1) It appears that the minhag in Eretz Yisrael to sing during Birkas Kohanim is really a Minhag that originated in Chutz la'Aretz. See Orchos Rabeinu (vol. 2, p. 67) which relates that in the Minyan of the Chazon Ish and the Steipler, the Kohanim did not sing during Birkas Kohanim.

2) It seems that the reason is because the Shulchan Aruch (OC 130:1) states that if someone saw a bad dream and does not know what he saw, he should stand in front of the Kohanim when they go up to the Duchan and say the prayer of "Ribono Shel Olam, I am Your's and my dreams are Your's...." The Bi'ur Halachah there writes that if someone did not have a dream on the previous night, he should not say the "Ribono Shel Olam" prayer. The Bi'ur Halachah writes that in our countries, where there is Nesi'as Kapayim only on Yom Tov, one should say the prayer on Yom Tov. The Mishnah Berurah (130:1) writes that it is impossible that he has not had a dream since the previous Yom Tov.

3) According to this, Rav Moshe Mordecai Karp shlit'a writes in Hilchos Chag b'Chag (Hilchos Yom Tov, p. 46, note 61) in the name of Rav Yechiel Michel Tuckachinsky zt"l that in Eretz Yisrael, where Birkas Kohanim is said every day and if one saw a bad dream one can say the Ribono Shel Olam every day, it follows that one does not say it on Yom Tov.

4) Since one does not say the prayer of "Ribono Shel Olam," it follows that the Kohanim do not sing, since the reason that they sing is to give the congregation time to say the prayer. However, many in Eretz Yisrael still do have the Minhag to sing and say the prayer in Musaf, as was the Minhag in Chutz la'Aretz, but in Shacharis where there was no Birkas Kohanim in Chutz la'Aretz, in Eretz Yisrael no one sings.

5) We saw above that a few authorities write that in Eretz Yisrael the Kohanim should not sing during Birkas Kohanim. However, the reality is that it seems that in the majority of Minyanim in Eretz Yisrael the Kohanim do in fact sing. I have looked around in the contemporary Halachic works but so far I have not found anyone who explains why they do sing even though there seem to be good Halachic reasons for saying they should not. So I will try, bs'd, to offer my own ideas.

a) The basis of my argument is that nowadays in Eretz Yisrael it is not so widespread if somebody has a dream during the middle of the year that he says the "Ribono Shel Olam" prayer the following day. Really one should. In fact, the Magen Avraham (OC 130:1) cites the Toras Chayim who says that it only has any effect if one says it the next day. The Magen Avraham disagrees with the Toras Chayim because according to the Toras Chayim the custom that everyone says it on Yom Tov would almost always be meaningless. However, everyone seems to agree that if one can say it the next morning, in Birkas Kohanim, then this is the best thing to do. For some reason, it has not become a widespread practice in Eretz Yisrael in our times to say the "Ribono Shel Olam" prayer the day after a dream.

c) Probably the main reason for this is that nowadays our dreams are not as powerful as they used to be.

We find in the Collected Letters of the Chazon Ish (2:149) that he wrote to someone:

"I have had dreams like these many times but I did not pay attention to them. However, it is correct that you should say the 'Ribono Shel Olam' prayer at the time of Birkas Kohanim."

In Orchos Rabeinu (vol. 1, p. 130) there is a paragraph entitled, "The Chazon Ish was not concerned about bad dreams." A reliable Talmid of the Chazon Ish is cited (I think this is Rav Pinchas Schreiber zt'l, the head of the Ashdod Beis Din) as explaining that the Chazon Ish believed that nowadays dreams do not tell us anything, because they are simply the result of what one was thinking about during the day.

d) Other reasons that it is not so widespread to say the "Ribono Shel Olam" prayer on an ordinary weekday may be since it is not so clear at which point one says it on days that the Kohanim do not sing. The Mishnah Berurah (OC 128:172) writes that one should say it only when they are singing, but not when they are saying the words of Birkas Kohanim, because then one must be quiet and have Kavanah for what they are saying. Another reason may simply be that the "Ribono Shel Olam" prayer is not printed in the Sidurim in the daily Shemoneh Esreh, only in the Yom Tov Shemoneh Esreh, and the public has remained with the Minhag brought from Chutz la'Aretz.

e) At any rate, for whatever reason, a large section of the public do not say the "Ribono Shel Olam" prayer on a regular weekday after a dream, and this is why it is still necessary to say it on Yom Tov to cover all the dreams of the last few months.

e) Clearly, if one was to say it in Shacharis on Yom Tov one would not then be able to say it in Musaf since one has not any dreams in between! This is why it remains as the old Minhag for the Kohanim to sing and for the people to say the "Ribono Shel Olam" prayer only during Musaf on Yom Tov.

Kol Tuv,

Dovid Bloom