“Symphomaniac” (symphony + nymphomaniac) is a portmanteau word that has been printed in several jokes. The word was posted on the newsgroup rec.arts.marching.drumcorps on November 6, 2004:
 
Q. What do you call a girl that thinks only of classical music?
A. A symphomaniac.
         
The word “symphomaniac”—without the joke—has been cited in print since at least 1930. American bandleader Duke Ellington (1899-1974) performed a composition called “Symphomaniac” at New York’s Carnegie Hall on November 13, 1948.
 
     
18 January 1930, Honolulu (HI) Star-Bulletin, “KFI Owners Says Radio Refines Musical Taste,” pg. 5, col. 3:
“For instance, some symphomaniac tunes in to hear Beethoven’s fifth symphony.”
 
OCLC WorldCat record
Carnegie Hall, November 13, 1948
Author: Duke Ellington; Duke Ellington Orchestra,
Publisher: [New York] : Vintage Jazz Classics, [1991] ℗1991
Edition/Format:   Musical CD : CD audio : No Linguistic Content
Contents:
The symphomaniac / Billy Strayhorn, Duke Ellington. Symphonic or bust (5:18)
 
15 November 1948, New York (NY) Times, “Ellington Presents 2 New Compositions, pg. 22, col. 2:
“Symphomaniac” and “Fantazm” were other new compositions of interest..
 
Google Books
BBC London Calling
Volumes 10-11
1981 (The Google Books date may be incorrect.—ed.)
Pg. ?:
World Service listeners are enjoying the mixture of musical erudition and spontaneous ingenuity. For instance, what do you call a girl who only likes classical music ’ Answer: A symphomaniac
 
Google Groups: rec.arts.marching.drumcorps
OT Some Musician Jokes
Jazzman
11/6/04
(...)
Q. What do you call a girl that thinks only of classical music?
A. A symphomaniac.
     
Twitter
Froccily Slox‏
@BroccoliFox
What do you call someone who compulsively listens to classical music?
A symphomaniac.
*dodges a flying tire iron*
5:52 AM - 18 Nov 2014
 
Twitter
Corrina Connor‏
@corrinacellist
Q: What do you call a woman who follows the NY Phil around?
A: A symphomaniac.
Probably #everydaymisogyny, but I laughed heartily.
1:23 AM - 30 Dec 2014 from Wellington City, New Zealand
 
Reddit—Jokes
What do you call a woman, that slept with the whole orchestra?
submitted June 19, 2017 by pm_me_your_wing
A symphomaniac
 
Twitter
Living Sarcasm‏
@SarcasmLiving
What do you call a woman, that slept with the whole orchestra?
A symphomaniac
3:42 AM - 19 Jun 2017