What is this : Half notes combined with thirty-second stems?

Question

I want to play Also Sprach Zarathustra (IMSLP PDF), but there is something I don't understand there. In the first few bars there are 4 half notes beamed in pairs as thirty-second notes. Because the time signature is common time I deduce each of those "hybrid" notes is equal to a quarter note. Am I correct? If so does the math add up?

In addition in the 6th bar in the second and third thirty-second notes beams are "broken." Why is that?

Answer 1

This type of notation is used to indicate tremolos.

A single figure is made up of two noteheads of identical value (in this case, half notes) that are beamed together in a way that indicates the speed of the tremolo.

The rhythmic length to be played is that of one of the beamed half notes. You would alternate between the two noteheads at a speed of 32nd notes for the duration of two beats.

In this 6th bar you see a variation of this, where the triple beaming stays constant to indicate 32nd note tremolos, but the rhythmic duration changes from two beats (half notes) to one beat (quarter notes) to three quarters of a beat (dotted 8th notes).