Connecting the breath with your voice is very important in singing. Lack of connection can lead to excess breathiness in the tone and/or problems with the vibrato. When developing flexibility in your voice (fast moving notes) you need to learn to ride the breath the way a surfer rides a wave. In this way the airflow does the work and moving from note to note seems effortless.
Lack of breath connection can lead to a wobble (vibrato that is too slow and too wide). Overly stressing this connection and tight abdominals can lead to a tremolo (vibrato which is too fast and sometimes too narrow).
Finding a natural relationship between your speaking voice and your singing voice is the best way to discover this connection: during lessons, you develop this connection through easy exercises that bridge the gap between these two seemingly separate activities.
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