, -8)')).toEqual([
+      'a: -1/8 - 1/8',
+      'a: 1/8 - 1/4',
+      'a: 1/4 - 1/2',
+      'a: 1/2 - 5/8',
+      'a: 5/8 - 7/8',
+      'a: 7/8 - 9/8',
+    ]);
+  });
   it("reproduces Toussaint's example euclidean algorithms", () => {
     const checkEuclid = function (spec, target) {
       expect(minS(`x(${spec[0]},${spec[1]})`)).toEqual(minS(target));
@@ -118,6 +134,40 @@ describe('mini', () => {
     checkEuclid([11, 24], 'x ~ ~ x ~ x ~ x ~ x ~ x ~ ~ x ~ x ~ x ~ x ~ x ~');
     checkEuclid([13, 24], 'x ~ x x ~ x ~ x ~ x ~ x ~ x x ~ x ~ x ~ x ~ x ~');
   });
+  it("reproduces Toussaint's example euclidean legato algorithms", () => {
+    const checkEuclid = function (spec, target) {
+      expect(minS(`x(${spec[0]},${spec[1]})`)).toEqual(minS(target));
+    };
+    checkEuclid([1, -2], 'x _');
+    checkEuclid([1, -3], 'x _ _');
+    checkEuclid([1, -4], 'x _ _ _');
+    checkEuclid([4, -12], 'x _ _ x _ _ x _ _ x _ _');
+    checkEuclid([2, -5], 'x _ x _ _');
+    // checkEuclid([3, 4], "x _ x x"); // Toussaint is wrong..
+    checkEuclid([3, -4], 'x x x _'); // correction
+    checkEuclid([3, -5], 'x _ x _ x');
+    checkEuclid([3, -7], 'x _ x _ x _ _');
+    checkEuclid([3, -8], 'x _ _ x _ _ x _');
+    checkEuclid([4, -7], 'x _ x _ x _ x');
+    checkEuclid([4, -9], 'x _ x _ x _ x _ _');
+    checkEuclid([4, -11], 'x _ _ x _ _ x _ _ x _');
+    // checkEuclid([5, 6], "x _ x x x x"); // Toussaint is wrong..
+    checkEuclid([5, -6], 'x x x x x _'); // correction
+    checkEuclid([5, -7], 'x _ x x _ x x');
+    checkEuclid([5, -8], 'x _ x x _ x x _');
+    checkEuclid([5, -9], 'x _ x _ x _ x _ x');
+    checkEuclid([5, -11], 'x _ x _ x _ x _ x _ _');
+    checkEuclid([5, -12], 'x _ _ x _ x _ _ x _ x _');
+    // checkEuclid([5, 16], "x _ _ x _ _ x _ _ x _ _ x _ _ _ _");  // Toussaint is wrong..
+    checkEuclid([5, -16], 'x _ _ x _ _ x _ _ x _ _ x _ _ _'); // correction
+    // checkEuclid([7, 8], "x _ x x x x x x"); // Toussaint is wrong..
+    checkEuclid([7, -8], 'x x x x x x x _'); // Correction
+    checkEuclid([7, -12], 'x _ x x _ x _ x x _ x _');
+    checkEuclid([7, -16], 'x _ _ x _ x _ x _ _ x _ x _ x _');
+    checkEuclid([9, -16], 'x _ x x _ x _ x _ x x _ x _ x _');
+    checkEuclid([11, -24], 'x _ _ x _ x _ x _ x _ x _ _ x _ x _ x _ x _ x _');
+    checkEuclid([13, -24], 'x _ x x _ x _ x _ x _ x _ x x _ x _ x _ x _ x _');
+  });
   it('supports the - alias for ~', () => {
     expect(minS('a - b [- c]')).toEqual(minS('a ~ b [~ c]'));
   });
diff --git a/test/__snapshots__/examples.test.mjs.snap b/test/__snapshots__/examples.test.mjs.snap
index ccb91377f..a0a81ada8 100644
--- a/test/__snapshots__/examples.test.mjs.snap
+++ b/test/__snapshots__/examples.test.mjs.snap
@@ -4264,13 +4264,16 @@ exports[`runs examples > example "euclidLegatoRot" example index 0 1`] = `
   "[ -1/5 ⇜ (0/1 → 1/5) | note:c3 ]",
   "[ 1/5 → 2/5 | note:c3 ]",
   "[ 2/5 → 4/5 | note:c3 ]",
-  "[ 4/5 → 6/5 | note:c3 ]",
+  "[ (4/5 → 1/1) ⇝ 6/5 | note:c3 ]",
+  "[ 4/5 ⇜ (1/1 → 6/5) | note:c3 ]",
   "[ 6/5 → 7/5 | note:c3 ]",
   "[ 7/5 → 9/5 | note:c3 ]",
-  "[ 9/5 → 11/5 | note:c3 ]",
+  "[ (9/5 → 2/1) ⇝ 11/5 | note:c3 ]",
+  "[ 9/5 ⇜ (2/1 → 11/5) | note:c3 ]",
   "[ 11/5 → 12/5 | note:c3 ]",
   "[ 12/5 → 14/5 | note:c3 ]",
-  "[ 14/5 → 16/5 | note:c3 ]",
+  "[ (14/5 → 3/1) ⇝ 16/5 | note:c3 ]",
+  "[ 14/5 ⇜ (3/1 → 16/5) | note:c3 ]",
   "[ 16/5 → 17/5 | note:c3 ]",
   "[ 17/5 → 19/5 | note:c3 ]",
   "[ (19/5 → 4/1) ⇝ 21/5 | note:c3 ]",
diff --git a/test/__snapshots__/tunes.test.mjs.snap b/test/__snapshots__/tunes.test.mjs.snap
index 1fb178801..d33592bb4 100644
--- a/test/__snapshots__/tunes.test.mjs.snap
+++ b/test/__snapshots__/tunes.test.mjs.snap
@@ -7322,12 +7322,12 @@ exports[`renders tunes > tune: randomBells 1`] = `
 [
   "[ -9/8 ⇜ (0/1 → 3/8) | gain:0.6 note:A3 velocity:0.598990320228 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ -3/4 ⇜ (0/1 → 3/4) | gain:0.6 note:C5 velocity:0.836992966942 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 0/1 → 3/2 | note:F2 s:bass clip:1 gain:0.8 ]",
+  "[ 0/1 → 3/2 | note:D2 s:bass clip:1 gain:0.8 ]",
   "[ 0/1 → 9/4 | gain:0.6 note:D3 velocity:0.5 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 3/8 → 21/8 | gain:0.6 note:F5 velocity:0.921303892508 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 3/4 → 3/1 | gain:0.6 note:C5 velocity:0.842607785016 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 3/2 → 9/4 | note:F2 s:bass clip:1 gain:0.8 ]",
-  "[ 9/4 → 3/1 | note:F2 s:bass clip:1 gain:0.8 ]",
+  "[ 3/2 → 9/4 | note:D2 s:bass clip:1 gain:0.8 ]",
+  "[ 9/4 → 3/1 | note:D2 s:bass clip:1 gain:0.8 ]",
   "[ 9/4 → 9/2 | gain:0.6 note:D4 velocity:0.700696257874 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 21/8 → 39/8 | gain:0.6 note:C4 velocity:0.650794394314 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 3/1 → 9/2 | note:D2 s:bass clip:1 gain:0.8 ]",
@@ -7339,12 +7339,12 @@ exports[`renders tunes > tune: randomBells 1`] = `
   "[ (21/4 → 6/1) ⇝ 27/4 | gain:0.6 note:D4 velocity:0.698815540411 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 39/8 ⇜ (6/1 → 51/8) | gain:0.6 note:D5 velocity:0.875811336562 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 21/4 ⇜ (6/1 → 27/4) | gain:0.6 note:D4 velocity:0.698815540411 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 6/1 → 15/2 | note:D2 s:bass clip:1 gain:0.8 ]",
+  "[ 6/1 → 15/2 | note:A2 s:bass clip:1 gain:0.8 ]",
   "[ 6/1 → 33/4 | gain:0.6 note:G4 velocity:0.75977108255 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 51/8 → 69/8 | gain:0.6 note:G4 velocity:0.774316444062 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 27/4 → 9/1 | gain:0.6 note:C5 velocity:0.836244757287 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 15/2 → 33/4 | note:D2 s:bass clip:1 gain:0.8 ]",
-  "[ 33/4 → 9/1 | note:D2 s:bass clip:1 gain:0.8 ]",
+  "[ 15/2 → 33/4 | note:A2 s:bass clip:1 gain:0.8 ]",
+  "[ 33/4 → 9/1 | note:A2 s:bass clip:1 gain:0.8 ]",
   "[ 33/4 → 21/2 | gain:0.6 note:A3 velocity:0.59140187595 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 69/8 → 87/8 | gain:0.6 note:G4 velocity:0.754063542932 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 9/1 → 21/2 | note:A2 s:bass clip:1 gain:0.8 ]",
@@ -7356,12 +7356,12 @@ exports[`renders tunes > tune: randomBells 1`] = `
   "[ (45/4 → 12/1) ⇝ 51/4 | gain:0.6 note:A4 velocity:0.797278589569 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 87/8 ⇜ (12/1 → 99/8) | gain:0.6 note:F4 velocity:0.734787144698 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 45/4 ⇜ (12/1 → 51/4) | gain:0.6 note:A4 velocity:0.797278589569 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 12/1 → 27/2 | note:A2 s:bass clip:1 gain:0.8 ]",
+  "[ 12/1 → 27/2 | note:G2 s:bass clip:1 gain:0.8 ]",
   "[ 12/1 → 57/4 | gain:0.6 note:G5 velocity:0.979763559997 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 99/8 → 117/8 | gain:0.6 note:C4 velocity:0.666239210404 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 51/4 → 15/1 | gain:0.6 note:F5 velocity:0.95169514697 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 27/2 → 57/4 | note:A2 s:bass clip:1 gain:0.8 ]",
-  "[ 57/4 → 15/1 | note:A2 s:bass clip:1 gain:0.8 ]",
+  "[ 27/2 → 57/4 | note:G2 s:bass clip:1 gain:0.8 ]",
+  "[ 57/4 → 15/1 | note:G2 s:bass clip:1 gain:0.8 ]",
   "[ 57/4 → 33/2 | gain:0.6 note:F5 velocity:0.918253320269 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 117/8 → 135/8 | gain:0.6 note:G3 velocity:0.571157105267 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 15/1 → 33/2 | note:G2 s:bass clip:1 gain:0.8 ]",
@@ -7373,12 +7373,12 @@ exports[`renders tunes > tune: randomBells 1`] = `
   "[ (69/4 → 18/1) ⇝ 75/4 | gain:0.6 note:F3 velocity:0.508127085865 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 135/8 ⇜ (18/1 → 147/8) | gain:0.6 note:F5 velocity:0.945647025481 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 69/4 ⇜ (18/1 → 75/4) | gain:0.6 note:F3 velocity:0.508127085865 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 18/1 → 39/2 | note:G2 s:bass clip:1 gain:0.8 ]",
+  "[ 18/1 → 39/2 | note:F2 s:bass clip:1 gain:0.8 ]",
   "[ 18/1 → 81/4 | gain:0.6 note:A3 velocity:0.608644555323 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 147/8 → 165/8 | gain:0.6 note:F3 velocity:0.506259439513 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 75/4 → 21/1 | gain:0.6 note:D4 velocity:0.671621939167 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
-  "[ 39/2 → 81/4 | note:G2 s:bass clip:1 gain:0.8 ]",
-  "[ 81/4 → 21/1 | note:G2 s:bass clip:1 gain:0.8 ]",
+  "[ 39/2 → 81/4 | note:F2 s:bass clip:1 gain:0.8 ]",
+  "[ 81/4 → 21/1 | note:F2 s:bass clip:1 gain:0.8 ]",
   "[ 81/4 → 45/2 | gain:0.6 note:D4 velocity:0.704345900565 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 165/8 → 183/8 | gain:0.6 note:D5 velocity:0.887838857248 s:bell delay:0.2 delaytime:0.333333333333 delayfeedback:0.8 ]",
   "[ 21/1 → 45/2 | note:F2 s:bass clip:1 gain:0.8 ]",