I came across a piece in my piano syllabus. It’s called ‘Terminal 2’ by Nathalie Béra-Tagrine. The piece is in 3/4 time signature. It starts with an anacrusis like below:
However, the last bar still has 3 crotchet beats:
AFAIK, since the anacrusis has 1 crotchet beat, the last bar should have 2 crotchet beats. Why does the piece have 3 crotchet beats in the last bar?
In the distant past there was a convention that the last measure should be shortened by the length of the anacrusis. Nowadays this 'rule' is largely ignored unless there is a repeat that goes back to the beginning (common in classic folk/dance forms or songs/hymns).
The core idea of the final measure plus anacrusis creating a full bar — leaving aside repeats — is to create balance in the music. One supposes that the listener will retain the opening anacrusis in such a way that a full measure at the end will feel as though there's an extra beat. This feeling is especially clear when each phrase opens with an anacrusis. That means that each phrase ends with an incomplete measure; thus, the final measure would be expected to end the same way.
In this piece, however, the situation is different. Even though the piece opens with an anacrusis, and the melodic phrases may well also begin with one, the left hand accompaniment overlaps the melodic phrasing. In the accompaniment, we always expect three beats per measure, so to have only two beats at the end would make for an abrupt ending. Of course, one could add an extra measure to the final chord, making it five beats long, but this would feel too long. Instead, the composer allows both the melodic and harmonic phrases to complete, requiring a full closing measure, and then adds the fermata to help dissipate the rhythmic momentum. This mitigates any rhythmic imbalance that might otherwise have occurred.
I think it's worth noting the origins of this "rule" - if a piece consistently uses anacruses in its rhythmic structure, then we might consider the final beat of each measure to consistently "belong to" its following measure. This would be true not just for the first measure, but fairly consistently through the piece.
In pieces where that is the case, such as music originating in a baroque or classical dance form or similar, it makes complete sense to omit the final beat in the final bar, because that would "imply" a continuation into the next bar. That's where the rule really comes from.
See the slow movement of Beethoven's 5th, which is rhythmically motivated in such a way: https://musescore.com/classicman/scores/4998836
However, if the piece "just happens to" have a pickup note before the first measure, but doesn't consistently reiterate this throughout, then no such implication is formed in the mind of the player or listener, and there's no reason to omit a beat at the end, though some people still might.
The notion of cutting the last measure short to "make up for" an extra note at the beginning of the piece, while sort of appealing to the mathematical-minded among us, isn't really what's going on in these situations IMO.
Were there a repeat sign after the last bar, it would be essential to have only minims in that bar, but since the piece is there in its entirety, it really doesn't matter that it's a full bar. 'Rules' may dictate that the 1st and last bars add up, but where's the point here?
Some pieces if music have a distinct beginning and a distinct end, but many others end in such a manner that would allow them to be looped back to the beginning if they were performed in a context that needed the music to keep going (e.g. if performers reached the end of a processional before everyone had reached their positions). A composer might not particularly intend that a piece be played through multiple times, but if multiple repetitions are required, it's useful to have the total length of the music be an integer number of bars (and typically a multiple of the length of each phrase).
If a piece of music is subdivided into different sections such that the ending wouldn't really flow back to the beginning, it may not make sense to try to deduct the length of the anacrusis from the length of the last measure. Likewise if the piece of music has a marked repeat from a first ending that contains a copy of the anacrusis to the start of the first full measure. The convention of having deducting the length of the anacrusis from last measure makes sense when it would be useful to loop from the end of a piece back to the beginning without explicit repetition or "DS al coda" markings.
