The scale of a map, plan, or model is its ratio to the actual size. Scale is the underlying concept behind everything from musical scales to blueprints and scale models of machinery and architecture.
Creating a scale involves four phases: item development, dimensionality testing, and reliability and validity assessments. This article will cover the first three of these, with a nod toward more technical issues such as content validity.
Pitch
The position of a sound in the range of frequencies a human hears is called pitch. Musical tones can have different pitches, separated by whole or half steps. This allows scales with two or three pitches to be used in monophonic music (that is, without harmony). Such scales often display a narrow range of interval sizes. Examples include the two-note and three-note scales used in Ceylon, eastern Siberia, California Indian cultures, and some European and Middle Eastern traditions.
The interval size a musician perceives as a step depends on the frequency of the sound: a step of a low frequency is perceived as a small interval while one of a high frequency is larger. This explains why equal-frequency intervals may sometimes seem to be close or far apart.
A scale is defined by a set of pitches whose pattern repeats in each octave, and the intervals between those notes. The tonic of a scale is usually the lowest pitch in the set, but this is not always the case.
Intervals
Interval scale measurements lack a true zero point, which restricts certain mathematical operations and complicates data interpretation. The arbitrary nature of the zero point makes it challenging to calculate ratios between interval measurement values and create meaningful comparisons. In addition, the limited range of interval scale measurements may limit the ability to capture extreme values accurately.
Interval quality, or whether an interval is major, minor or augmented, is determined by comparing the upper note with the major scale of the bottom note. Intervals that fit the major scale perfectly are categorized as perfect; those that don’t are either diminished or augmented.
To leverage the full potential of interval scale measurements, stakeholders must adhere to best practices for data collection and analysis. Standardized measurement protocols, rigorous data validation checks and outlier detection algorithms enhance the integrity and quality of interval scale data. Additionally, transparent reporting and documentation of research methods and analyses facilitates peer review and scrutiny of research findings.
Conventions
Few things seem to elicit more opinions, exaggerations, and accusations than the conventions that govern rating scale response options. Whether it’s the “right” number of points, the use (or absence) of labels, or the presentation order, conventions – often viewed as rules – can have a powerful influence on survey results.
Musical scales are commonly based on the principle of octave equivalence: each interval of one note is divided by an octave and each octave repeats the same pattern. This is usually a diatonic scale, although some music uses other types such as the harmonic minor or the anhemitonic pentatonic.
It’s important to be aware of the conventions that govern rating scales when developing a latent construct, so the scale is designed to reflect the true construct under study. For example, the respondent: item ratio of a survey must be high enough to ensure that the data can adequately model the construct under study (59, 65). Larger sample sizes and higher respondent: item ratios lead to lower measurement errors, more stable factor loadings, replicable factors, and generalizable results.
Cultures
Scale is a ratio that allows the dimensions of a figure or object to be represented on paper using smaller dimensions. It is often used to scale maps and blueprints.
Highly developed cultures have complex systems governing scale usage. These systems may vary, but all have some similarities. For example, music of these cultures – known as art music, classical music or cultivated music – is composed in full awareness of rules or conventions regarding scale usage.
Top scale-up managers have different perspectives on the culture their company has. The results showed that clan and adhocracy culture types are the most present in their organizations and even more preferred, while the market and hierarchy culture types are less present in their organizations and even more preferred to decrease. This means that the top scale-up management team should focus more on these underlying characteristics to improve the performance of their companies. This can be done by implementing flexible and linear schedules for the employees of each culture.