When a chord is written such that the chord tones are as close together as possible, like this...
X:1 K:C M:4/4 L:1/1 [CEG] | [EGc] | [Gce] |
...what is the correct term: "Close position" or "Closed position"?
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Both are correct.
Is "close position" more formally used [in Western classical music institutions]? Probably, but that's a very long way from making "closed position" incorrect.
First, it's important to point out that this is not analogous to confusing "intents and purposes" as being "intensive purposes." The term "closed" is descriptively accurate and conveys the intended meaning.
The reality of language is that there are often two alternative usages that are both accepted. This phenomenon is common in language, and is even documented in dictionaries. But dictionaries don't define language; new words are added to dictionaries each year because dictionaries lag behind trends. This lag is greater in niche areas like musical terminology, which are not exhaustively covered in general dictionaries and for which universally accepted authorities do not exist. Different genres, regions, and groups have different usages.
We must be cautious about using "authority" in these circumstances and telling a large group that the term they use, intend, and understanding is incorrect because it doesn't appear in a book written by a very narrow cultural/historical subset. Before going down that road, a relevant question to ask is: what defines authority in the domain of language, and how closely is that authority linked to institutions that historically represent white, male, Western classical traditions? (A quick search of the authors/editors you cited shows there might be something here.) You've acknowledged the ubiquity of "closed position." Where does the authority come from to deem this legitimate use of language incorrect. In what sense is the usage "closed position" not legitimate?
It's really not necessary, but here are some examples of the use of "closed position":
Suzanne Davis, associate professor of piano at Berklee College of Music:
If you can learn closed position and spread voicings with tension in your jazz voicings, you can pretty much apply them to any style of music. (Source)
Bill Evans pioneered a technique of using rootless 4-note voicings in his jazz piano playing. Also called closed-position voicings or Mehegen voicings, they consist of two guide tones (3rd and 7th) as well as two other notes (5th/6th and root/9th) and are usually voiced with a guide tone as the bottom note... (Source)
IMO the most reasonable position is that both terms are accepted, well-defined, descriptively accurate, and well-understood. In other words, they are both correct.
Close position is the correct term.1
See, for example, Wikipedia: Voicing (music): Vertical placement.
Also, from "The Complete Musician" by Steven Laitz:
The third and the fifth of each triad are arranged directly above the root. This tight spacing ... of chordal members is called close position.2
position. ... (2). Chords may be described as being in 'close' or 'open' position, depending on their layout.3
Close position [close harmony] The spacing of a chord in such a way that the upper voices lie as close together as possible or the interval between the highest and lowest is relatively small.4
Of the many [possible chord voicings], two general types are commonly distinguished: open position and close position.5
When the three upper voices are as close together as possible, the spacing is described as close position.6
People often mishear [close position] as "closed" position because the meaning seems somehow logical, and you may by now even see it written that way in some sources.
Stemmed beams are often the best notation for close-position chords and also for sustained durations that overlap.
1 One possible source of confusion is that "close" and "closed" sound very similar, and "closed" makes intuitive sense, being the opposite of "open". It can be helpful to think of "open" in its meaning as "spacious" (the open prairie).
2 Steven G. Laitz, "The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening", 2nd ed. (2008, Oxford University Press), p. 117.
3 The Oxford Companion to Music, ed. Alison Latham (Oxford University Press, 2003), p. 986.
4 The Norton/Grove Concise Encyclopedia of Music, ed. Stanley Sadie (Macmillan Press Ltd., 1994), p. 172.
5 Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. (Harcourt Brace Jovanovich, 1989), p. 67.
6 Walter Piston, Harmony, 5th ed., rev. Mark DeVoto (W. W. Norton & Co., 1987), p. 18.