Refers to the ordinal "steps" in a diatonic scale, usually designated with Roman numerals: I II III IV V VI VII.
Arabic numerals are normally used (in their ordinal form) for the names of intervals, and are also sometimes used to refer to degrees as well -- however, for purposes of chord-analysis Roman numerals are much more common. The Arabic numbers are often spelled out as words ("prime", "second", "third", etc.) -- in this Encyclopedia the numeral format is always used.
Six of the degrees also have a Latin name, and one degree a vernacular name, associated with them:
Refers to the pitches in an equal-tempered scale, one degree being the basic "step" size in the scale.
The degree is also the numerator of the rational exponent of 2 which gives the frequency ratio of the interval, the total number of degrees in the scale (i.e., its cardinality) being the denominator.
For example, the 7th degree of the 12-edo scale has the ratio 2(7/12).
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