# Scales of Measurement

Scales of measurement are important to understand when performing data analysis. They determine what technique to use to analyze the data.

In particular, scale developers must be aware of how to create items that can accurately measure the continuum they are trying to capture. This involves ensuring that the responses are unipolar or bipolar and choosing the correct response format.

## Definition

A ratio representing the relation of a model or figure’s dimensions to those of the actual figure or object. Also known as a scale factor, or the ratio by which an image is multiplied to achieve its correct size. Scale is used in preparing blueprints for construction of buildings. Conformal maps have an isotropic scale factor which preserves angles and maintains the shape of small elements (as shown in the right-hand diagram).

Musical scales, which differ in their interval patterns, are classified into categories including diatonic, chromatic, major, minor, etc. They are used in the composition of music, and explicit instruction in scales is part of most composers’ training. Highly developed, complex systems of scales exist in the music traditions of several cultures, particularly those of Ceylon, eastern Siberia, California Indian culture and the Muslim world. However, scales do not function uniformly in such cultural music, since they may serve only as a means of description or analysis.

## Meaning

Generally, a scale is a ratio that describes the relationship between the dimensions of a model or blueprint and the corresponding dimensions of a real object. For example, a scale model of a building is smaller than the actual building, but it has all of the same parts and features.

In music, a scale is a fixed sequence of musical notes that rise or descend by intervals (the distances between pitches). A specific pattern of interval relationships defines every scale. In most musical traditions, a scale may also be described as being hemitonic or cohemitonic, and the emphasis placed on certain pitches or the simultaneous (harmonic) or successive (melodic) occurrence of pitches adds to its overall characteristic sonority.

Scale is also used to refer to the number or magnitude of an event. For example, an earthquake is measured on the Richter scale. Also, someone’s paycheck is rated on the pay scale. “Scale” can also be used as a verb, meaning to grow or shrink in size.

## Origin

A system of measuring or classifying in a series of steps or degrees according to some standard of relative size, amount, rank, etc. Also, a series of steps or degrees that ascends or descends according to some standard, as in a ladder or the scale of a mountain. From Middle English, Old French escalle, from Latin scala (ladder), from scala (sheep skin) or scalae (scales), from skala (plate).

Musically, a definite and standard series of tones within a range, usually an octave. It is the basis of most Western music, but there are many other interval patterns, as in the grama scale of India, the dastgah and maqam scales of Iran and the Muslim world, and a large number of non-Western cultures have their own scales.

In mapmaking, a method of transforming a three-dimensional Earth into a two-dimensional visual representation, the scaled map. The term is often used synonymously with the terms “scale factor” and “scaled image”. See also map scale, map projection.

## Usage

The use of scales has been a central feature of many cultures. Examples include grama in India, dastgah in Iran, and maqam in Muslim cultures. Musically, the scale serves as a basis for melodic construction. Explicit instruction in scales has been part of compositional training for centuries. Scales are also used precompositionally to guide and limit the compositional structure of a piece, such as in the opening pages of Claude Debussy’s L’Isle Joyeuse.

The usage of scales is an ever-evolving continuum, with some being more enduring than others. To minimize the potential for drift from the intended construct, researchers should first clearly define the construct being measured and the domain within which it is to be employed. Then, they should carefully review sources to find a scale that matches the construct and domain and that has been vetted in accordance with appropriate validation guidelines. Finally, they should report the scale as fully utilized in their manuscript and include reliability results (alpha or omega) and convergent and discriminant validity in an appendix.

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