In the daily prayer service we recite the "Yag Middot," the thirteen divine attributes of mercy ("Va'ya'abor Hashem Al Panav Va'yikra…"). This is likely the most ancient prayer text that we recite. God Himself declared this passage to Moshe, and informed him that whenever Am Yisrael are in need of divine compassion and forgiveness, they should recite this prayer, which has the ability to arouse God's mercy and earn forgiveness for our misdeeds.
Due to the special stature of this prayer, the Sages instituted that it may be recited only together with a Minyan. If one prays without a Minyan, then he may recite this passage only with the Te'amim (cantillation notes). He will thus be considered as though he simply reads this passage from a Humash, rather than reciting it as a prayer, which requires the presence of a Minyan. Many Siddurim include the Te'amim of this passage for the benefit of one praying without a Minyan.
An interesting question arises in a case of one who prays with a Minyan but recites the "Yag Middot" more slowly than the rest of the congregation. He begins the recitation with a Minyan, but once the congregation completes the "Yag Middot" he must recite the rest of it privately, without a Minyan. In such a case, must the person read the remainder of the "Yag Middot" with the Te'amim, since he now recites it privately, or does the fact that he began the recitation with a Minyan allow him to complete the recitation privately even without the Te'amim?
The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909) held that one need not recite the remainder of the "Yag Middot" with the Te'amim in such a case. He draws a comparison between this situation and the case where a number of congregants leave the synagogue in the middle of Kaddish, such that less than a Minyan remains. In such a case, Halacha allows the Kaddish to be completed despite the absence of a Minyan, since a Minyan was present when the recitation was begun. Similarly, the Ben Ish Hai argues, a person who began reciting the "Yag Middot" with a Minyan may continue doing so – even without the Te'amim – after there is no longer a Minyan reciting this section.
Hacham Ovadia Yosef, however, disagrees with the Ben Ish Hai's ruling. He notes that even in the case of Kaddish, the remainder of Kaddish may be recited only if at least six men remain in the synagogue. If so many congregants leave that fewer than six men remain, the Kaddish recitation cannot be continued. With regard to the "Yag Middot," then, a person may, at least theoretically, continue reciting the "Yag Middot" even after the Hazzan completed the recitation if six or more people have yet to complete the recitation. Of course, in the middle of the prayer service it would be very difficult to determine how many people have yet to complete the "Yag Middot." Therefore, once the Hazzan completes the "Yag Middot" one who has yet to complete the section should read the remaining passage only with the Te'amim.
Some people have the practice of counting the thirteen divine attributes with their fingers as they recite them, just as we count the spices of the Ketoret (incense) as we recite them in the prayer service. Hacham Ovadia, however, disapproves of this custom, noting that the Rabbis disagree in precisely identifying the thirteen attributes. It would be very presumptuous for somebody to assert which position is the correct one, and it is therefore preferable not to count the attributes with one's fingers. The "Yag Middot" differ in this regard from the spices of the Ketoret, regarding which no debate exists at all.
Summary: If one recites the section of the "Yag Middot" ("Va'ya'abor Hashem Al Panav Va'yikra…") without a Minyan, he may recite it only with the Te'amim. Moreover, if a person began reciting this section with the Minyan but the congregation completed the recitation before he did, he must recite the remainder of the section with the Te'amim. It is improper to count the thirteen attributes with one's fingers during the recitation.
