diff --git a/doc/api/next_api_changes/deprecations/29358-TH.rst b/doc/api/next_api_changes/deprecations/29358-TH.rst
new file mode 100644
index 000000000000..513628e0bd42
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/29358-TH.rst
@@ -0,0 +1,10 @@
+3rd party scales do not need to have an *axis* parameter anymore
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Since matplotlib 3.1 `PR 12831 <https://github.com/matplotlib/matplotlib/pull/12831>`_
+scales should be reusable and therefore independent of the Axis. Therefore the use of
+of the *axis* parameter in the ``__init__`` had been discouraged. However, that
+parameter was still necessary for API compatibility. This is no longer the case.
+
+`.register_scale` now accepts scale classes with and without this parameter.
+3rd party scales can and should remove that parameter.
diff --git a/lib/matplotlib/scale.py b/lib/matplotlib/scale.py
index ccaaae6caf5d..6f533f3fbd1a 100644
--- a/lib/matplotlib/scale.py
+++ b/lib/matplotlib/scale.py
@@ -690,6 +690,9 @@ def limit_range_for_scale(self, vmin, vmax, minpos):
     'functionlog': FuncScaleLog,
     }
 
+# caching of signature info
+_scale_has_axis_parameter = {}
+
 
 def get_scale_names():
     """Return the names of the available scales."""
@@ -706,7 +709,19 @@ def scale_factory(scale, axis, **kwargs):
     axis : `~matplotlib.axis.Axis`
     """
     scale_cls = _api.check_getitem(_scale_mapping, scale=scale)
-    return scale_cls(axis, **kwargs)
+
+    # We support scales that may or may not have an initial *axis* parameter.
+    # This information is cached, so that we do not need to inspect the signature
+    # on every time we create a scale.
+    if scale not in _scale_has_axis_parameter:
+        _scale_has_axis_parameter[scale] = (
+            "axis" in inspect.signature(scale_cls).parameters
+        )
+
+    if _scale_has_axis_parameter[scale]:
+        return scale_cls(axis, **kwargs)
+    else:
+        return scale_cls(**kwargs)
 
 
 if scale_factory.__doc__:
diff --git a/lib/matplotlib/tests/test_scale.py b/lib/matplotlib/tests/test_scale.py
index 727397367762..945cbfc48f28 100644
--- a/lib/matplotlib/tests/test_scale.py
+++ b/lib/matplotlib/tests/test_scale.py
@@ -6,8 +6,12 @@
     LogTransform, InvertedLogTransform,
     SymmetricalLogTransform)
 import matplotlib.scale as mscale
-from matplotlib.ticker import AsinhLocator, LogFormatterSciNotation
+from matplotlib.ticker import (
+    AsinhLocator, AutoLocator, LogFormatterSciNotation,
+    NullFormatter, NullLocator, ScalarFormatter
+)
 from matplotlib.testing.decorators import check_figures_equal, image_comparison
+from matplotlib.transforms import IdentityTransform
 
 import numpy as np
 from numpy.testing import assert_allclose
@@ -293,3 +297,35 @@ def test_bad_scale(self):
             AsinhScale(axis=None, linear_width=-1)
         s0 = AsinhScale(axis=None, )
         s1 = AsinhScale(axis=None, linear_width=3.0)
+
+
+def test_custom_scale_without_axis():
+    """
+    Test that one can register and use custom scales that don't take an *axis* param.
+    """
+    class CustomTransform(IdentityTransform):
+        pass
+
+    class CustomScale(mscale.ScaleBase):
+        name = "custom"
+
+        def __init__(self):
+            self._transform = CustomTransform()
+
+        def get_transform(self):
+            return self._transform
+
+        def set_default_locators_and_formatters(self, axis):
+            axis.set_major_locator(AutoLocator())
+            axis.set_major_formatter(ScalarFormatter())
+            axis.set_minor_locator(NullLocator())
+            axis.set_minor_formatter(NullFormatter())
+
+    try:
+        mscale.register_scale(CustomScale)
+        fig, ax = plt.subplots()
+        ax.set_xscale('custom')
+        assert isinstance(ax.xaxis.get_transform(), CustomTransform)
+    finally:
+        # cleanup - there's no public unregister_scale()
+        del mscale._scale_mapping["custom"]