Scale

Scale is a broad concept used to express size, proportion, or order of magnitude, and to relate a representation to a real object. In common use, a scale indicates how large or small something is in comparison with a reference size. In technical contexts, scales describe measurement systems, drawings, maps, and models that preserve proportional relationships.

Measurement scales classify how data are quantified. Nominal scales assign labels without order (eye color). Ordinal scales rank order without uniform differences (ranking). Interval scales have consistent differences but no true zero (temperature in Celsius). Ratio scales have meaningful zero and allow comparisons of magnitude (mass, length).

Maps, diagrams, and models use scales to relate drawing units to real-world units. A map scale such as 1:50,000 means one unit on the map equals 50,000 units in reality. Scale factors enable sizes to be increased or reduced while preserving shape.

Musical scales are ordered sequences of notes within an octave that establish pitch centers and tonal color. Common scales include major and natural minor in Western music, with several other scales such as harmonic minor, melodic minor, and pentatonic.

In science and engineering, scaling describes how a system's properties change with size. Scaling laws express relationships between variables, often as power laws. Allometry studies how biological traits change non-proportionally with body size, yielding insights into metabolism, locomotion, and ecology.

In computing and graphics, scaling refers to resizing images, user interfaces, or numerical data. It involves algorithms that maintain quality or proportionality under change of magnitude, and may require normalization to compare variables with different units.