How to interpret 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).

Answer 2

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
}

Answer 3

One has to add that the left hand tremolo notation in bar 6 of the OP is sub-optimal and rather confusing.

A better way is already demonstrated in the melody of the same bar. A half-note + a double dotted quarter-note would be the perfect notation for the tremolos as well. Conformity in every line of the score is key! Just imagine a full-score with a different notation of the same notion in every line!

The two computer prints by User8773 show of two confusing versions of both extremes. The triple dotted half-note doesn't convey as much information about the rhythmical structure of the bar as a split model does - but don't split it too much, like the second example - above all without necessity. But be careful with long notes stretching over the midst of a bar, sometimes a ligature of two shorter notes is better and preferred. The editor could have written a triple dotted half-note in the melody but he didn't for clarity reasons. So he should have done for the left hand as well - there's no reason against it. The melody of the OP shows the accurate way how to do it for the whole score...

And by the way - the 32th notation on half notes just means TREMOLO in general. It has nothing to do with 32th notes - just as fast as you can - imitating the Timpanis. In a very slow tempo you would definitely hear the rhythm of 32th notes which is definitely not desired, so just TREMOLO. In order not to be confused with regular 32th notes the beams have to be detached from the stems of shorter notes. For half-notes there's no danger as they can't have beams anyway.

Some editors - for conformity reasons - even detach the tremolo-beams from the stems of half-notes. Others even write two whole-notes (one above the other) with the tremolo-beams above or below them - never in-between.

But IMHO the latter doesn't convey the idea of fast changing between two notes (to imitate the tremolo) as good as the split model does. And further down the line you would have problems to write grouped-note tremolos like in bar 7 (both hands). This applies to piano-scores.

For an instrument like a violin you will rather find single melody notes - no chords. This would just mean a tremolo on one note so a notation with whole-note tremolos would be accurate. In case there were two or more notes in a violin orchestral-score you will very likely find a 'div.' annotation which stands for 'divisi', meaning that you group your violins in two or more groups (beside the division of 1st and 2nd violins) and let them play a tremolo on one note each group. More than one note at a time would rather be played and annotated as arpeggio and is something for solo players and rarely used for groups.

Listen to the intro of 'Sibelius - The Swan of Tuonela'.

Even 'con sordino' - beautiful.

EDIT: I've found some similar articles that might be of interest:

Unknown notation - thick horizontal bars between notes
What is this notation? Tremolo?