The development of scales involves a number of steps: (1) identification of the domain(s), (2) item generation, (3) sampling and survey administration, (4) item reduction, (5) extraction of latent factors. This phase should be followed by tests of dimensionality and reliability.
It is essential that a scale measures only the construct intended. Otherwise, it may produce misleading results and contribute to contaminated research.
Definition
In mathematics, a scale is a ratio used to compare a given figure’s dimensions with the corresponding dimensions of an actual object. For example, a map is drawn to a standard scale that makes it easier to discern the distances between objects and locations on the Earth.
A scale is also a measurement tool for comparing the weights of different materials. For example, if you hung two pans from opposite ends of a balance scale, you could determine the approximate weights of each by placing a peg on one end and balancing that against a peg placed at the other end of the scale.
Musically, a scale is a graduated sequence of pitches (or tones) that divides an octave. A scale’s interval pattern defines its unique identity, and it is generally named after the note chosen as its tonic. Despite the many differences between cultures and musical traditions, certain scales have become conventionalized throughout the world.
Functions
A scale is a ratio used to represent the relation between the dimensions of a model or a drawn figure and the corresponding dimensions of an actual figure or object. The purpose of a scale is to make the figure easier to interpret by presenting it in a smaller or larger size than its original size. A builder would use a scale drawing to prepare a blueprint for the construction of a new house.
In music, a scale functions as a set of fixed interval relationships between pitches within an octave. Other features of a scale, such as whether it is hemitonic or cohemitonic, may influence its sound, but are not essential to its identity.
In mathematics, a function can be scaled by multiplying its coordinates or by dividing them. Scaling a function vertically, for example, shrinks its graph so that all of its y-values take up half as much space as they did before.
Variations
The scale of an event or a system can vary dramatically depending on the chosen level of analysis. For example, geographic trends may reveal different patterns when analyzed at a local, national, or global level. Understanding scale variation is critical to accurate data interpretation as it impacts the way patterns are interpreted at different levels of analysis.
Musical scales can also have many variations, some containing more or less notes than others. For instance, the chromatic scale is often used to create tension and drama in music, while the whole tone scale has been a common tool for composers to convey a sense of time or place in their compositions.
A ratio scale is the peak level of data measurement and satisfies all four properties of interval scales; it is compatible with both central tendency measures (mean, median, mode) and dispersion measures (range, standard deviation). A ratio scale also enables researchers to compare relative magnitudes.
Origins
The word scale derives from the Latin scala, meaning ladder or staircase. Its earliest use in English referred to climbing, as in using a ladder to ascend to a higher place. Geographers adapted the term to describe how well a map represented an area, by comparing its size to that of the actual terrain.
Scales have also been used in the arts and in commerce. In ancient Egypt, traders used a system called the Balance Scale, which consisted of two weighing pans that could be moved to different locations. Merchants could then weigh the contents of a package and determine its value.
Musicologists have long debated the origin of musical scales. One theory is that the interval spacings of a particular scale—a whole tone plus/minus a semitone, for example—were determined by vocal-motor constraints, such as the need to fit sounds within the range of human voice pitch. Another theory is that the scales were constructed from the bottom up, with the sequential addition of stably spaced tones.