Forbidden Joy during the Seven and Thirty Days of Mourning

What kind of joy is forbidden for a mourner during the seven and thirty days, and what is the difference between them?

During the seven days, a person is forbidden to laugh, even if it is a brief laugh, as laughter is an external joy on the face, but in the heart, one should be in joy. After the seven days, there is no prohibition against showing laughter on the face, but one must perform actions that demonstrate mourning, such as not cutting hair, etc.

It is stated in the Gemara Moed Katan, page 26b: "Rav Papa said: It is taught in Avel Rabbati: A mourner should not hold a baby in his lap because it leads him to laughter, and he becomes disgraced in the eyes of people. And so it is written in Shulchan Aruch, Yoreh De'ah, Siman 391: A mourner is forbidden joy; therefore, he should not hold a baby in his lap all seven days, lest he come to laughter."

This implies that after seven days, it is permitted to hold the baby in his lap, and so it is explicitly stated in Tur and Beit Yosef.

And Bach wrote: "It seems that this is what is said: all thirty days are equal in that joy is forbidden, but there is a distinction between joy and joy: holding a baby in his lap is forbidden all seven days and no more, as it is only a concern that it may lead to laughter, and this is the saying of Rav Papa at the end of the chapter 'Elu Megalchin', but entering a banquet hall, where there is definite joy, is forbidden all thirty days for all the deceased, but for one's father and mother, twelve months, etc."

However, in Aruch HaShulchan it is written: "And know that laughter is also somewhat joy and is not real joy, and it is only forbidden within the seven days, and therefore Rambam wrote in the fifth chapter: 'If greeting is forbidden for a mourner, all the more so is he forbidden to speak much and laugh, as it is said: 'Be silent' and do not hold a baby in his lap to bring him to laughter, etc.' And laughter is the opposite of crying, as it is said in Kohelet: 'A time to weep and a time to laugh', and therefore in the seven days when crying is prevalent, laughter is forbidden, but not all thirty days, and Tur and Shulchan Aruch also wrote so, but their language requires explanation."

And in Levush it is written differently, that the disgrace is greater when laughing during the seven days, and therefore it is forbidden only during the seven days.

And according to the approach of Aruch HaShulchan, that laughter is external joy and is forbidden during the seven days and afterwards permitted, one can question, for it is said in Berachot 31: "A person is forbidden to fill his mouth with laughter in this world." And so it is ruled in Shulchan Aruch, Siman 560, paragraph 5. And it must be said, as Aruch HaShulchan wrote there, paragraph 8: "And this is when engaging in laughter for a long time with others." And therefore here it is about brief laughter.

And even during the seven days, one must be in internal joy, as it is said in the Gemara Sukkah, page 25b: "And Rabbi Abba bar Zavda said, Rav said: A mourner is obligated in the sukkah. - It is obvious! - What might you say: since Rabbi Abba bar Zavda said, Rav said: one who is distressed is exempt from the sukkah - this one too is distressed, it informs us: this is only in the case of distress that comes by itself, but here - he is causing himself distress, he should calm his mind."