diff --git a/docs/3d-envelopes.png b/docs/3d-envelopes.png
index 0f6cc07..1ec9cdc 100644
Binary files a/docs/3d-envelopes.png and b/docs/3d-envelopes.png differ
diff --git a/experiments/piano_heterodyne.ipynb b/experiments/piano_heterodyne.ipynb
index b89ffb3..4a12c89 100644
--- a/experiments/piano_heterodyne.ipynb
+++ b/experiments/piano_heterodyne.ipynb
@@ -1422,10 +1422,14 @@
    "source": [
     "def time_mapper(t, boundary=0.25, magnification=8.0):\n",
     "    \"\"\"Convert time in secs to a nonlinear projection.\"\"\"\n",
-    "    #return np.log10(0.01 + t)\n",
-    "    t = np.asarray(t)\n",
-    "    magnified = (t < boundary)\n",
-    "    return magnified * t + (1 - magnified) * (boundary + (t - boundary) / magnification)\n",
+    "    return np.log10(0.01 + t)\n",
+    "    #t = np.asarray(t)\n",
+    "    #magnified = (t < boundary)\n",
+    "    #return magnified * t + (1 - magnified) * (boundary + (t - boundary) / magnification)\n",
+    "\n",
+    "def inv_time_mapper(mapped_t, boundary=0.25, magnification=8.0):\n",
+    "    magnified = mapped_t < boundary\n",
+    "    return magnified * mapped_t + (1 - magnified) * (boundary + magnification * (mapped_t - boundary))\n",
     "\n",
     "from matplotlib.collections import PolyCollection\n",
     "\n",
@@ -1458,6 +1462,10 @@
     "    \n",
     "    plt.title(filename)\n",
     "    plt.xlabel('time / s')\n",
+    "    #tick_times = np.array([0, 0.1, 0.2, 1.0, 2.0, 3.0, 4.0])\n",
+    "    tick_times = np.array([0, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0])\n",
+    "    plt.xticks(time_mapper(tick_times), tick_times)\n",
+    "    #plt.xlim([-0.05, 0.8])\n",
     "    plt.ylabel('harm #')\n",
     "    plt.yticks(np.arange(2, 22, 2), np.arange(19, -1, -2))\n",
     "    #plt.zlabel('level / dB')\n",