# How to interpret half notes combined with thirty-second stems?

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?

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I used to know this ... :( –  Matthew Read May 12 '11 at 19:55
Something I was wondering just a couple days ago! –  Ben Alpert May 12 '11 at 20:38
You will find this as early as Beethoven (for instance Pathetic Sonata). –  ogerard May 12 '11 at 21:24
when I first read the question, I thought you were saying a half note followed by a 32nd note; but now I see you mean the head of a half note with the beaming of a thirty-second note. The accepted answer is correct; this is used for tremolos –  James Tauber May 13 '11 at 3:25

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).

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Ah, so the broken lines are to help you distinguish 8ths and 16ths from 32nds. Great! –  Matthew Read May 12 '11 at 20:51

In addition to the above answers, let me show you a different version of the next to last bar, as well as the note-by-note expansions. The LilyPond input is quite instructive as well since it shows how often the two-note phrase is repeated in the various versions:

```mus = {  \repeat tremolo 15 { c,32 c } <c g c'>16\f-> }
musII = { \repeat tremolo 8 { c,32 c }
\repeat tremolo 4 { c,32 c }
\repeat tremolo 3 { c,32 c } <c g c'>16\f-> }
\new Staff {
\clef bass
\mus \unfoldRepeats \mus
\musII \unfoldRepeats \musII
}
```

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