Cadences are two chords which come, usually, at the end of phrases. There are basically four of them, although U.S. defines some in more specific ways.
The Andalusian (Spanish) 'cadence' is a well known sequence of four repeating chords - i, VII, VI, V. So surely cannot be a cadence - would Andalusian Sequence be a more accurate name? The cadence itself could be VI>V, making it an imperfect (U.K. naming) cadence.
The common harmony textbook classification of cadences used just two chord to define cadence types. But that seems to be just a matter of minimal information to classify cadences.
From an old music dictionary in Google books (Baker, A Dictionary of Musical Terms)...
...closing strains of a melody or harmonic movement...harmonic formula leading to a momentary or complete musical repose...
While the full definition includes the typical four cadence types using two chords, the (b) definition is fairly open regarding the length of a cadential progression.
A more general definition from Merriam-Wester https://www.merriam-webster.com/dictionary/cadence includes:
the beat, time, or measure of rhythmical motion or activity
a regular and repeated pattern of activity
a musical chord sequence moving to a harmonic close or point of rest and giving the sense of harmonic completion
Another resource to read regarding cadence is this overview of partimento cadences, https://partimenti.org/partimenti/about_parti/beginners_guide/learning_cadences.pdf, it includes some extended cadence forms that become more of a chord progression leading to a closing. The point being those cadences are not categories simply by the last two chords.
"Andalusia Cadence" certainly fits the general meaning of a regular rhythmic pattern as the way that particular chord sequence is presented it would be repeated over and over. The four chords leading to a dominant chord also fits the meaning of a strain leading to a momentary repose, even if it does not necessarily involve a formal phrase ending.
I've always understood the meaning of "Andalusian Cadence" to be the more general sense of repeating pattern with something of a half cadence. I've only seen the term on the internet so I never thought of it as a standard music theory term.
From Wikipedia
Despite the name it is not a true cadence (i.e., occurring only once, when ending a phrase, section, or piece of music[2]); it is most often used as an ostinato (repeating over and over again).
I'm with Andy Bonner here:
I guess the key is "cadences are two chords" —are they always, by definition?
The meaning of "cadence" has come to be used in a specific context to denote various combinations of two chords at the end of a phrase, but even in that context it's not necessarily limited to two chords. For example, it would be entirely reasonable to compare and contrast II-V-I cadences with IV-V-I cadences.
Google Books ngram viewer suggests that the term arose in the middle of the 20th century, so an examination of other meanings of "cadence" is probably not necessary to shed light on the phrase. In particular, we can probably reject the hypothesis that the phrase arose before "cadence" took on its specialized two-chord sense; that clearly didn't happen.
So the answer probably lies in the slightly broader sense in which we can speak of II-V-I cadences and IV-V-I cadences. These are common cadential patterns that have slightly different functions.
Now the Andalusian cadence has two: first, a single instance of the four-chord progression ends on the dominant, which as you note is a cadence of an intermediate variety (in functional tonal harmony, at least), whatever your preferred system of terminology. Second, on the repeat, the dominant is followed by the tonic, giving a full (perfect, authentic, normal, what have you) cadence. This of course sets the music into an endless cycle of short repeating phrases, giving us some of the most infectious examples of music from the 17th century onward. Three centuries later, of course, entire genres of popular music were based on this technique, and the words "progression" and "changes" were favored. Interestingly, that style of popular music arose around the same time as the phrase "Andalusian cadence."
would Andalusian Sequence be a more accurate name?
Perhaps so, but people frequently adopt words and phrases that are less than precise.
I would note, however, that there are some inaccuracies in the Wikipedia article. For example, it cites the Lamento della ninfa, where the progression is mostly A-Em/G-Dm/F-E rather than A-G-F-E (while there are occasional F major chords and E7 chords, these are used sparingly for color, so the article's assertion that the basic progression is A-Em-F-E7 is misleading). In general, you will not often find the descending tetrachord harmonized with root position i-VII-VI-V very frequently in classical music before the 20th century because of the parallel fifths.
