First staff in 'Patterns for Jazz' (1970) by Jerry Coker+, doesn't seem to add up to the time signature. How would you interpret this? I'm just starting to learn notation, so not sure if this is normal, but I thought it should add up..
They add up fine. The first three notes you see, with the 3 underneath them are to be played on the count of one quarter. These are called triplets. The same for the second three notes and then the half note lasts for two quarters, all of which sum up to 4/4.
Are to be played on the count of one quarter.
The same as above.
Lasts two quarters.
It actually adds up pretty nicely! From what I can see you interpret the first six notes as eighth notes. The thing with those are that they are grouped into three notes and notated with a 3 right below them. This means that they are triplets and not eighth notes.
The confusing thing about that is that they are written as eighth notes. How that works is that they are eighth note triplets. This means that three eighth note triplets last one quarter note (1/4). They should be divided in three equally big parts of one quarter note.
The trick is to look for that little 3 written below them (or above them if they would be written higher up).
What this also means is that your 1/4 notations should be changed; move your second 1/4 one note to the right and remove the last 1/4.
(There are also quarter note triplets, where three of those lasts a half note. Also sixteenth note triplets, where three of those lasts one eighth note. So, the general thing is that three triplets of one "speed" lasts one value of the "next slower speed" straight note. Like the three cases I described above.)
The current answers are all good, but I think it would helpful to make one thing very clear:
When you have a triplet, the entire triplet takes up the space of two of the rhythmic units within the triplet. (This assumes the triplet is comprised of three equal note values.)
For instance, in your example, you have a triplet comprised of eighth notes. Thus this entire triplet will last a duration of two eighth notes, or one quarter note. (Now you see the very clear 1 + 1 + 2 pattern in the first measure.)
If you have triplets made of quarter notes, the entire triplet will last a duration of a half note (= two quarter notes). If the triplet is made of sixteenth notes, the entire triplet will be the duration of an eighth note (= two sixteenth notes). And so on.