diff --git a/qiskit_experiments/calibration_management/basis_gate_library.py b/qiskit_experiments/calibration_management/basis_gate_library.py
index bf48dd7f47..c5fd5a6781 100644
--- a/qiskit_experiments/calibration_management/basis_gate_library.py
+++ b/qiskit_experiments/calibration_management/basis_gate_library.py
@@ -36,6 +36,9 @@ class BasisGateLibrary(ABC, Mapping):
     # Location where default parameter values are stored. These may be updated at construction.
     __default_values__ = {}
 
+    # Parameters that do not belong to a schedule, a set of names
+    __parameters_without_schedule__ = set()
+
     def __init__(
         self,
         basis_gates: Optional[List[str]] = None,
@@ -204,12 +207,18 @@ class FixedFrequencyTransmon(BasisGateLibrary):
           The amplitude of the ``sx`` and ``sy`` pulses is half the provided value.
         - angle: The phase of the complex amplitude of the pulses.
 
+    Parameters without schedule:
+        - meas_freq: frequency of the measurement drives.
+        - drive_freq: frequency of the qubit drives.
+
     Note that the β and amp parameters may be linked between the x and y as well as between
     the sx and sy pulses. All pulses share the same duration and σ parameters.
     """
 
     __default_values__ = {"duration": 160, "amp": 0.5, "β": 0.0, "angle": 0.0}
 
+    __parameters_without_schedule__ = {"meas_freq", "drive_freq"}
+
     def __init__(
         self,
         basis_gates: Optional[List[str]] = None,
diff --git a/qiskit_experiments/calibration_management/calibrations.py b/qiskit_experiments/calibration_management/calibrations.py
index 7ace1fba3b..0ee98c707b 100644
--- a/qiskit_experiments/calibration_management/calibrations.py
+++ b/qiskit_experiments/calibration_management/calibrations.py
@@ -63,12 +63,6 @@ class Calibrations:
     ScheduleBlock are supported.
     """
 
-    # The name of the parameter under which the qubit frequencies are registered.
-    __drive_freq_parameter__ = "drive_freq"
-
-    # The name of the parameter under which the readout frequencies are registered.
-    __readout_freq_parameter__ = "meas_freq"
-
     def __init__(
         self,
         coupling_map: Optional[List[List[int]]] = None,
@@ -153,7 +147,6 @@ def __init__(
                 libraries = [libraries]
 
             for lib in libraries:
-
                 # Add the basis gates
                 for gate in lib.basis_gates:
                     self.add_schedule(lib[gate], num_qubits=lib.num_qubits(gate))
@@ -163,6 +156,10 @@ def __init__(
                     for param_conf in lib.default_values():
                         self.add_parameter_value(*param_conf, update_inst_map=False)
 
+                # Add the parameters that do not belong to a schedule.
+                for param_name in lib.__parameters_without_schedule__:
+                    self._register_parameter(Parameter(param_name), tuple())
+
         # This internal parameter is False so that if a schedule is added after the
         # init it will be set to True and serialization will raise an error.
         self._has_manually_added_schedule = False
@@ -170,12 +167,6 @@ def __init__(
         # Instruction schedule map variables and support variables.
         self._inst_map = InstructionScheduleMap()
 
-        # Use the same naming convention as in backend.defaults()
-        self.drive_freq = Parameter(self.__drive_freq_parameter__)
-        self.meas_freq = Parameter(self.__readout_freq_parameter__)
-        self._register_parameter(self.drive_freq, ())
-        self._register_parameter(self.meas_freq, ())
-
         # Backends with a single qubit may not have a coupling map.
         self._coupling_map = coupling_map if coupling_map is not None else []
 
@@ -187,6 +178,28 @@ def __init__(
         # Push the schedules to the instruction schedule map.
         self.update_inst_map()
 
+    @property
+    @deprecate_func(
+        is_property=True,
+        since="0.6",
+        package_name="qiskit-experiments",
+        additional_msg="The drive_freq is moved to FixedFrequencyTransmon basis gate library.",
+    )
+    def drive_freq(self):
+        """Parameter object for qubit drive frequency."""
+        return self._parameter_map.get(("drive_freq", (), None), None)
+
+    @property
+    @deprecate_func(
+        is_property=True,
+        since="0.6",
+        package_name="qiskit-experiments",
+        additional_msg="The meas_freq is moved to FixedFrequencyTransmon basis gate library.",
+    )
+    def meas_freq(self):
+        """Parameter object for qubit measure frequency."""
+        return self._parameter_map.get(("meas_freq", (), None), None)
+
     def _check_consistency(self):
         """Check that the attributes defined in self are consistent.
 
@@ -237,7 +250,7 @@ def from_backend(
             libraries: A list of libraries from which to get template schedules to register as
                 well as default parameter values.
             add_parameter_defaults: A boolean to indicate whether the default parameter values of
-                the given library should be used to populate the calibrations. By default this
+                the given library should be used to populate the calibrations. By default, this
                 value is ``True``.
 
         Returns:
@@ -260,11 +273,13 @@ def from_backend(
         )
 
         if add_parameter_defaults:
-            for qubit, freq in enumerate(backend_data.drive_freqs):
-                cals.add_parameter_value(freq, cals.drive_freq, qubit, update_inst_map=False)
+            if ("drive_freq", (), None) in cals._parameter_map:
+                for qubit, freq in enumerate(backend_data.drive_freqs):
+                    cals.add_parameter_value(freq, "drive_freq", qubit, update_inst_map=False)
 
-            for meas, freq in enumerate(backend_data.meas_freqs):
-                cals.add_parameter_value(freq, cals.meas_freq, meas, update_inst_map=False)
+            if ("meas_freq", (), None) in cals._parameter_map:
+                for meas, freq in enumerate(backend_data.meas_freqs):
+                    cals.add_parameter_value(freq, "meas_freq", meas, update_inst_map=False)
 
         # Update the instruction schedule map after adding all parameter values.
         cals.update_inst_map()
@@ -449,7 +464,6 @@ def _get_full_qubits_of_schedule(
         """
         for key, circuit_inst_num_qubits in self._schedules_qubits.items():
             if key.schedule == schedule_name:
-
                 if len(partial_qubits) == circuit_inst_num_qubits:
                     return [partial_qubits]
 
@@ -888,7 +902,6 @@ def _get_channel_index(self, qubits: Tuple[int, ...], chan: PulseChannel) -> int
 
             # Control channels name example ch1.0$1
             if isinstance(chan, ControlChannel):
-
                 channel_index_parts = chan.index.name[2:].split("$")
                 qubit_channels = channel_index_parts[0]
 
diff --git a/qiskit_experiments/calibration_management/update_library.py b/qiskit_experiments/calibration_management/update_library.py
index eac5e32d04..ff6009432c 100644
--- a/qiskit_experiments/calibration_management/update_library.py
+++ b/qiskit_experiments/calibration_management/update_library.py
@@ -149,7 +149,7 @@ def update(
         calibrations: Calibrations,
         exp_data: ExperimentData,
         result_index: Optional[int] = None,
-        parameter: str = None,
+        parameter: str = "drive_freq",
         group: str = "default",
         fit_parameter: Optional[str] = None,
         **options,
@@ -163,16 +163,13 @@ def update(
             exp_data: The experiment data from which to update.
             result_index: The result index to use which defaults to -1.
             parameter: The name of the parameter to update. If None is given this will default
-                to :code:`calibrations.__qubit_freq_parameter__`.
+                to `drive_freq`.
             group: The calibrations group to update. Defaults to "default."
             options: Trailing options.
             fit_parameter: The name of the fit parameter in the analysis result. This will default
                 to the class variable :code:`__fit_parameter__` if not given.
 
         """
-        if parameter is None:
-            parameter = calibrations.__drive_freq_parameter__
-
         super().update(
             calibrations=calibrations,
             exp_data=exp_data,
diff --git a/qiskit_experiments/library/calibration/fine_frequency_cal.py b/qiskit_experiments/library/calibration/fine_frequency_cal.py
index 049712b7f9..66c9479918 100644
--- a/qiskit_experiments/library/calibration/fine_frequency_cal.py
+++ b/qiskit_experiments/library/calibration/fine_frequency_cal.py
@@ -37,6 +37,7 @@ def __init__(
         physical_qubits: Sequence[int],
         calibrations: Calibrations,
         backend: Optional[Backend] = None,
+        cal_parameter_name: Optional[str] = "drive_freq",
         delay_duration: Optional[int] = None,
         repetitions: List[int] = None,
         auto_update: bool = True,
@@ -54,11 +55,13 @@ def __init__(
                 fine frequency calibration.
             calibrations: The calibrations instance with the schedules.
             backend: Optional, the backend to run the experiment on.
+            cal_parameter_name: The name of the parameter to update in the calibrations.
+                This defaults to `drive_freq`.
             delay_duration: The duration of the delay at :math:`n=1`. If this value is
                 not given then the duration of the gate named ``gate_name`` in the
                 calibrations will be used.
-            auto_update: Whether or not to automatically update the calibrations. By
-                default this variable is set to True.
+            auto_update: Whether to automatically update the calibrations or not. By
+                default, this variable is set to True.
             gate_name: This argument is only needed if ``delay_duration`` is None. This
                 should be the name of a valid schedule in the calibrations.
         """
@@ -72,7 +75,7 @@ def __init__(
             schedule_name=None,
             repetitions=repetitions,
             backend=backend,
-            cal_parameter_name=calibrations.__drive_freq_parameter__,
+            cal_parameter_name=cal_parameter_name,
             auto_update=auto_update,
         )
 
diff --git a/qiskit_experiments/library/calibration/frequency_cal.py b/qiskit_experiments/library/calibration/frequency_cal.py
index 82e52c4eb2..79c3d7bc47 100644
--- a/qiskit_experiments/library/calibration/frequency_cal.py
+++ b/qiskit_experiments/library/calibration/frequency_cal.py
@@ -36,6 +36,7 @@ def __init__(
         physical_qubits: Sequence[int],
         calibrations: Calibrations,
         backend: Optional[Backend] = None,
+        cal_parameter_name: Optional[str] = "drive_freq",
         delays: Optional[List] = None,
         osc_freq: float = 2e6,
         auto_update: bool = True,
@@ -46,6 +47,8 @@ def __init__(
                 frequency calibration.
             calibrations: The calibrations instance with the schedules.
             backend: Optional, the backend to run the experiment on.
+            cal_parameter_name: The name of the parameter to update in the calibrations.
+                This defaults to `drive_freq`.
             delays: The list of delays that will be scanned in the experiment, in seconds.
             osc_freq: A frequency shift in Hz that will be applied by means of
                 a virtual Z rotation to increase the frequency of the measured oscillation.
@@ -58,7 +61,7 @@ def __init__(
             backend=backend,
             delays=delays,
             osc_freq=osc_freq,
-            cal_parameter_name=calibrations.__drive_freq_parameter__,
+            cal_parameter_name=cal_parameter_name,
             auto_update=auto_update,
         )
 
diff --git a/qiskit_experiments/library/calibration/rough_frequency.py b/qiskit_experiments/library/calibration/rough_frequency.py
index a618c53749..da7a15baa9 100644
--- a/qiskit_experiments/library/calibration/rough_frequency.py
+++ b/qiskit_experiments/library/calibration/rough_frequency.py
@@ -40,6 +40,7 @@ def __init__(
         backend: Optional[Backend] = None,
         auto_update: bool = True,
         absolute: bool = True,
+        cal_parameter_name: Optional[str] = "drive_freq",
     ):
         """See :class:`.QubitSpectroscopy` for detailed documentation.
 
@@ -53,6 +54,8 @@ def __init__(
                 automatically update the frequency in the calibrations.
             absolute: Boolean to specify if the frequencies are absolute or relative to the
                 qubit frequency in the backend.
+            cal_parameter_name: The name of the parameter to update in the calibrations.
+                This defaults to `drive_freq`.
 
         Raises:
             QiskitError: If there are less than three frequency shifts.
@@ -66,6 +69,7 @@ def __init__(
             absolute=absolute,
             updater=Frequency,
             auto_update=auto_update,
+            cal_parameter_name=cal_parameter_name,
         )
 
     def _attach_calibrations(self, circuit: QuantumCircuit):
diff --git a/releasenotes/notes/params_without_schedule-20555d98875a626b.yaml b/releasenotes/notes/params_without_schedule-20555d98875a626b.yaml
new file mode 100644
index 0000000000..5c1c019ac8
--- /dev/null
+++ b/releasenotes/notes/params_without_schedule-20555d98875a626b.yaml
@@ -0,0 +1,11 @@
+---
+upgrade:
+  - |
+    The variables `__drive_freq_parameter__` and `__readout_freq_parameter__`
+    have been removed from `Calibrations`. These variables were given special
+    treatment which is inconsistent with the framework. To replace them a
+    mechanism to define and add parameters without a schedule has been added to
+    the basis gate library. This has the added benefit of making the API of 
+    frequency calibration experiments more consistent with the other calibration
+    experiments. Calibration developers can now add parameters to their library that are not 
+    attached to a schedule in a meaningful way.
diff --git a/test/calibration/test_calibrations.py b/test/calibration/test_calibrations.py
index af70681421..0d8f4d78a7 100644
--- a/test/calibration/test_calibrations.py
+++ b/test/calibration/test_calibrations.py
@@ -217,12 +217,12 @@ def test_remove_schedule(self):
         self.cals.add_schedule(sched, num_qubits=1)
 
         self.assertEqual(len(self.cals.schedules()), 4)
-        self.assertEqual(len(self.cals.parameters), 9)
+        self.assertEqual(len(self.cals.parameters), 7)
 
         self.cals.remove_schedule(sched)
 
         self.assertEqual(len(self.cals.schedules()), 3)
-        self.assertEqual(len(self.cals.parameters), 8)
+        self.assertEqual(len(self.cals.parameters), 6)
         for param in [self.sigma, self.amp_xp, self.amp_x90p, self.amp_y90p, self.beta]:
             self.assertTrue(param in self.cals.parameters)
 
@@ -323,7 +323,7 @@ def test_from_backend(self):
         """Test that when generating calibrations from backend
         the data is passed correctly"""
         backend = FakeBelemV2()
-        cals = Calibrations.from_backend(backend)
+        cals = Calibrations.from_backend(backend, libraries=[FixedFrequencyTransmon()])
         with self.assertWarns(DeprecationWarning):
             config_args = cals.config()["kwargs"]
         control_channel_map_size = len(config_args["control_channel_map"].chan_map)
@@ -565,8 +565,6 @@ def test_default_schedules(self):
             self.sigma,
             self.beta,
             self.duration,
-            self.cals.drive_freq,
-            self.cals.meas_freq,
         }
         self.assertEqual(len(set(self.cals.parameters.keys())), len(expected))
 
diff --git a/test/calibration/test_setup_library.py b/test/calibration/test_setup_library.py
index 04b40a95a2..1c1307c97a 100644
--- a/test/calibration/test_setup_library.py
+++ b/test/calibration/test_setup_library.py
@@ -92,7 +92,7 @@ def test_standard_single_qubit_gates(self):
         self.assertListEqual(library.basis_gates, ["x", "y", "sx", "sy"])
 
     def test_unlinked_parameters(self):
-        """Test the we get schedules with unlinked parameters."""
+        """Test that we get schedules with unlinked parameters."""
 
         library = FixedFrequencyTransmon(link_parameters=False)
 
diff --git a/test/calibration/test_update_library.py b/test/calibration/test_update_library.py
index a9404d64fd..0cc8186dfc 100644
--- a/test/calibration/test_update_library.py
+++ b/test/calibration/test_update_library.py
@@ -21,6 +21,7 @@
 from qiskit_experiments.library import QubitSpectroscopy
 from qiskit_experiments.calibration_management.calibrations import Calibrations
 from qiskit_experiments.calibration_management.update_library import Frequency
+from qiskit_experiments.calibration_management.basis_gate_library import FixedFrequencyTransmon
 from qiskit_experiments.test.mock_iq_backend import MockIQBackend
 from qiskit_experiments.test.mock_iq_helpers import MockIQSpectroscopyHelper as SpectroscopyHelper
 
@@ -55,7 +56,7 @@ def test_frequency(self):
         self.assertEqual(result.quality, "good")
 
         # Test the integration with the Calibrations
-        cals = Calibrations.from_backend(FakeAthensV2())
-        self.assertNotEqual(cals.get_parameter_value(cals.__drive_freq_parameter__, qubit), value)
+        cals = Calibrations.from_backend(FakeAthensV2(), libraries=[FixedFrequencyTransmon()])
+        self.assertNotEqual(cals.get_parameter_value("drive_freq", qubit), value)
         Frequency.update(cals, exp_data)
-        self.assertEqual(cals.get_parameter_value(cals.__drive_freq_parameter__, qubit), value)
+        self.assertEqual(cals.get_parameter_value("drive_freq", qubit), value)
diff --git a/test/library/calibration/test_fine_frequency.py b/test/library/calibration/test_fine_frequency.py
index 09f40471ac..b9f256dd02 100644
--- a/test/library/calibration/test_fine_frequency.py
+++ b/test/library/calibration/test_fine_frequency.py
@@ -80,14 +80,14 @@ def test_calibration_version(self):
         fine_freq = FineFrequencyCal([0], self.cals, backend)
         armonk_freq = BackendData(FakeArmonkV2()).drive_freqs[0]
 
-        freq_before = self.cals.get_parameter_value(self.cals.__drive_freq_parameter__, 0)
+        freq_before = self.cals.get_parameter_value("drive_freq", 0)
 
         self.assertAlmostEqual(freq_before, armonk_freq)
 
         expdata = fine_freq.run()
         self.assertExperimentDone(expdata)
 
-        freq_after = self.cals.get_parameter_value(self.cals.__drive_freq_parameter__, 0)
+        freq_after = self.cals.get_parameter_value("drive_freq", 0)
 
         # Test equality up to 10kHz on a 100 kHz shift
         self.assertAlmostEqual(freq_after, armonk_freq + exp_helper.freq_shift, delta=1e4)
diff --git a/test/library/calibration/test_ramsey_xy.py b/test/library/calibration/test_ramsey_xy.py
index 391700b8b6..a3c9d11252 100644
--- a/test/library/calibration/test_ramsey_xy.py
+++ b/test/library/calibration/test_ramsey_xy.py
@@ -76,7 +76,7 @@ def test_update_calibrations(self):
 
         tol = 1e4  # 10 kHz resolution
 
-        freq_name = self.cals.__drive_freq_parameter__
+        freq_name = "drive_freq"
 
         # Check qubit frequency before running the cal
         f01 = self.cals.get_parameter_value(freq_name, 0)
diff --git a/test/library/calibration/test_rough_frequency.py b/test/library/calibration/test_rough_frequency.py
index bc4171f774..3b32ad3d26 100644
--- a/test/library/calibration/test_rough_frequency.py
+++ b/test/library/calibration/test_rough_frequency.py
@@ -58,7 +58,7 @@ def test_update_calibrations(self):
         library = FixedFrequencyTransmon()
         cals = Calibrations.from_backend(self.backend, libraries=[library])
 
-        prev_freq = cals.get_parameter_value(cals.__drive_freq_parameter__, (0,))
+        prev_freq = cals.get_parameter_value("drive_freq", (0,))
         self.assertEqual(prev_freq, freq01)
 
         frequencies = np.linspace(freq01 - 10.0e6, freq01 + 10.0e6, 11)
@@ -69,7 +69,7 @@ def test_update_calibrations(self):
         self.assertExperimentDone(expdata)
 
         # Check the updated frequency which should be shifted by 5MHz.
-        post_freq = cals.get_parameter_value(cals.__drive_freq_parameter__, (0,))
+        post_freq = cals.get_parameter_value("drive_freq", (0,))
         self.assertTrue(abs(post_freq - freq01 - 5e6) < 1e6)
 
     def test_experiment_config(self):