The vocalise we pick to solve a particular problem has several basic elements. There is the vowel, sometimes a consonant with the vowel so as to form a syllable, the sequence of pitches to be sung, where in the range the vocalise lies, the volume desired, sometimes a suggested timbre, and rhythm.
I have noticed that the vast majority of vocalises that singers and teachers use are rhythmically similar. Sometimes the notes are slower or faster, but they are almost always equal-time notes in groups of 3 or 4, or multiples thereof. Scale patterns are almost always down in multiples of 4 equal-time values, arpeggios are almost always triads done in smooth triplets. Probably the reason for this is that these patterns are easy to grasp. Patterns of five are especially tricky. Patterns of 7 can be fairly easy to grasp if the 7 notes form a diatonic scale, but they are exceedingly rare in exercises.
But what do we do within those groups of 3 or 4 that are so ubiquitous among vocalises? What happens if we alter the rhythms?
With any of the standard patterns in common use, notice how it feels to change the rhythm to long-short, long-short or short-long, short-long. Notice which pitch transitions must happen fast and which can happen slower. Notice what your body and mind do to make the rhythm happen. What is the difference in feel and energy between a dotted eighth+sixteenth (quadruple subdivision) as compared to a quarter+eighth (triple subdivision)? Changing a smooth 5-note scale into one of these other patterns can be great for waking up underenergized voices/minds, improving pitch accuracy and articulation on steps 2, 3, and 4 of the 123454321 pattern, and simply providing variety so as to keep the attention of the singer. It is also a rhythmic activity that occurs often in real music.
For groups of 4, another easy change of rhythm is quarter+triplet eighth notes, and the reverse of that. This is an especially good one for working out long scales where the singer might want to feel a slight pulse on every group of 4.
For high arpeggios, using the 1358531 pattern, try long-short-short-long-short-short-long. The energy of the two quick notes can sometimes cause a different coordination on the top note. When done quickly, it can lead to a more reflexive responsive with less push to the top. Short-short-long, short-short-long can be illuminating as well.
One other pattern that is very rare is scalar triplets, such as 1234321, or 1234567654321. Why is that? Simply “tradition”, or is there a good reason? Doesn’t real music do that? Aren’t there a lot of scale patterns in music that are not 123454321?
I dare you to mix it up rhythmically and see what happens.