: Problem Understanding Specific Rules of Adding Rests I am currently studying music theory via https://mymusictheory.com and I can't perhaps understand the English this teacher is using while trying to explain these two rules

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Is it also necessary to say "beat or sub-beat"? Isn't it suffice to
pick "beat" or "sub-beat" and just say one of them since they both
serve the same purpose here?

It's necessary, because you generally need to complete each "beat level" first before moving onto completing any higher beat levels. Whether you call them "beats" or "sub-beats" or whatever is immaterial. Start at the lowest duration level and work your way up.

As for the second rule, it's straight out wrong as stated, so I don't know what it's supposed to mean. I think it's trying to point out that it's okay for longer notes to occur on stronger beats, but not on weaker beats (or sub-beats). In such cases, it's commonly (though not always) true to have the longer notes/rests occur first.

But the rule as stated is very unclear. Perhaps there are more exceptions that aren't listed in the question?

So in Example e. we need to have a 16th rest after the 16th note in
order for it to be a complete beat?

Well, "sub-beat" I suppose, but yes.

In Example f. we incorrectly find a longer rest after a shorter one
but, in its current position, won't that quaver note + shorter rest
equal a dotted crotchet? Isn't two dotted crotchets a fine way to
organize bar f? Perhaps it's only necessary to complete the smaller
"beat" when dealing with compound time..

I'm really not sure whether these examples are supposed to be in 6/8 and 3/4, which will make some determinations as to proper notation.

In 3/4, the first note would generally be followed by a semiquaver rest, then a quaver rest, then two crotchet rests. (Some looser usage would allow some of these rests to be joined, either the first two into a dotted quaver rest or the second two into a minim rest, or both. The first practice is more common than the second; both are likely to frowned upon in exams and traditional "classical" practice.)

If the example if 6/8 (as Rosie F noted in a comment), the expected notation following the note would be semiquaver rest, two quaver rests, dotted crotchet rest. (Again, some looser notation methods might join the two quaver rests as in example f, but this isn't common in exam/classical notation. The "rule," such as it is, tends to disallow the joining of rests on the last two beats or sub-beats within a group of three. That's also the reason for the two crotchet rests in 3/4 as discussed above.)

And in Example e. we could argue that the dotted crotchet being at the
end of the bar is wrong, no?

Under the second rule, I suppose. But, as noted, the second rule is WRONG in general. In 6/8 the dotted crotchet would be correct (even though it would violate the second rule). If we're talking about 3/4, the correct notation would be two crotchet rests at the end of the bar, as noted above.

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I've spent a few minutes looking round mymusictheory.com and, although nothing is actually WRONG, I'm not impressed with the clarity of explanation.

You've covered up vital information in your examples, in particular the key signature. Is it 3/4 or 6/8? In 6/8, f is correct (except for people who eschew dotted rests under any circumstance).

But yes, the rule is to complete the sub-beat, then complete the beat, then complete the half-bar, then complete the bar. Syncopated notes are acceptable, syncopated rests generally aren't.

These are 'theory exam' rules. Usage in modern, particularly jazz styles is sometimes freer.