diff --git a/packages/core/euclid.mjs b/packages/core/euclid.mjs
index 49f96384b..c477ddfc7 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
@@ -138,6 +143,9 @@ const _euclidRot = function (pulses, steps, rotation) {
 };
 
 export const euclid = register('euclid', function (pulses, steps, pat) {
+  if (steps < 0) {
+    return _euclidLegato(pulses, -steps, 0, pat);
+  }
   return pat.struct(_euclidRot(pulses, steps, 0));
 });
 
@@ -150,12 +158,17 @@ export const bjork = register('bjork', function (euc, pat) {
 });
 
 export const { euclidrot, euclidRot } = register(['euclidrot', 'euclidRot'], function (pulses, steps, rotation, pat) {
+  if (steps < 0) {
+    return _euclidLegato(pulses, -steps, rotation, pat);
+  }
   return pat.struct(_euclidRot(pulses, steps, rotation));
 });
 
 /**
  * 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
@@ -168,26 +181,33 @@ export const { euclidrot, euclidRot } = register(['euclidrot', 'euclidRot'], fun
  */
 
 const _euclidLegato = function (pulses, steps, rotation, pat) {
-  if (pulses < 1) {
-    return silence;
-  }
-  const bin_pat = _euclidRot(pulses, steps, 0);
+  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).div(steps));
+  return pat.struct(timeCat(...gapless)).late(Fraction(rotation + firstOnset).div(steps));
 };
 
 export const euclidLegato = register(['euclidLegato'], function (pulses, steps, pat) {
+  if (steps < 0) {
+    return pat.struct(_euclidRot(pulses, -steps, 0));
+  }
   return _euclidLegato(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
@@ -198,6 +218,9 @@ export const euclidLegato = register(['euclidLegato'], function (pulses, steps,
  * note("c3").euclidLegatoRot(3,5,2)
  */
 export const euclidLegatoRot = register(['euclidLegatoRot'], function (pulses, steps, rotation, pat) {
+  if (steps < 0) {
+    return pat.struct(_euclidRot(pulses, -steps, rotation));
+  }
   return _euclidLegato(pulses, steps, rotation, pat);
 });
 
diff --git a/packages/core/test/euclid.test.js b/packages/core/test/euclid.test.js
index 6169abd71..bf02a6109 100644
--- a/packages/core/test/euclid.test.js
+++ b/packages/core/test/euclid.test.js
@@ -29,6 +29,34 @@ 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)),
+    );
+  });
 });
 
 describe('euclidRot', () => {
@@ -67,6 +95,34 @@ 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)),
+    );
+  });
 });
 
 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]'));
   });