Today is the first time I've heard the term "scale degree". When was the term coined? Or where did it originate?
Scale and degree ultimately come from Latin words meaning "ladder" and "step," respectively, so the concept of "scale degree" is several centuries old, predating even the development of modern English. The specific phrase "scale degree" is at least 134 years old, but "degree" as an element of the musical scale is at least a couple of centuries older.
The first edition of the Oxford English Dictionary shows the earliest use of the word "scale" in the musical sense in 1597, in Morley's A Plaine and Easie Introduction to Practicall Musicke. It also gives a citation for "scale degree" from 1889,1 but it illustrates an obsolete sense of "scale" meaning "musical staff" with this quotation from a 1704 technical dictionary:
Scale of the Gamut, or Musical Scale, is a kind of Diagram, consisting of certain Lines and Spaces drawn to shew the several Degrees, whereby a Natural or Artificial Voice or Sound may either ascend or descend.
Before that, the concept of scale degrees will be found using different words, often in different languages, since Latin was for many centuries the primary language of music theory. The Latin word gradus, meaning "step" or "steps," is the source of many English words of related meaning, including both "degree" and "grade"; Latin scala, meaning "ladder" (or eventually "stairway") is of course the source of scale. You can certainly find instances of gradum in the Thesaurus Musicarum Latinarum that may reasonably be translated "scale degree," or that denote a similar concept, but in many instances they might just as well be translated "step" or even "level."
One line of inquiry I don't have time to follow now is the history of the application of the French word degré to the musical scale, but it probably dates to the earliest development of that word from gradus or to the earliest theory treatises in vernacular French, whichever came later.
- Quoting another dictionary:
Century Dict, s.v. Degree, To distinguish between degrees of the staff and degrees of the scale, the terms staff-degree and scale-degree are sometimes used.