I am scoring simple tunes for the Anglo-Saxon lyre (just started to build them), and any musicianship I have is almost entirely self-taught. If my piece ends on note that takes up half a measure, say, do I need to add a following rest? At the very end of the piece, with no repeats, no DS or DC, the rest looks redundant to me.
Yes, you do. Every measure has to be completely 'filled'.
If your last measure isn't followed by a repeat sign, a dal segno or dal capo, and your last note(s) don't make up for a full measure you have to complete it with a rest.
However, things get more complicated when an anacrusis or pick-up is used at the beginning of the piece:
When your 'last' measure is followed by a repeat sign, a dal segno or dal capo, the rest of the measure has to be at the beginning of the part that is to be repeated. When this part is at the very beginning of the piece, it acts as a pick-up or anacrusis the first time it is played.
But even if there is no repeat sometimes a rule is used that the completion of the measure with rests isn't necessary, because it is supposed to be completed by the anacrusis at the beginning. (Of interest is following SE Music-question: Why must the final bar complete the anacrusis?)
It depends.Starting the tune on beat 1 of a bar, there will be no problem, even if you want the last note to be a short one beat, put in rests to complete the bar. If there is an anacrucis at the beginning, say, lasting one beat, then the end bar should contain the other beats to make up one whole bar together. However, there seems to be a certain laxity over that 'rule', and a lot of stuff is written with an anacrucis start, and a full bar at the end. Sometimes the issue is fudged by the last bar having a pause mark over it.Yes, the rest at the end of the last bar appears pointless, but technically it ought to be there.Particularly with handwritten dots, to say 'no, I haven't forgotten to put another note in'.
To simplify Tim H's answer:
In traditional music notation, in a piece with a single time signature, the total number of beats with or without a repeat must be a multiple of the number of beats in the time signature.
Since only the measures at the beginning and end of the piece can be truncated without changing the time signature, this means that if there is an incomplete measure at the beginning of the piece, the incomplete measure at the end must "complete" the measure at the beginning by having exactly as many beats as were left out of the first measure. Similarly, if there is an incomplete measure at the end of the piece, there must be a complementary incomplete measure at the beginning as well.
An incomplete measure at the beginning of the piece is called an "anacrusis" or "pick-up".
If a piece of music is of a form that might be sung multiple times, even in the absence of marked repeats (e.g. a hymn with multiple verses), it can be helpful to write the music in such a fashion that concatenating a second copy of the piece would yield a clean transition between one verse and the next. If a piece in 4/4 started with a quarter-note pickup and ended with a whole note, it would be unclear whether someone should:
Sing all beats a written, i.e. .sing the whole note for four beats, then the pickup for one beat, and then proceed with the rest of the second verse.
Add a partial measure to balance the pickup, i.e. sing the whole note for four beats, then rest for three beats, then sing the quarter note pickup on beat 4 and proceed with the rest of the second verse.
Shorten the whole note to three beats, and sing the quarter-note pickup as beat 4 of the last measure.
Note that these issues only arise if there would be a plausible reason to make an unmarked repeat from the end of a piece back to the beginning. The existence of repeats within a piece would not preclude such a possibility if the end of the piece is not itself within a repeated section, but the style of a piece might. If a piece starts with an introduction which is very different from everything else, such that repeating from the end of the piece back to the very start would sound odd, it's probably better to fill out the last measure than to balance the first one. Further, if a piece starts in 6/8 and ends in 4/4, it may be unclear what should be done to "balance" the first and last measures.
Thank you, everyone, for very helpful answers. I am using Musescore to write my notation, and of course, in the final measure, if the note(s) do not fill it, the programme automatically includes the appropriate rests. I can 'suppress' the rests by making them grey on my screen, and these are not printed when you print to paper or to a pdf. I suppose I could figure out which rests to grey-out, so that the remaining rest(s) create the balance with the anacrusis (which start almost all my efforts). When I do repeats, I start the repeat at the measure following the anacrusis and include, as likely as not, the very same note(s) in the measure BEFORE the repeat instruction that takes you back to the start. That measure is labelled 1., and then the second time round, measure 2 sorts out what happens after the repeat. I am pretty much trying to copy the format of some of the classical guitar scores that I have kept from 30 years ago.