Obviously for 3 and 4/4 you use the respective semebreve or dotted minim, but what about 7/8, 9/8 and 15/16?
I heard the convention is to just use a semibreve, but that doesn't make sense to me over using tied notes.
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It doesn't make sense to me either, but it seems it's a valid convention, according to Wikipedia... http://en.wikipedia.org/wiki/Whole_note
I suppose it's only valid for measures of 4/4 or less; it would definitely look bad on 5/4, 7/4, etc.
I would say the convention is as you say, but in modern music some composers write the "real" length of the bar in pauses. When so it has to do with sight seeing ("à vista") reading, to make it easier to count empty bars and have a visual representation for the swing/rhythm.
So, yes, the convention is so for most cases. Found this on wikipedia (with references to music theory books: The AB Guide to Music Theory & Music Notation: A Manual of Modern Practice):
When an entire bar is devoid of notes, a whole (semibreve) rest is used, regardless of the actual time signature. The only exceptions are for a 4/2 time signature (four half notes per bar), when a double whole rest is typically used for a bar's rest, and for time signatures shorter than 3/16, when a rest of the actual measure length would be used.
Note, however, that a semibreve rest is placed at the beginning of the bar, where a semibreve note would go. A whole bar rest, which uses the same symbol as the semibreve rest, is centered in the bar.
Adding to my comment above, in 5/4 for instance, the piece may have a 3-2 feel, if so, a dotted minim and minim rest cover it nicely.
In classic music theory when you have a full bar of rest you use the semi breve rest regardless of what time signature you are in. This is to aid in reading the rest. Unlike notes the grouping of rest always aims to use as few rest as possible in attempt to not make reading the score unnecessarily difficult.
If you are playing in a symphony and you have to sight read 40 - 50 pages of music in a night you are definitely going to do it easier when you have one rest indicating a full bar of rests.