This looks like a dupe of Why are notes named the way they are? but it isn't. I want to know about rhythm.
I understand that in the international (British) system, a breve is what we Americans call a double whole note.
Semibreve is a whole note, 4 beats in common time.
Minim is a half note.
Crochet is a quarter note, 1 beat in common time.
Quaver is an eighth note.
Once I get below quaver, I get lost. Is it hemi? semi? demi? And what is the logic for choosing which to use?
Wikipedia has a very good breakdown of how notes are named. Here's a snippet of just the names of the ones that are different:
American Name British Name double note | breve whole note | semibreve half note | minim quarter note | crotchet eighth note | quaver sixteenth note | semiquaver thirty-second note | demisemiquaver sixty-fourth note | hemidemisemiquaver hundred twenty-eighth note | semihemidemisemiquaver
As you can see in the British naming scheme, the quaver is the smallest unit. The prefixes semi, demi, and hemi all just mean half and they all are applied in that order when referring to something smaller. Which is why you see the notes above in the following order. There is no "official" British name for a 256th notes, but based on the naming pattern to that point, you could call it a demisemihemidemisemiquaver. Although this pattern gets wordy very fast, you could name much smaller notes also using this system.
It's kind of a strange story. In an early form of notation there were two kinds of notes, long and short. "Longa" means "long" and "breve" means short.
So the longest note you are ever likely to see in modern music (twice as long as the longest note you usually see) is a "short".
At some point someone needed a shorter note than the short, thus the "half short", or semi-breve.
That wasn't short enough, so the smallest possible, or minimal, note was invented: the minim.
Which still wasn't short enough. A note was invented that looked like a small hook, thus "crotchet". The next smaller note could be used to represent a quavery sound, and after that they just went with every synonym for "half" they could find.
It's like money inflation, but in reverse. Notation deflation. There was a time when you could buy a good meal for a penny and sing four breves in one second. Now a semi-breve is enough for a full second at MM crotchet=120 and a penny won't buy you half a biscuit.
Postscript:
I decided to look for evidence of my assertions, so I got out the Oxford English Dictionary which gives dated examples of early use of words. You can't count on it for the very earliest use of a word but it is helpful.
"Maxima", "longa", "breve" and "minim" (longest, long, short, shortest) seem to have appeared around the same time, with a citation of "minim" and "maxima" from 1440 and "longa" and "breve" from 1460. Also "crotchet" appears in 1440 defined as "semiminima". That would appear to indicate that at the same time they defined the shortest note, they also defined a shorter one!
"Semibreve" appears in 1594; "quaver" in 1570 and "semiquaver" in 1576. I don't know what the relation of breve and minim was in 1460; perhaps the minim was half of the breve and later became one quarter of the breve. An expert in early music notation can clear this up for us.
In 1706, someone named Phillips defines "demisemiquaver" as "The least note in music." By this time of course Bach was using as many beams as he needed so there was no such thing as a "least" note; any note could be split in two.
The OED defines "hemidemisemiquaver" as an example in the entry for "hemi-" but does not give any citation.
