Scales and arpeggios are a critical part of my vocal warm-up routine, which I suspect is unusual among singers. Perhaps it's a remnant of my initial training as an instrumentalist. I do have a reputation as a singer with a very flexible voice, and I'm good with roulades, arpeggios, and trills. Other singers have asked me, “How do you do that?” and I answer “Practice! Every day!” It's too bad that singers generally do not receive this sort of training, which is so basic to instrumental musicians.
I find that working the scales and arpeggios in different keys, and (for arpeggios) from different starting points is very instructive, and requires real concentration. Singers have to do this entirely by ear and “muscle feel” since we do not have keys, strings, bows, or frets to guide us.
I’ll sometimes start the arpeggio from the third or the fifth of the chord, then run it up and down two or two-and-a-half octaves, then move up or down to another key, usually a half step away, but sometimes a whole step or minor third away. And I try to cover two or three key changes in a single breath; this is a good way to extend the breath over the entire range. I usually run the arpeggios at a quick tempo, in sixteenth notes, where the quarter note is at about MM=80. (Needless to say, this is done after preliminary warm-ups, when my voice is limber and comfortable.) Typically, the last 5-10 minutes of my warm-up routine consists of scales and arpeggio exercises. I do this away from the piano; I don't have perfect pitch, and it's good just to sing across the breadth of my range without thinking about specific pitches. Being away from the piano also requires that I be responsible for maintaining pitch in general, and especially for maintaining exactly correct intervals between notes. (It's not as easy for a singer as for an instrumentalist.)
It’s tempting (and easier!) to practice arpeggios in major keys only, since these are the ones that come most easily to the ear. But working in other keys yields greater vocal flexibility and a more responsive ear. Arpeggios based on minor, augmented, and diminished chords require intense concentration to fight against the muscle-memory and ingrained aural memories of the major keys. Whew! These are as much "warm-ups" for the mind and ear as they are for the voice. And that makes them doubly useful.
Arpeggio exercises are useful for
* Increasing flexibility of the voice
* Improving and extending breath control
* Improving aural skills
* Increasing range
More of my essays on the life of a chorister, and more about choral rehearsals and choral music, may be found here: http://quodlibet-sarah.blogspot.com/search/label/Chorister