diff --git a/packages/core/pattern.mjs b/packages/core/pattern.mjs
index aa5e1060f..0f5083901 100644
--- a/packages/core/pattern.mjs
+++ b/packages/core/pattern.mjs
@@ -1002,7 +1002,7 @@ export const arpWith = register('arpWith', (func, pat) => {
  * */
 export const arp = register(
   'arp',
-  (indices, pat) => pat.arpWith((haps) => reify(indices).fmap((i) => haps[i % haps.length])),
+  (indices, pat) => pat.arpWith((haps) => reify(indices).fmap((i) => haps[_mod(i, haps.length)])),
   false,
 );
 
@@ -1529,7 +1529,9 @@ export function slowcat(...pats) {
   // Array test here is to avoid infinite recursions..
   pats = pats.map((pat) => (Array.isArray(pat) ? fastcat(...pat) : reify(pat)));
 
-  if (pats.length == 1) {
+  if (!pats.length) {
+    return silence;
+  } else if (pats.length == 1) {
     return pats[0];
   }
 
@@ -1537,10 +1539,6 @@ export function slowcat(...pats) {
     const span = state.span;
     const pat_n = _mod(span.begin.sam(), pats.length);
     const pat = pats[pat_n];
-    if (!pat) {
-      // pat_n can be negative, if the span is in the past..
-      return [];
-    }
     // A bit of maths to make sure that cycles from constituent patterns aren't skipped.
     // For example if three patterns are slowcat-ed, the fourth cycle of the result should
     // be the second (rather than fourth) cycle from the first pattern.
@@ -1557,11 +1555,14 @@ export function slowcat(...pats) {
  * @return {Pattern}
  */
 export function slowcatPrime(...pats) {
+  if (!pats.length) {
+    return silence;
+  }
   pats = pats.map(reify);
   const query = function (state) {
-    const pat_n = Math.floor(state.span.begin) % pats.length;
-    const pat = pats[pat_n]; // can be undefined for same cases e.g. /#cHVyZSg0MikKICAuZXZlcnkoMyxhZGQoNykpCiAgLmxhdGUoLjUp
-    return pat?.query(state) || [];
+    const pat_n = _mod(Math.floor(state.span.begin), pats.length);
+    const pat = pats[pat_n];
+    return pat.query(state);
   };
   return new Pattern(query).splitQueries();
 }
diff --git a/packages/core/signal.mjs b/packages/core/signal.mjs
index 4398e2ab7..b86f16e8a 100644
--- a/packages/core/signal.mjs
+++ b/packages/core/signal.mjs
@@ -6,6 +6,7 @@ This program is free software: you can redistribute it and/or modify it under th
 
 import { Hap } from './hap.mjs';
 import { Pattern, fastcat, pure, register, reify, silence, stack, sequenceP } from './pattern.mjs';
+import { _mod } from './util.mjs';
 import Fraction from './fraction.mjs';
 
 import { id, keyAlias, getCurrentKeyboardState } from './util.mjs';
@@ -33,7 +34,7 @@ export const signal = (func) => {
  * .scale('C major')
  *
  */
-export const saw = signal((t) => t % 1);
+export const saw = signal((t) => _mod(t, 1));
 
 /**
  *  A sawtooth signal between -1 and 1 (like `saw`, but bipolar).
@@ -56,7 +57,7 @@ export const saw2 = saw.toBipolar();
  * .scale('C major')
  *
  */
-export const isaw = signal((t) => 1 - (t % 1));
+export const isaw = signal((t) => 1 - _mod(t, 1));
 
 /**
  *  A sawtooth signal between 1 and -1 (like `saw2`, but flipped).
@@ -113,7 +114,7 @@ export const cosine2 = sine2._early(Fraction(1).div(4));
  * n(square.segment(4).range(0,7)).scale("C:minor")
  *
  */
-export const square = signal((t) => Math.floor((t * 2) % 2));
+export const square = signal((t) => Math.floor(_mod(t * 2, 2)));
 
 /**
  *  A square signal between -1 and 1 (like `square`, but bipolar).
@@ -123,6 +124,22 @@ export const square = signal((t) => Math.floor((t * 2) % 2));
  */
 export const square2 = square.toBipolar();
 
+/**
+ *  A square signal between 1 and 0 (like `square` but flipped).
+ *
+ * @return {Pattern}
+ * @tags generators
+ */
+export const isquare = signal((t) => 1 - Math.floor(_mod(t * 2, 2)));
+
+/**
+ *  A square signal between 1 and -1 (like `isquare`, but bipolar).
+ *
+ * @return {Pattern}
+ * @tags generators
+ */
+export const isquare2 = isquare.toBipolar();
+
 /**
  *  A triangle signal between 0 and 1.
  *
@@ -396,7 +413,7 @@ export const randrun = (n) => {
       .map((n, i) => [n, i])
       .sort((a, b) => (a[0] > b[0]) - (a[0] < b[0]))
       .map((x) => x[1]);
-    const i = t.cyclePos().mul(n).floor() % n;
+    const i = _mod(t.cyclePos().mul(n).floor(), n);
     return nums[i];
   })._segment(n);
 };
diff --git a/packages/core/test/pattern.test.mjs b/packages/core/test/pattern.test.mjs
index aaa14bd27..cb5345610 100644
--- a/packages/core/test/pattern.test.mjs
+++ b/packages/core/test/pattern.test.mjs
@@ -18,6 +18,7 @@ import {
   fastcat,
   firstOf,
   slowcat,
+  slowcatPrime,
   cat,
   sequence,
   palindrome,
@@ -53,6 +54,7 @@ import {
   stepcat,
   sometimes,
   expand,
+  arp,
 } from '../index.mjs';
 
 import { log, logValues } from '../pattern.mjs';
@@ -544,6 +546,9 @@ describe('Pattern', () => {
     });
   });
   describe('slowcat()', () => {
+    it('Can be empty', () => {
+      expect(slowcat().firstCycle()).toStrictEqual([]);
+    });
     it('Can concatenate things slowly', () => {
       expect(
         slowcat('a', 'b')
@@ -576,6 +581,38 @@ describe('Pattern', () => {
       sameFirst(slowcat('a', ['b', 'c']).fast(4), sequence('a', ['b', 'c']).fast(2));
     });
   });
+  describe('slowcatPrime()', () => {
+    it('Can be empty', () => {
+      expect(slowcatPrime().firstCycle()).toStrictEqual([]);
+    });
+    it('Can slowcat patterns swapping back and forth skipping the expected notes', () => {
+      expect(
+        slowcatPrime(fastcat(0, 1, 2, 3).slow(2), fastcat(4, 5, 6, 7).slow(2))
+          .fast(4)
+          .firstCycle()
+          .map((a) => a.value),
+      ).toStrictEqual([0, 1, 6, 7, 0, 1, 6, 7]);
+    });
+    it('Can go into negative time', () => {
+      expect(
+        slowcatPrime(fastcat(0, 1, 2, 3).slow(2), fastcat(4, 5, 6, 7).slow(2))
+          .fast(4)
+          .late(8)
+          .firstCycle()
+          .map((a) => a.value),
+      ).toStrictEqual([0, 1, 6, 7, 0, 1, 6, 7]);
+    });
+  });
+  describe('arp()', () => {
+    it('It wraps around with both positive and negative indices', () => {
+      expect(
+        stack('a', 'b', 'c')
+          .arp(fastcat(-3, -2, -1, 0, 1, 2, 3, 4))
+          .firstCycle()
+          .map((a) => a.value),
+      ).toStrictEqual(['a', 'b', 'c', 'a', 'b', 'c', 'a', 'b']);
+    });
+  });
   describe('rev()', () => {
     it('Can reverse things', () => {
       expect(
diff --git a/packages/core/test/signal.test.mjs b/packages/core/test/signal.test.mjs
index 26c1d656a..628864c79 100644
--- a/packages/core/test/signal.test.mjs
+++ b/packages/core/test/signal.test.mjs
@@ -8,7 +8,23 @@ import Fraction from 'fraction.js';
 
 import { describe, it, expect, vi } from 'vitest';
 
-import { saw, saw2, isaw, isaw2, per, perx, cyclesPer } from '../signal.mjs';
+import {
+  saw,
+  saw2,
+  isaw,
+  isaw2,
+  tri,
+  tri2,
+  itri,
+  itri2,
+  square,
+  square2,
+  isquare,
+  isquare2,
+  per,
+  perx,
+  cyclesPer,
+} from '../signal.mjs';
 import { fastcat, sequence, State, TimeSpan, Hap, note } from '../index.mjs';
 
 const st = (begin, end) => new State(ts(begin, end));
@@ -24,17 +40,61 @@ const sameFirst = (a, b) => {
 
 describe('signal()', () => {
   it('Can make saw/saw2', () => {
-    expect(saw.struct(true, true, true, true).firstCycle()).toStrictEqual(
-      sequence(0, 1 / 4, 1 / 2, 3 / 4).firstCycle(),
-    );
-
+    expect(saw.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(0, 0.25, 0.5, 0.75).firstCycle());
     expect(saw2.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(-1, -0.5, 0, 0.5).firstCycle());
   });
   it('Can make isaw/isaw2', () => {
     expect(isaw.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 0.75, 0.5, 0.25).firstCycle());
-
     expect(isaw2.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 0.5, 0, -0.5).firstCycle());
   });
+  it('Can make tri/tri2', () => {
+    expect(tri.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(0, 0.5, 1, 0.5).firstCycle());
+    expect(tri2.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(-1, 0, 1, 0).firstCycle());
+  });
+  it('Can make itri/itri2', () => {
+    expect(itri.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 0.5, 0, 0.5).firstCycle());
+    expect(itri2.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 0, -1, 0).firstCycle());
+  });
+  it('Can make square/square2', () => {
+    expect(square.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(0, 0, 1, 1).firstCycle());
+    expect(square2.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(-1, -1, 1, 1).firstCycle());
+  });
+  it('Can make isquare/isquare2', () => {
+    expect(isquare.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 1, 0, 0).firstCycle());
+    expect(isquare2.struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 1, -1, -1).firstCycle());
+  });
+  it('Can go into negative time', () => {
+    expect(saw.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(0, 0.25, 0.5, 0.75).firstCycle(),
+    );
+    expect(saw2.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(-1, -0.5, 0, 0.5).firstCycle(),
+    );
+    expect(isaw.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(1, 0.75, 0.5, 0.25).firstCycle(),
+    );
+    expect(isaw2.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(1, 0.5, 0, -0.5).firstCycle(),
+    );
+    expect(tri.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(0, 0.5, 1, 0.5).firstCycle(),
+    );
+    expect(tri2.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(-1, 0, 1, 0).firstCycle());
+    expect(itri.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(1, 0.5, 0, 0.5).firstCycle(),
+    );
+    expect(itri2.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(1, 0, -1, 0).firstCycle());
+    expect(square.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(sequence(0, 0, 1, 1).firstCycle());
+    expect(square2.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(-1, -1, 1, 1).firstCycle(),
+    );
+    expect(isquare.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(1, 1, 0, 0).firstCycle(),
+    );
+    expect(isquare2.late(1).struct(true, true, true, true).firstCycle()).toStrictEqual(
+      sequence(1, 1, -1, -1).firstCycle(),
+    );
+  });
 });
 
 describe('cyclesPer', () => {
diff --git a/test/__snapshots__/tunes.test.mjs.snap b/test/__snapshots__/tunes.test.mjs.snap
index fc77616c4..1fb178801 100644
--- a/test/__snapshots__/tunes.test.mjs.snap
+++ b/test/__snapshots__/tunes.test.mjs.snap
@@ -7203,8 +7203,12 @@ exports[`renders tunes > tune: holyflute 1`] = `
 
 exports[`renders tunes > tune: juxUndTollerei 1`] = `
 [
+  "[ -99/200 ⇜ (0/1 → 1/200) | note:63 s:triangle pan:0 cutoff:758.852817928549 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
+  "[ -99/200 ⇜ (0/1 → 1/200) | note:67 s:triangle pan:1 color:green cutoff:758.852817928549 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
   "[ 0/1 → 1/4 | note:c3 s:sawtooth pan:0 cutoff:1100 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
   "[ 0/1 → 1/4 | note:bb3 s:sawtooth pan:1 color:green cutoff:1100 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
+  "[ 1/200 → 101/200 | note:55 s:triangle pan:0 cutoff:1103.534282651425 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
+  "[ 1/200 → 101/200 | note:65 s:triangle pan:1 color:green cutoff:1103.534282651425 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
   "[ 1/4 → 1/2 | note:eb3 s:sawtooth pan:0 cutoff:1275.581289814515 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
   "[ 1/4 → 1/2 | note:g3 s:sawtooth pan:1 color:green cutoff:1275.581289814515 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",
   "[ 1/2 → 3/4 | note:g3 s:sawtooth pan:0 cutoff:1444.415089128581 lpattack:0.2 lpenv:-2 decay:0.05 sustain:0 room:0.6 delay:0.5 delaytime:0.1 delayfeedback:0.4 ]",