It seems that there are notes, like D above middle C, where the octave key is called out to press, yet it does not open the octave valve or seem to do anything while the other required keys are pushed for the D.
If the octave valve does not open then why do you have to press it???
And a similar variation of this question,
The third key from the top on the chart makes my octave key not work
Actually, you’re probably fine.
There are two octave mechanisms on the saxophone, let’s say the one on top of the neck is the primary mechanism, there is a secondary one that opens when you have the octave key pressed but also have the third key on the left hand (bottom finger for G) pressed.
When you play notes with the octave key pressed you will have one of the two mechanisms opened, but not both.
It’s good to know about both of the mechanisms for a few reasons. On my alto, sometimes the ‘secondary’ mechanism sticks and at first it took me a little while to figure out what was wrong. Then I cleaned it off and the horn played better.
Here’s a video to show what’s going on.
The octave mechanism on the neck works for the highest notes, A with the octave key and above (as long as the G key is not pressed) and the other octave mechanism works for notes G and below with the octave key pressed.
Basically the effective length of the saxophone is from the mouthpiece to the open holes (can be all the way to the bell if you’re playing low Bb). So the octave mechanism is higher on the horn (on the neck) for the higher notes and you use the lower one for the lower notes.
The distance between the octave mechanism and where the air leaves the saxophone is more similar for all the notes and makes the effect more even. That’s my understanding of what is going on.