Bhashya
अथ यत् सप्रतिमध्यन्दिने ऋजुमध्यन्दिने इत्यर्थः, स उद्गीथभक्तिः, तदस्य देवा अन्वायत्ताः, द्योतनातिशयात्तत्काले ।तस्मात्ते सत्तमा विशिष्टतमा प्राजापत्यानां प्रजापत्यपत्यानाम्, उद्गीथभाजिनो हि एतस्य साम्नः ॥
In plain words
Now, that which occurs right at midday—meaning true noon—is the udgītha division. To it the gods are connected, because of the intense brilliance at that time. Therefore they are the most supreme and exalted among all creatures of Prajāpati, because they partake in the udgītha of this sāman.
Close to the Sanskrit
Now, what is precisely at midday—that is, straight midday—that is the udgītha division. To that the gods are dependent, because of the excess of illumination at that time. Therefore they are the most excellent, the most distinguished among the offspring of Prajāpati, because they are sharers in the udgītha of this sāman.