Don't let anyone tell you that "diaphragmatic," "intercostal" or "abdominal" breathing alone is the only safe course; perfect breathing is a combination of these and more.
By practicing the above exercises you will find in a short time all the organs that nature intended to be used for breathing will be in play.
The reason the beginner is instructed to place the hands on the ribs is to work from the central point, and as the student progresses, by continuation of the exercises it will be found that the costal, intercostal, dorsal, diaphragmatic and abdominal muscles are all doing their share.
Place your hands as in the first position. Exhale—inhale. Sustain the syllable "saw" on an easy medium tone. As you attack the tone do not let the ribs collapse, but as you sustain it, let the ribs very slowly collapse under the palm of your hands. Try to resist so as to not let too much breath escape. Don't let your chest collapse any more than is absolutely necessary. The lower the tones you sing the less resistance you need, while the higher tones you sing the more resistance you need. In order to sustain a high tone, draw in slightly under the ribs, leaving the chest extended. Singing the tone, now takes the place of the exhaling exercise.
The word "saw," besides giving you the vowel "ä," also gives you the correct sound of the Italian "ah" and what the "ah" should be in singing.
The average beginner sings too much on the tone color of "a" as in hat, which, as you ascend the scale, would finally land the tone in the region of the back of your neck.
In learning to sing the "ah" or Italian "ä," always use words like "saw," "raw," "law," "paw," "daw," "gnaw," sustaining the tone.
THE VOWELS
a e i o u