I wrote a peice for piano and flute but I don't know if it should be called duet or duo. I see that duet is when the players have equal importance but that is not necessarily the case fo my composition. Would duo work? There is no Wikipedia article for it. Also, I'm not referring to pop terms like "duo"=a pair for singers Did classical composers write pieces named "duo per/pour x and y"?
Think most people would consider a duo as two players, just as a trio is three.
And consider a duet as a piece for two players. However, the words appear to be synonymous, so you could use either for the piece, although duet would make more sense to more people.
If you make it for three, trio gets even more confusing...
I would have argued like Tim and Tetsujin, but my research has shown that e.g. Beethoven calls a piece: Duo in Eb. Thus it seems that the term duo is also used like trio to name the piece and not only the performers, while duett is mostly used for the note arrangement but it can also be related to the formation and performers:
A Duo or Duett of this description, is a piece for two concerting instruments, without accompaniment. It must not only contain as complete an harmony throughout, as has been required for Solos without accompaniments, (§ 7 :) but the two parts should also be constantly imitating each other, or at least the one have as good a share in the harmony and the passages as the other. It may be set, either for two performers on one Keyed Instrument, such as the Organ or the Piano Forte; or for two familiar instruments, such as two Violins or two Violoncellos ; or for two inftruments of å different nature, such as a Violin and Hautboy ; or a Violin and Violoncello. And in all three cases it may consist either of two regular parts or melodics only ; or of passages which contain a harmony of three and four parts. See my Essay on Harmony, Chap. XIII, § 14, 15. I shall endeavour to speak of the pieces in question in the following order: 1, Duetts for two Performers on one Keyed Instrument may be set for three or four hands. Of the former sort is Haesssler's grand Sonata for three hands, published by Wornum; and my Fugue at Plate XVIII, which also may be considered as a trio on one instrument ; and of the latter fort Dussek's grand overture for two performers; and similar fine works by Kozeluch, Clementi, and other composers. These duetts for four hands may also be set as Quatuors on one instrument, when each hand has an obligato part different from the others; of which sort, I have not yet feen a good example. The particular rule for pieces of all these descriptions is, that the parts must be distributed according to what I have said in my Essay on Harmony, Chap. III, § 2 ; and so, that neither the bass be too noisy for the upper parts, nor the parts of the first and second performer be in each other's way. 2, Duetts for two keyed instruments are the most refpectable fort of the fecond clafs; or of thofe for similar instruments: but as it is seldom that two such instruments can be found in the same room, as well as the same pitch of tune, there have been but few attempts made to write them. But two excellent Fugues of this description are in Seb. Bach's Art of the Fugue, which might be played on the two Sets of keys of one Organ. This great Author has also written Concertos for two, three, and even four Keyed Instruments. Duetts for two Violins or two Flutes, or two Hautboys, &c. are more frequent. But in regard to these Duetts, I must mention a fault which is very frequently committed, viz : that of repeating a passage with the mere change of primo for secondo, or vice versa. This change in similar instruments such as the above-mentioned, has no other effect than a mere repetition without a change of the parts; and consequently is no proper variety for the duetts in question. But for those of the following class it produces a variety in the effect. The third class of Duetts are those, for two different instruments. In regard to these, one of the principal considerations is : to choose such instruments as may have a good effect together. Another consideration is : that if a Duett is set for a Bass and a Treble Instrument, and intended to be alfo executed by two Basses or two Trebles, the harmony must be calculated accordingly. If thereforeDuett for a Violin and Violoncello shall ..also calculated lated for two Violins or two Violoncellos, care must be taken, that it produces no irregular intermixture, or no disallowed inversion of the parts when contracted on two similar instruments. $ 16.
IME: A song for two singers (with or without instruments) is a duet.
A piece for two players at a single piano is a piano duet.
A piece for two instruments, or for a larger ensemble with two soloists, may be called a duo. Weber's sonata for clarinet and piano op.48, and Alkan's sonata for violin and piano op.21, are each called Grand Duo Concertant.