This question is asked by the Birkos Avraham here.

He answers (page 134 DH veLicheorah) that it may be that if one sings the mizmor of chol on Yomtov this signifies a disrespect of Yomtov. Conversely, if one sings the Yomtov mizmor and it transpires that it is really chol this means that one is degrading the holiness of Yomtov.

Birkas Avraham concludes that this matter still requires further explanation.

I have, LeAniyus Da'ati, a different idea to answer this question. The point is that the mizmorim that they sang every day in the Beit Hamikdash were an expression of joy. The joy of Yomtov is different than the joy of a weekday. One cannot be happy "on condition"; if one does not know for sure whether or not today is Yomtov.

I then discovered that this is the question of the Mikdash David:-

1) The Mikdash David Kodashim Siman 10 (about "Nesachim") #8, DH veHineh Amrinan b'Erchin, asks this question. He cites the Gemara Erchin 11a (4 lines from the bottom in the name of Resh Lakish) that the Leviim may say a Shir of Nedavah. If so, he asks that on Rosh Hashanah 30b they could have said both the Shir of weekday and the shir of Yomtov and made a condition that one of them would be a Nedavah?!

2) I remain with my suggestion of how to answer this question; that one cannot sing "on condition". Singing is an expression of joy, which is a spontaneous feeling. One cannot say "If today is Yomtov I possess a Yomtov feeling of joy, and if today is a weekday I only possess a weekday feeling of joy when I sing the shir".

3) It should be pointed out that Rashi here; 3 lines from the bottom of 30b; does write that one can say a Shir "MiSafek". However, it seems that this is different since one is saying different parts of the same Mizmor. This is included in the answer of the Gemara top 31a; "Sha'ni Hatam deShirah deYomei Hu:' this is all part of that day's Mizmor, whilst the question of the Mikdash David and Birkas Avraham relates to making a condition on Mizmorim of different days.

Shavua Tov

Dovid Bloom