The majority of exercises that voice teachers give to their students consist of part of a major scale or arpeggio. Each repetition of the pattern is changed to a new key with the same relationships between the notes. A typical pattern is illustrated below:
In the vocalises from the 19th century, however, this was rarely the case. Exercises from Rossini, Garcia, Marchesi, and many others retain a key throughout the exercise, resulting in varying intervals throughout the exercise, more closely resembling one piece of tonal music. Here is an example from Rossini:
When did the chromatic fragments replace the diatonic exercises? Why? Is it because music became more chromatic? Is it because the growth of the Industrial Age encouraged atomization and componentization? Is it because pianos are tuned differently than back then, making modulation simpler?
I have found advantages to using extended diatonic exercises such as those from the Bel Canto era. One is that the singer has to pay attention to the different intervals and chord qualities (harmonies), which is a necessary skill in real singing. Another is that there is a sense of movement and arrival on the various steps of the scale that feels very different from modulating over and over with no home base.
Beginners with pitch-matching challenges can benefit from an exercise that stays in one key for a minute or two, rather than transposing every repetition to a higher or lower key. The constant shifting to a new tonality can be quite confusing to some newer singers.
For more advanced singers, exploring the nuances of the different steps of the scale in both scales and arpeggios can lead to more interesting performances of passage work. Diatonic vocalises contain many of the same sequences that the singer will encounter in repertoire. They also encourage an experienced student to pay attention to where they are within the key of the exercise rather than mindlessly “cranking it up a notch” with each repetition.