I have seen classical music listed in programs, sometimes with a K as in the thread title, and sometimes with an Op. as in Concerto No. 3 in B minor Op. 61. I know the Op stands for opus, but what does the K stand for? And what do they really mean? Are there 218 other concertos in A major? Is a K just another name for an Op.?
Köchel catalogue numbers.
https://allaboutmozart.com/mozart-kochel-catalogue-works-compositions-koechel/
(post edited to avoid having identical Wikipedia links in 3 successive posts).
Köchel did an important job but had a really bad hairstyle.
I’ve typically seen “K.” used in reference to Mozart’s works; it stands for “Kochel catalogue,” the work of Ludwig von Kochel, who created a chronological catalog of Mozart’s compositions.
(Post similarly edited. 
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It applies specifically to Mozart’s music. Here’s the wiki article on it.
The pieces are numbered in the order they are presumed to have been composed. K1 is Mozart’s first composition. K 626 is his last piece, the famous requiem that he didn’t complete before his death.
And, just to answer the OP’s question more directly: K. 219 is the 219th work of Mozart’s, in the Kochel catalog.
I think it means the music is kosher.
A lot of baroque era and some classical era composers have similar styles of numbering their compositions. Antonio Vivaldi’s works have RV numbers, but are organized based on type and key rather than order of composition. His cello concertos, for example, start at RV 399 and go on up consecutively through RV 424. They start with the C Major, then C Minor, D Major, and so on until B Flat Major. JS Bach’s compositions use BWV numbers and also are organized by type. Both of those were used by people who cataloged their works later, not the composers themselves. Opus numbers were mostly used a little later, and were used by the composers themselves as they published their compositions. Chopin’s works are a good example of this style.
ETA. The catalog numbers do tend to get a little messy, as some compositions are determined to not have been written by who they were previously attributed to and so have their number removed from the catalog. There’s also sometimes recently discovered works that are genuine having numbers added on at the end of a catalog, so that a number might go from the 200s to the 1000s for similar pieces, because the latter were discovered after the initial catalog was completed.
Just for fun, I looked both of those pieces up. They’re both violin concertos, so it makes sense that they would be part of the same performance. Whatever orchestra was performing them must have had a virtuoso violinist available to perform with them.
Here’s a list of classical music catalogues; K for Mozart, BWV for JS Bach and RV for Vivaldi, mentioned above, are among the best known. There’s also Hob for Haydn, TWV for Telemann (who were both very prolific) and WoO for “without opus number” for unnumbered works of composers including Beethoven.
I dunno, I think it makes him look kinda distinguished, like a Mayor.
…of the Munchkin City/In the County of the Land of Oz…
I really thought @K364 should have been the user to answer this question.
Too slow on the draw I guess.
BTW, “K” numbers are used for other composers, Domenico Scarlatti being the most famous. That “K” is for Ralph Kirkpatrick a famous harpsichordist.
In Peter Schikele’s P.D.Q. Bach concerts, he would introduce P.D.Q. compositions with something like, “The Abduction of Figaro, Canine Cantata: ‘Wachet Arf!’ (Schickele number K9.)” The classical music enthusiasts in the audience would laugh appreciatively while the people who only knew it was supposed to be a funny concert never got the reference.
Another question, why are opus numbers so random? Why do some composers publish as Opus 39 when they didn’t have Opi 1-38?
Same thought exactly!
They actually do, it’s just that those other compositions tend to be less well known. Here’s the wiki for Beethoven’s works, neatly lined up from opus 1 through 138.
Chopin’s are listed here. Opus 4 was published posthumously but the others are all in order.
The “missing” opus numbers can be thought of as being similar to all the songs that are missing from a pop artists “greatest hits” album if those artists had named their songs Album 1, Song 1; Album 1, Song 2; Album 5, Song 7 and so on rather than giving them names like Hey Jude or Thriller.
“Opi” ???
anyway you could have unpublished opera:
From about 1800, composers usually assigned an opus number to a work or set of works upon publication. After approximately 1900, they tended to assign an opus number to a composition whether published or not. However, practices were not always perfectly consistent or logical. For example, early in his career, Beethoven selectively numbered his compositions (some published without opus numbers), yet in later years, he published early works with high opus numbers. Likewise, some posthumously published works were given high opus numbers by publishers, even though some of them were written early in Beethoven’s career.
Plural of opus: opera!
ETA: Damn you, DPRK!