How do I plot a spectrogram the same way that pylab's specgram() does?

Use pcolor or pcolormesh. pcolormesh is much faster, but is limited to rectilinear grids, where as pcolor can handle arbitrary shaped cells. specgram uses pcolormesh, if I recall correctly. (It uses imshow.)

As a quick example:

import numpy as np
import matplotlib.pyplot as plt

z = np.random.random((11,11))
x, y = np.mgrid[:11, :11]

fig, ax = plt.subplots()
ax.set_yscale('symlog')
ax.pcolormesh(x, y, z)
plt.show()

The differences you're seeing are due to plotting the "raw" values that specgram returns. What specgram actually plots is a scaled version.

import matplotlib.pyplot as plt
import numpy as np

x = np.cumsum(np.random.random(1000) - 0.5)

fig, (ax1, ax2) = plt.subplots(nrows=2)
data, freqs, bins, im = ax1.specgram(x)
ax1.axis('tight')

# "specgram" actually plots 10 * log10(data)...
ax2.pcolormesh(bins, freqs, 10 * np.log10(data))
ax2.axis('tight')

plt.show()

Notice that when we plot things using pcolormesh, there's no interpolation. (That's part of the point of pcolormesh--it's just vector rectangles instead of an image.)

If you want things on a log scale, you can use pcolormesh with it:

import matplotlib.pyplot as plt
import numpy as np

x = np.cumsum(np.random.random(1000) - 0.5)

fig, (ax1, ax2) = plt.subplots(nrows=2)
data, freqs, bins, im = ax1.specgram(x)
ax1.axis('tight')

# We need to explictly set the linear threshold in this case...
# Ideally you should calculate this from your bin size...
ax2.set_yscale('symlog', linthreshy=0.01)

ax2.pcolormesh(bins, freqs, 10 * np.log10(data))
ax2.axis('tight')

plt.show()