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diff --git a/testing/web-platform/tests/webaudio/the-audio-api/the-audioparam-interface/set-target-conv.html b/testing/web-platform/tests/webaudio/the-audio-api/the-audioparam-interface/set-target-conv.html
new file mode 100644
index 0000000000..2ed076cccf
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+++ b/testing/web-platform/tests/webaudio/the-audio-api/the-audioparam-interface/set-target-conv.html
@@ -0,0 +1,93 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+  <head>
+    <title>Test convergence of setTargetAtTime</title>
+    <script src="/resources/testharness.js"></script>
+    <script src="/resources/testharnessreport.js"></script>
+    <script src="/webaudio/resources/audit.js"></script>
+    <script src='/webaudio/resources/audio-param.js'></script>
+  </head>
+
+  <body>
+    <script>
+      let audit = Audit.createTaskRunner();
+
+      audit.define(
+          {task: 'setTargetAtTime', label: 'convergence handled correctly'},
+          (task, should) => {
+            // Two channels:
+            //  0 - actual result
+            //  1 - expected result
+            const context = new OfflineAudioContext(
+                {numberOfChannels: 2, sampleRate: 8000, length: 8000});
+
+            const merger = new ChannelMergerNode(
+                context, {numberOfChannels: context.destination.channelCount});
+            merger.connect(context.destination);
+
+            // Construct test source that will have tha AudioParams being tested
+            // to verify that the AudioParams are working correctly.
+            let src;
+
+            should(
+                () => src = new ConstantSourceNode(context),
+                'src = new ConstantSourceNode(context)')
+                .notThrow();
+
+            src.connect(merger, 0, 0);
+            src.offset.setValueAtTime(1, 0);
+
+            const timeConstant = 0.01;
+
+            // testTime must be at least 10*timeConstant. Also, this must not
+            // lie on a render boundary.
+            const testTime = 0.15;
+            const rampEnd = testTime + 0.001;
+
+            should(
+                () => src.offset.setTargetAtTime(0.5, 0.01, timeConstant),
+                `src.offset.setTargetAtTime(0.5, 0.01, ${timeConstant})`)
+                .notThrow();
+            should(
+                () => src.offset.setValueAtTime(0.5, testTime),
+                `src.offset.setValueAtTime(0.5, ${testTime})`)
+                .notThrow();
+            should(
+                () => src.offset.linearRampToValueAtTime(1, rampEnd),
+                `src.offset.linearRampToValueAtTime(1, ${rampEnd})`)
+                .notThrow();
+
+            // The reference node that will generate the expected output.  We do
+            // the same automations, except we don't apply the setTarget
+            // automation.
+            const refSrc = new ConstantSourceNode(context);
+            refSrc.connect(merger, 0, 1);
+
+            refSrc.offset.setValueAtTime(0.5, 0);
+            refSrc.offset.setValueAtTime(0.5, testTime);
+            refSrc.offset.linearRampToValueAtTime(1, rampEnd);
+
+            src.start();
+            refSrc.start();
+
+            context.startRendering()
+                .then(audio => {
+                  const actual = audio.getChannelData(0);
+                  const expected = audio.getChannelData(1);
+
+                  // Just verify that the actual output matches the expected
+                  // starting a little bit before testTime.
+                  let testFrame =
+                      Math.floor(testTime * context.sampleRate) - 128;
+                  should(actual.slice(testFrame), `output[${testFrame}:]`)
+                      .beCloseToArray(
+                          expected.slice(testFrame),
+                          {relativeThreshold: 4.1724e-6});
+                })
+                .then(() => task.done());
+          });
+
+      audit.run();
+    </script>
+  </body>
+</html>