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Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio.
In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 ( Play ⓘ ), 1.5, and may be approximated by an equal tempered perfect fifth ( Play ⓘ ) which is 2 7/12 (about 1.498).
The size of an interval between two notes may be measured by the ratio of their frequencies.When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).
If a scale uses an interval of 21:20, it is a 7 limit just intonation, since 21 is a multiple of 7. The interval 9 / 8 is a 3 limit interval because the numerator and denominator are multiples of 3 and 2, respectively. It is possible to have a scale that uses 5 limit intervals but not 2 limit intervals, i.e. no octaves, such as Wendy ...
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths [2] which are "pure" or perfect, with ratio :. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio 2 : 1 {\displaystyle 2:1} ), and hence is the ...
For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale). Various attempts have been made to produce a taxonomy of levels of measurement.
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.. In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale. [2]
However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales. [1] [4] Measurement is a cornerstone of trade, science, technology and quantitative research in many disciplines.