The measure of sadness is Tishah B’Av, observed with the traditional postures and practices of mourning. On Yom Kippur there is no lamentation, apart from the brief moment of Yizkor.
Our fasting is not out of sadness but because the spiritual exaltation of the day lifts us above mundane concerns (the Chassidim say, “On Tishah B’Av who can eat? On Yom Kippur who needs to eat?”).
Rabbi Akiva anointed this as a happy day when he said, “Happy are you, O Israel. Before whom are you made pure, and who purifies you? Your Father in Heaven!” (Mishnah Yoma 8:9).
Rabbi Yisrael Salanter used to say after Yom Kippur, “I feel as if a heavy load has been lifted from my shoulders” – not because the day was burdensome but because of the joy of knowing that God had forgiven his sins.