A measure is a classification of raw data such as numbers and values. They include items such as sales, profits and customer satisfaction. These measures help a business understand their strengths and weaknesses.
In mathematics, a measure is a function of a set such that all intervals in the corresponding metric space are invariant under translation. It is also a fundamental concept in integration theory.
Units
Units are a reference point that can be used to compare other measures. For example, a leg of a chair must be the same length as all the other legs, or it will topple over when you sit in it. If you measure a leg in inches, and then measure the same leg in meters, you need to know how much longer or shorter the second measurement is in order to be confident that the first one was accurate.
The rapid advances in science and technology of the 19th and 20th centuries spurred many different systems of units to develop as scientists improvised to meet the practical needs of their disciplines. To reduce this confusion, an international system was created called the metre-kilogram-second (MKS) system.
This system consists of seven base units and 22 coherent derived units with special names and symbols. It also contains twenty-four prefixes that, when added to the name and symbol of a coherent unit, produce non-coherent units that are decimal-based multipliers or sub-multiples of the base unit.
Uncertainty
Uncertainty, as the name suggests, is the amount of doubt that is inherent in any measurement. It may stem from calibration error, environmental factors, resolution of the measuring device and so on. Regardless of the source of uncertainty, it is important to know and understand because measurements are used to make decisions every day in all types of industries. Without accurate measurement results decisions can be risky and costly. For example, a faulty calibration in an oil and gas pipeline could lead to catastrophic failure resulting in environmental damage, financial cost, loss of reputation or even loss of life.
The good news is that it is possible to quantify uncertainty and it is not as complex as it may seem. One way to do this is through the use of uncertainty intervals, which are a set of bounds around a measured value that indicate the probability that any new measurement will lie within those bounds.
Scales
Scales are the building blocks of music and a critical component of constructing melodies, riffs, harmonies and solos. They are a way to organize notes so that they sound melodic and coherent together. A scale consists of different notes that belong to the same family and are grouped together by their pitch. They are usually octave-repeating, with the same pattern of notes repeated in each octave.
Each scale has its own unique sound, due to the pattern of intervals it uses. A major scale, for example, consists of seven different notes grouped in a particular order. Each note is a certain pitch and each interval has a specific name. For example, the distance between two adjacent notes is called a semitone (also known as a tone).
A key is the name given to a particular scale and is used to distinguish it from others. It also identifies the starting point for modulation to another scale. Examples of this would be moving from a diatonic major scale to a dominant major scale or a chromatic scale.