diff --git a/sasdata/abscissa.py b/sasdata/abscissa.py
new file mode 100644
index 00000000..a0c16a1e
--- /dev/null
+++ b/sasdata/abscissa.py
@@ -0,0 +1,123 @@
+from abc import ABC, abstractmethod
+
+import numpy as np
+from exceptions import InterpretationError
+from numpy._typing import ArrayLike
+from quantities.quantity import Quantity
+from util import is_increasing
+
+
+class Abscissa(ABC):
+
+    def __init__(self, axes: list[Quantity]):
+        self._axes = axes
+        self._dimensionality = len(axes)
+
+    @property
+    def dimensionality(self) -> int:
+        """ Dimensionality of this data """
+        return self._dimensionality
+
+    @property
+    @abstractmethod
+    def is_grid(self) -> bool:
+        """ Are these coordinates using a grid representation
+        (as opposed to a general list representation)
+
+        is_grid = True: implies that the corresponding ordinate is n-dimensional tensor
+        is_grid = False: implies that the corresponding ordinate is a 1D list
+
+        If the data is one dimensional, is_grid=True
+        """
+
+    @property
+    def axes(self) -> list[Quantity]:
+        """ Axes of the data:
+
+        If it's an (n1-by-n2-by-n3...) grid (is_grid=True): give the values for each axis, returning a list like
+          [Quantity(length n1), Quantity(length n2), Quantity(length n3) ... ]
+
+        If it is not grid data (is_grid=False), but n points on a general mesh, give one array for each dimension
+          [Quantity(length n), Quantity(length n), Quantity(length n) ... ]
+        """
+
+        return self._axes
+
+    @staticmethod
+    def _determine_error_message(axis_arrays: list[np.ndarray], ordinate_shape: tuple):
+        """ Error message for the `.determine` function"""
+
+        shape_string = ", ".join([str(axis.shape) for axis in axis_arrays])
+
+        return f"Cannot interpret array shapes axis: [{shape_string}], ordinate: {ordinate_shape}"
+
+    @staticmethod
+    def determine(axis_data: list[Quantity[ArrayLike]], ordinate_data: Quantity[ArrayLike]) -> "Abscissa":
+        """ Get an Abscissa object that fits the combination of axes and data"""
+
+        # Different posibilites:
+        #   1: axes_data[i].shape == axes_data[j].shape == ordinate_data.shape
+        #    1a: axis_data[i] is 1D =>
+        #      1a-i:  len(axes_data) == 1 => Grid type or Scatter type depending on sortedness
+        #      1a-ii: len(axes_data) != 1 => Scatter type
+        #    1b: axis_data[i] dimensionality matches len(axis_data) => Meshgrid type
+        #    1c: other => Error
+        #   2: (len(axes_data[0]), len(axes_data[1])... ) == ordinate_data.shape => Grid type
+        #   3: None of the above => Error
+
+        ordinate_shape = np.array(ordinate_data.value).shape
+        axis_arrays = [np.array(axis.value) for axis in axis_data]
+
+        # 1:
+        if all([axis.shape == ordinate_shape for axis in axis_arrays]):
+            # 1a:
+            if all([len(axis.shape)== 1 for axis in axis_arrays]):
+                # 1a-i:
+                if len(axis_arrays) == 1:
+                    # Is it sorted
+                    if is_increasing(axis_arrays[0]):
+                        return GridAbscissa(axis_data)
+                    else:
+                        return ScatterAbscissa(axis_data)
+                # 1a-ii
+                else:
+                    return ScatterAbscissa(axis_data)
+            # 1b
+            elif all([len(axis.shape) == len(axis_arrays) for axis in axis_arrays]):
+
+                return MeshgridAbscissa(axis_data)
+
+            else:
+                raise InterpretationError(Abscissa._determine_error_message(axis_arrays, ordinate_shape))
+
+        elif all([len(axis.shape)== 1 for axis in axis_arrays]) and \
+                tuple([axis.shape[0] for axis in axis_arrays]) == ordinate_shape:
+
+            # Require that they are sorted
+            if all([is_increasing(axis) for axis in axis_arrays]):
+
+                return GridAbscissa(axis_data)
+
+            else:
+                raise InterpretationError("Grid axes are not sorted")
+
+        else:
+            raise InterpretationError(Abscissa._determine_error_message(axis_arrays, ordinate_shape))
+
+class GridAbscissa(Abscissa):
+
+    @property
+    def is_grid(self):
+        return True
+
+class MeshgridAbscissa(Abscissa):
+
+    @property
+    def is_grid(self):
+        return True
+
+class ScatterAbscissa(Abscissa):
+
+    @property
+    def is_grid(self):
+        return False
diff --git a/sasdata/data.py b/sasdata/data.py
index 73e64e61..afb280d8 100644
--- a/sasdata/data.py
+++ b/sasdata/data.py
@@ -11,6 +11,58 @@
 
 
 class SasData:
+    """ General object containing data in the SasView ecosystem"""
+
+    def __init__(self,
+                 name: str,
+                 ordinate: Quantity,
+                 mask: Quantity,
+                 abscissae: list[Quantity],
+                 dependents: list["SasData"]):
+
+        self._ordinate = ordinate
+        self._abscissae = abscissae
+        self._mask = mask
+
+    @property
+    def ordinate(self) -> Quantity:
+        return self._ordinate
+
+    @property
+    def abscissae(self) -> list[Quantity]:
+        return self._abscissae
+
+    @property
+    def mask(self) -> Quantity:
+        return self._mask
+
+    def scatter_data(self):
+        """ Return data in the coordinate/value form [(x1, x2, x3, y)...]"""
+
+
+class SasDerivedMeasurement(SasData):
+    """ General object sas measurement that has not come directly from a file,
+    for example, the difference between two datasets"""
+
+
+    def __init__(self,
+                 name: str,
+                 ordinate: Quantity,
+                 abscissae: list[Quantity],
+                 dependents: list["SasData"],
+                 metadata: DerivedMetadata):
+
+        super().__init__(
+            name=name,
+            ordinate=ordinate,
+            abscissae=abscissae,
+            dependents=dependents)
+
+        self.metadata = metadata
+
+
+class SasMeasurement(SasData):
+
     def __init__(
         self,
         name: str,
@@ -119,7 +171,6 @@ def _save_h5(self, sasentry: HDF5Group):
         for idx, (key, sasdata) in enumerate(self._data_contents.items()):
             sasdata.as_h5(group, key)
 
-
     @staticmethod
     def save_h5(data: dict[str, typing.Self], path: str | typing.BinaryIO):
         with h5py.File(path, "w") as f:
@@ -130,7 +181,6 @@ def save_h5(data: dict[str, typing.Self], path: str | typing.BinaryIO):
                 data._save_h5(sasentry)
 
 
-
 class SasDataEncoder(MetadataEncoder):
     def default(self, obj):
         match obj:
diff --git a/sasdata/exceptions.py b/sasdata/exceptions.py
new file mode 100644
index 00000000..6fc3e545
--- /dev/null
+++ b/sasdata/exceptions.py
@@ -0,0 +1,2 @@
+class InterpretationError(Exception):
+    """ Error interpreting data """
diff --git a/sasdata/util.py b/sasdata/util.py
index 8decc68b..5dd0d404 100644
--- a/sasdata/util.py
+++ b/sasdata/util.py
@@ -1,6 +1,8 @@
 from collections.abc import Callable
 from typing import TypeVar
 
+import numpy as np
+
 T = TypeVar("T")
 
 def cache[T](fun: Callable[[], T]):
@@ -16,3 +18,15 @@ def wrapper() -> T:
         return cache_state[1]
 
     return wrapper
+
+def is_increasing(data: np.ndarray):
+    """ Check if a 1D array is sorted in strictly increasing order"""
+    return np.all(data[1:] > data[:-1])
+
+def is_decreasing(data: np.ndarray):
+    """ Check if a 1D array is sorted in strictly decreasing order"""
+    return np.all(data[1:] < data[:-1])
+
+def is_sorted(data: np.ndarray):
+    """ Check if a 1D array is strictly sorted """
+    return is_increasing(data) or is_decreasing(data)
diff --git a/test/utest_asbscissa.py b/test/utest_asbscissa.py
new file mode 100644
index 00000000..49debb3d
--- /dev/null
+++ b/test/utest_asbscissa.py
@@ -0,0 +1,71 @@
+import numpy as np
+import pytest
+from abscissa import Abscissa, GridAbscissa, MeshgridAbscissa, ScatterAbscissa
+from exceptions import InterpretationError
+from quantities.quantity import Quantity
+from quantities.units import none
+
+
+def test_deterimine_1d_grid():
+    """ Test that 1D ordered data is grid type"""
+    q = Quantity(np.arange(10), units=none)
+
+    determined = Abscissa.determine([q], q)
+
+    assert isinstance(determined, GridAbscissa)
+
+def test_deterimine_1d_scatter():
+    """ Test that 1D unordered data is scatter type """
+    a = Quantity(np.array([1, 2, 3, 4, 5, 0, 9, 8, 7, 6]), units=none)
+    d = Quantity(np.arange(10), units=none)
+
+    determined = Abscissa.determine([a], d)
+
+    assert isinstance(determined, ScatterAbscissa)
+
+def test_2D_scatter():
+    """ Test the nD scatter case with 2D data """
+    q = Quantity(np.arange(10), units=none)
+
+    determined = Abscissa.determine([q, q], q)
+
+    assert isinstance(determined, ScatterAbscissa)
+
+def test_2D_meshgrid():
+    """ Test the meshgrid case with 2x5"""
+    q = Quantity(np.arange(10).reshape(2, 5), units=none)
+
+    determined = Abscissa.determine([q, q], q)
+
+    assert isinstance(determined, MeshgridAbscissa)
+
+
+def test_2D_grid():
+    """ Test the nD grid case with 2x5 """
+    a1 = Quantity(np.arange(2), units=none)
+    a2 = Quantity(np.arange(5), units=none)
+
+    d = Quantity(np.arange(10).reshape(2, 5), units=none)
+
+    determined = Abscissa.determine([a1, a2], d)
+
+    assert isinstance(determined, GridAbscissa)
+
+def test_2D_grid_axis_error():
+    """ Test the nD grid case with bad axes """
+
+    a1 = Quantity(np.arange(2), units=none)
+    a2 = Quantity(np.arange(5), units=none)
+
+    d = Quantity(np.arange(10).reshape(5, 2, 1), units=none)
+
+    with pytest.raises(InterpretationError):
+        Abscissa.determine([a1, a2], d)
+
+def test_2D_meshgrid_error_mismatched_dimensionality():
+    """ Test the nD meshgrid case with bad axes """
+
+    q = Quantity(np.arange(10).reshape(5, 2), units=none)
+
+    with pytest.raises(InterpretationError):
+        Abscissa.determine([q, q, q], q) # three axes, each 2D