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Developing your mixed voice is a complex task that is one of the most complicated vocal techniques in singing. Many classically-trained voice teachers cannot do it! If you're determined to learn how to do it, find a vocal coach with experience in this area to guide you. Chromatic scales are composed of notes in sequence, like the keys of a piano. Start with a scale a few notes below the break point in your register—the moment you normally switch from chest voice to head voice. Sing 5-note chromatic scales above, through, and below the break, in ascending and descending patterns.  Keep your tone even, and go slowly. Don't rush the difficult notes. You will naturally blend your head and chest voices if you sing below and above your register break without changing your tone. Play along on a piano as you sing, or sing along to a recording of vocal exercises. You can easily find free recordings of 5-note chromatic scales for vocal exercise online. While warming up, sing short scales. Rather than singing each note distinctly, "slide" your voice from one note to the next. Sing up and down a scale. Go slowly and do not allow yourself to vary your speed, so that you don't skip over your register break. Yawn widely to stretch your lips. Purse your lips and say "buh-buh-buh" while singing a scale. Try to make a good clear noise, not releasing too much air. If your lips keep losing the trill, stop and yawn, or put a finger in each cheek on either side of your mouth.  Use this exercise regularly. The beginning of your routine is a good time for it, as it warms up your mouth. Do your trills for a scale longer each time. When singing using your chest voice, focus on not straining your throat.

Summary:
Find a vocal coach to help you learn this technique. Sing 5-note chromatic scales. Slur your scales. Practice lip trills.