Baruch Shem Kivod Malchuto VI
“Whoever offers his evil inclination and confesses his sins, has honored Me in two worlds.” (Sanhedrin 43b) On Yom Kippur we recite ten confessions, and, in our abstaining from physical pleasures, we offer our evil inclinations as a sacrifice. We honor God in two worlds, Heaven and Earth, and so we can recite Baruch Shem aloud.
The six wings of the angels that praise God correspond to the six words of Baruch Shem. The same wings correspond to the six words of the song of Shema. Our willingness to confess and repair our sins, causes the wings of the angels to vibrate in praise and song to God.
When we do not recite public confessions, we may only whisper Baruch Shem. (Based on Lechem Rav page 310)