From the skewed spring scale hanging around the produce aisle to the pit-and-girder monsters that weigh train cars and tractor-trailers, scales are a vital part of modern life. They are also a fascinating scientific concept that’s worth exploring.
Scaling is often defined in different ways, causing conceptual fuzzyness that hinders cumulative knowledge development and scientific progress. This is a problem because it inhibits the usefulness of scaling as an analytical concept.
Definition
Scale is a ratio that represents the relationship between the dimensions of a model and the corresponding dimensions of the actual figure or object. This helps in representing real-world things on paper with comparatively smaller dimensions, such as maps and blueprints used for construction of buildings.
A scale is also a series of musical notes, tones or intervals dividing what is called an octave. Different cultures have their own unique scales, such as grama in India, dastgah in Iran or maqam in Muslim culture.
In terms of business, a clear understanding of scaling is important for two reasons. First, it ensures that a growth strategy is aligned with a firm’s ability to deliver on the value proposition. Secondly, it is important for the management of businesses to have an internal transformation that allows them to scale their operations and manage complexity. Without this, a growth strategy is unlikely to deliver an exponential return on investment and will only create friction among stakeholders.
Origin
The origin of scale is not entirely clear. The word comes from a Latin scala, meaning ladder, but it acquired its musical sense from the fact that it is a standard and definite series of tones within a range, typically an octave.
The earliest known use of the term was as part of the name of a system of leverage arms differing in length, used for weighing objects. The mechanism subsequently evolved into the first column scales, and this development is directly connected with the origin of our company’s name – seca.
The bottom-up scale model proposed by comparative musicologist Curt Sachs suggests that the octave-based interval spacing in Western musical scales is determined by vocal-motor constraints rather than by harmonic ratios. This generative model of scale construction is a compelling alternative to the traditional perception-driven theory that octave-based scale sequences derived from simple harmonic ratios.
Function
The scale function is a data normalization process that changes all variables in a dataset to have the same mean and standard deviation. This is usually done for comparing values from different data sets. The scale() function in R performs this operation by default when it is called on a vector, matrix or data frame.
The term scale is also used for a system of names that identify the pitch classes of a musical scale. The major scale, for example, is based on seven pitch classes, with each class having a name, such as the tonic or keynote. Other pitch classes are the dominant, subdominant, leading tone, and semitone above or below the tonic.
Scale functions are important in many areas, from measuring weight (by comparing it to a reference weight) to designing mechanical devices like spring scales and hydraulic load cells for industrial use. These devices use hydraulic pressure to measure the force of an object on a piston, and they can be calibrated to produce accurate results.
Examples
Nominal scale is a measurement mechanism that classifies data points into mutually exclusive categories. Examples include male/female, working-class population/unemployed people and vaccinated/unvaccinated people. It’s also used to categorize responses by ordering them based on their rank. This type of measurement can only show order, but not the difference in value between the various data points.
Ordinal scale is similar to nominal scale, except it can order and rank data points in a meaningful way. The rankings can be based on either the number of participants or their performance in the task. For example, a participant’s ranking in a race may be first, second or third.
Interval scale includes the properties of ordinal and nominal scales, as well as a calculable difference between variables and an actual zero value. Temperature and time are common interval measurement scales, but there are many other examples, including the Likert scale and Net Promoter Score. Musical scales can also be classified as an interval measure.