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I am fairly new to music theory and i find these 2 topics related but not explained in depth in...pretty much every resource i have found.

  1. How are beats normally calculated? I went through the process of converting each note using equivalent fractions so every note had the same denominator and then added them all, making the result the number of beats out of a maximum of 4. However, i have the feeling i am over-complicating the process and there is a much simpler way to do it:

enter image description here

  1. I noticed musescore writes beams in a way i do not understand, it writes the beams of the quaver, semiquaver and demisemiquaver to the right or the left in what feels an arbitrary way, making confusing when should i write the beams to the right and when to the left. What's the rule involving the direction of the beams for quaver, semiquaver and demisemiquaver?

This example shows what i mean about the arbitrary beam location:

enter image description here

If possible i would like easy-to-understand answers to this topic, that do not use much musical jargon as i would not understand overly-technical answers with my currently limited music theory knowledge.

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  • In your examples where you state its beams are in the opposite direction - I can honestly say I've never seen it not done this way when using a bar to join notes (as in your examples). Do you have any example where it's not done this way? So the answer to that part, is: because that how it's done.
    – freedomn-m
    Oct 21 at 9:03
  • @freedomn-m often things are done a certain way because there is some benefit, such as making the music easier to read. Of course, it can be difficult to determine whether people find something more legible because of some objective factor or because of familiarity. If it's purely because of familiarity, the practice may nonetheless have arisen because it makes the music easier to write.
    – phoog
    Oct 22 at 8:15
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Wow, thanks for a well-documented and clear question!

You calculated correctly that the example adds up to 2 beats. However, it normally wouldn't be as challenging as that example, since it breaks a convention of beaming: Beams are normally organized to avoid connecting across beats, making it easier to see beats as groups at a glance. What if you had this:
enter image description here
... It's hard to tell at a glance which notes belong to the first beat and which to the second. It ought, properly, to be beamed like this:
enter image description here
... making it much easier to see the beats.

To beam your example properly: The dotted quaver "overflows" beat 1; all there's room for in the beat is a quaver. So the dotted quaver should be split up into a quaver tied to a semiquaver (since the pitch is the same, it will sound as one note):
enter image description here

To the second part of your question, about the direction of beams: The central point is that beams connect notes. The example you give is complicated somewhat by the dotted semiquaver followed by a demisemiquaver.
enter image description here
If the dotted semiquaver were split up, it would yield a semiquaver plus a demisemiquaver:
enter image description here
... and that's why the partial beam of the B demisemiquaver, in the dotted example, points left: it "belongs" to the other demisemiquaver contained within the dotted semiquaver. (See this earlier question, or rather its answer; the question is rather confusing.)

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  • I agree that the left-pointing partial beam helps to group the note with its associated dotted note, but if the shorter note is unbeamed, this doesn't happen with its flag or flags (for example if it is vocal music in older style of syllabic beaming or if the notes are a dotted quarter and an eighth). I wonder how this was done in older styles where stem-down flagged notes had their flags on the left side of the stem.
    – phoog
    Oct 22 at 8:22
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Your first question is partially correctly answered. The only issue is that you should consider note values as relations to the reference meter, not only the beat.

For instance, while technically a quaver is a quarter of a beat (in an x/4 meter where x is between 1 and 4), you also have to remember that there are meters that have different layouts; for instance, the compound meter of 6/4 considers 2 subdivisions of 3 "sub-beats", but it's also commonly considered as a 2-beats based meter (similarly to 6/8). So, one could say that a semiquaver, in that case, is not a quarter of a beat, but a 12th.

A very important thing to remember in rhythmic notation (and music in general) is that it's all relative.

Regarding your second question, these are some rules to keep in mind:

  1. beams are always grouped based on their "siblings" (notes that have the same duration): in your last image, that further line makes no sense, since it's preceeded by a note that has a similar duration;
  2. beams usually extend only within the beat or subdivision, not over;
  3. notes that share a common parent duration also share the beam related to the biggest duration;

Considering the above, this is not completely unusual, and it has the benefit of clearly showing the quaver grouping within the beat:

demisemiquaver grouping

  1. "broken" beams exist only for notes that have no "siblings" (both preceding or following notes that have a different duration);
  2. "broken" beams are always towards their closest "parent" beamed note: a demisemiquaver between a quaver and a semiquaver is always beamed towards the semiquaver; if, for musical reasons, you need to group them differently, the parent beam is separated;
  3. in special situations for which the parent beamed notes are the same (consider a semiquaver between two quavers in a 5/16 meter), the direction is based on the beat, subdivision or musical requirement (phrasing); considering the 5/16 case above, the direction depends on the subdivision: if it's a 2+3 meter, then the beam is on the right, otherwise, and in the rare situation for which there's no actual sub-beat, it's on the left;[1]

Finally, consider that what you're asking is about very rare and specific situations. Your first image and the first example related to the second questions are generally considered as bad notation practice.
Remember that the first rule of notation is to ensure the score can be read as much easily as it's possible: the performer should focus on making music, not decypher how it's written. Beams (and groups) should always help the musicians, not distract them.[2]

In both cases, you have notes grouped along more than one beat (or grouped subdivision), which makes them really awkward.

Here are better versions of them:

much more readable music

While they might seem more complex than your examples, they're actually much more readable and understandable, since the hierarchy of beats and durations is much more clear: the musician can clearly see where (and when) one beat ends and the other starts.

[1] I've seen very special situations for double-sided broken beams, but that's generally a very odd case for very odd notations that cannot be considered as standard.
[2] obviously, the first real rule is music theory, so you could get properly written sheet music that's still hard to read for some reason (consider cases with lots of double sharps or flats), but, as with any rule, there are exceptions; for instance, sheet music for harp sometimes ignores harmonic rules, as the technical "limitations" of the instrument suggest that it's better to write an enharmonic note that properly indicates the string to play instead of the harmonically correct note; for percussion instruments, you can get "pointless" durations (you'll get the same sound and sustain from a snare drum hit, no matter if you write a crotchet, a quaver or a demisemiquaver), but specifying them is actually nonsensical most of the times.

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Just an idea, fuse pairs of notes with same duration next to eachother mentally so they become a note with one flag less, split the ones with dots so there is another note next to it with one more flag and then continue fusing. Is a bit more intuitive than bringing out calculator. (You might need to go dots first, then do the ones with the most flags bottom up, not sure).

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