Wound up combining CT Zhu's answer with tcaswell's hint:
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sbn
x = np.linspace(0, 2 * np.pi, 100)
y = np.sin(x)
fig, ax = plt.subplots(1, 1)
ax.scatter(x, y)
ax.get_xaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())
ax.get_yaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())
ax.grid(b=True, which='major', color='w', linewidth=1.0)
ax.grid(b=True, which='minor', color='w', linewidth=0.5)