Of American-English origin, the phrase to face the music means: to accept or confront the inevitable, or the unpleasant consequences of one’s actions.

The underlying idea (i.e., what music is being faced, and where) is uncertain and disputed. Suggestions include reference to a nervous performer coming onstage in musical theatre, or to the practice of drumming a soldier out of his regiment, or to various military uses of the noun music (such as music in the sense of the component of a military force charged with sounding signals on musical instruments, and music in the sense of the sound of gunfire or other ordnance). However, none of those suggestions is based on specific evidence.

The texts containing the earliest occurrences of to face the music that I have found give no clue as to the origin of this phrase. These early occurrences are as follows, in chronological order:

1-: From Police Court, published in The Boston Morning Post (Boston, Massachusetts, USA) of Friday 22^nd November 1833 [page 2, column 2]:

Robert Mahan, for disorderly conduct at the Warren Theatre, was arraigned. On Wednesday evening, a couple of the Goddesses, who hold their court near the region of the steeds of Apollo, amused themselves by carrying on a correspondence with some of their “familiars” in the pit. This being a departure from the discipline of the establishment, the offenders were ejected from the premises.
Robert, who had but “just come down from Sterling,” felt deeply interested in the fate of the fair couple, and, with that recklessness of personal consequences, proper to a true chevalier, attempted their rescue, and had the supreme felicity of delivering them from the grasp of the officers. His happiness might have been too intense for his endurance, if it had not been fortunately qualified by the circumstance, that he himself was lodged in jail, instead of them.—Should any be surprised at his Quixotism, in behalf of such ladies, let them remember, that
          “What to the valiant knight of Spain
           Was Donna del Tobossa,
           Such is the idol of his brain
           To every virtuoso.”
Robert pleaded “drunk—a sick mother—and a loss of $10.” And the court replied, by sentencing him to give bonds to keep the peace, pay the costs of prosecution, and stand committed for want of the means to face the music.

2-: From the New-Hampshire Statesman and State Journal (Concord, New Hampshire, USA) of Saturday 2^nd August 1834 [page 3, column 2]:

By the way, the mention of the late Sheriff of Merrimack brings again to mind the lost law. The editor of the Courier has not, probably, forgotten that this individual was accused by him of stealing that bill, while he held it in his possession, by virtue of the arrangement with one Charles F. Gove. Will the editor of the Courier explain this black affair. We want no equivocation—“face the music” this time—Gove and Barton are able backers. And when this is done with, we may perhaps take occasion to read another lesson or two pertaining to his official conduct, before we touch his private affairs.

3 & 4-: From the Dover Enquirer (Dover, New Hampshire, USA):

3-: Of Tuesday 19^th May 1835 [page 2, column 5]:

One of the brightest feathers in Gen. Jackson’s cap, in the estimation of the tories of this state, is his pertinacity in vetoing all projects for internal improvement; and one of the strongest claims which Van Buren possesses to the old man’s shoes, according to the same gentry, is his determination to follow up the work. As Van, however, has now given ‘assurances’ that he will not be a Vetoite, we are curious to see how the tories will get over it. Come gentlemen—no dodging—face the music.

4-: Of Tuesday 15^th September 1835 [page 2, column 3]:

Notice is given in the Concord papers, that all “$100 Judges,” who intend to follow the “patriotic example” of Judge Stark, are requested to send in their resignations before Monday the 21^st inst. when the Governor and Council will be in session to fill the vacancies. Come Judge Simpson, “face the music!”

5-: From Police Court, published in the Boston Morning Post (Boston, Massachusetts, USA) of Saturday 26^th March 1836 [page 2, column 4]:

A very fine looking gentleman, who calls himself John Page Arlen, was brought up, on complaint of Wm. D. Ticknor, for stealing sundry new and valuable books from the store of Messrs Allen & Ticknor, within the last three months. […]
So far as personal appearances might go, Arlen is the very last man who would have been suspected of the robberies fixed on him—there is not a single trait of flash about him—the expression of his countenance is what they call “intellectual,”—a poetic langour [sic] marks every feature, and his complexion is romantically sallow and melancholic. When arraigned, he confronted the witnesses, with his arms folded, and head erect, like Damon looking Dyonisius [sic] into nothing. So far from bearing the abashed air of a culprit, he looked like a posture-master, giving a lesson in dignified attitudes—so magnificently did he swell round to face alternately the Court and spectators: It was ideal dignity personified in flesh and blood.
The court appeared to be somewhat struck with the sublime indifference with which he faced the music, or rather the fire of the witnesses, and asked him if he did not wish to question them. He replied—“No; I only want them to state facts, and they must know there is such a thing as being too sure: and I hope the next time they come to court, they will behave like gentlemen, and confine themselves to the facts.”

6-: From the Barre Gazette (Barre, Massachusetts, USA) of Friday 15^th April 1836 [page 4, column 3]:

Young Ladies’ Ball The young Ladies in Peterborough, made use of the Leap year prerogative, and gave a splendid Ball, on the evening of the 30^th ult. They held their meeting preparatory, chose fourteen managers from their own number, issued their cards of invitation, provided the means of conveyance, faced the music, and footed the bills; and so gay a ball was never known in that well regulated town.
Dunstable Tel.

7-: From the Portland Advertiser (Portland, Maine, USA) of Tuesday 26^th July 1836 [page 1, column 2]:

The Argus and some other prpers [sic] are excusing Mr. Van Buren’s casting vote on the “gag law,” by saying that it was Mr. Grundy’s amendment, and not the original bill of Mr. Calhoun, that Mr. Van Buren voted for. It was so. Van Buren thought the bill would be popular in the slave states & in order that his friends in the South might claim it as an administration measures [sic], it was dexterously taken off Mr. Calhoun’s hands, by an amendment of Mr. Grundy, of the post office committee. The amendment was as bad as the original bill.—The magician did not mean to commit himself either way; for his presses at the South were to say he was for it, and those at the North to say he was against it. But he was cought [sic] napping, and compelled to “face the music.”—Kennebec Journ.

8-: From a letter, dated “Harford, May 30^th, Ayteen Hundrid and thorty sevin”, from ‘Up River Raftsman’ to ‘Bruther Amus’, published in The Times (Hartford, Connecticut, USA) of Saturday 3^rd June 1837 [page 1, column 3]:

Im regulaten matters in the Leggislatar here, and shant cum up till they get threw. Ive got in chareman of the Commyttee on Banks in the thurd house […]. I go in every day to see tother houses—the Senat gits on middlin well, but in the other house they want their constitterents to cum and nock em on the hed a leetle, so as to giv em moral currage to face gret questeons. Sum on em have got so menny sydes to em, yew cant tell what town they cum from without taken the yaze and nays every two minnits.—Im detarmined if they dont face the music better, to rite to their constiterents and have em cum and take the lofers home, for they aynt good for nothin here only to eat shad and be oats [?] pors for the fedrals.

9-: From The Gloucester Democrat (Gloucester, Massachusetts, USA) of Tuesday 11^th July 1837 [page 2, column 4]:

Public Spirit “Down East.” About as great an attempt at celebration upon the 4^th as has reached us, was made in a certain town in Maine. Several meetings were called and all preliminary arrangements necessary, made; among which was the selection of an Orator: but when Mr. Finance—rather a stiff old character, to be sure—made his appearance to perform his part of the ceremony, all ideas of ‘glory,’ ‘patriotism,’ ‘liberty,’ and ‘Bunker Hill’ vanished instanter; and the pure descendents of ’76 concluded not ‘to face the music!’ Like the monument upon the summit of the above named consecrated mound, they “got so far and couldn’t get any farther.”

10-: From the Connecticut Herald (New Haven, Connecticut, USA) of Tuesday 25^th July 1837 [page 2, column 4]:

From the Hartford Courier.
LEGISLATIVE GLIMPSES.—No. 4.

Samuel Raymond, of New Canaan. […] He is decidedly a man of more native talent than any of the majority! a fact by no means complimentary, and yet flattering, since it must be vastly more gratifying to be a “king among hogs, than a hog among kings.” Mr. Raymond stops much short of “going the entire animal.” True, he went the whole Niles, in proscribing his fellow citizens for the unpardonable sin of venturing to think for themselves, but on subjects affecting the interest of the people at large, he voted just precisely as Sam. Raymond told him to vote. There he “faced the music,” and, like Balaam’s ass, plainly told his riders the truth.

Note: The phrase to face the music seems to have no connection with when the band begins to play, a phrase of obscure origin, too, which means: when matters become difficult or serious.