Dear Rav Mordechai,
I had thought that the ceremony for the daily tamid was always the same, even on Shabbat and Yom Tov, and that the special korbanot and shirim were for the mussaf offerings/service.
We discussed this point in the Insights at the end of Sukah, which I am including here for your benefit.
1) THE "SONG OF THE DAY" ON SPECIAL DAYS
QUESTION: The Beraisa discusses the various Shirim that are recited on the different days of Chol ha'Mo'ed Sukos. Rashi explains that the Beraisa is referring to the Shir that is recited at the time of the Korban Musaf (as opposed to the Shir at the time of the Korban Tamid). Rashi's reasoning is that the Beraisa could not have been referring to the Shir of the Korban Tamid, because then the Gemara would have no proof from the Beraisa that on Shabbos Chol ha'Mo'ed only one Shir is recited during Musaf. When the Beraisa says that on Shabbos Chol ha'Mo'ed only one Shir is recited, it may be referring to the Shir of the Tamid, but at the time of the Musaf two Shirim are indeed sung. It must be that the Beraisa is referring to the Shir of Musaf, and even so only one Shir is sung for the two Musafim.
How, though, did the Gemara know that the Beraisa is talking about the Shir of Musaf? It seems that the Gemara took for granted that there is no special Shir for the Tamid on Chol ha'Mo'ed. The only unique Shir on Chol ha'Mo'ed is the one recited at the time of the Korban Musaf.
However, this contradicts the Gemara in Rosh Hashanah (30b and 31a). The Gemara there states that it happened once, at the end of Elul, that witnesses who came to testify about the siting of the new moon arrived late in the day, after the afternoon Tamid had been brought. The Levi'im, unaware that that day was going to be declared Rosh ha'Shanah, mistakenly sang the weekday Shir at the time of the Tamid and not the Rosh ha'Shanah Shir that they were supposed to sing. The Gemara there goes on to list the unique Shirim of Rosh ha'Shanah and of Shabbos which are recited with each of the three Korbanos -- the two Temidim and the Musaf!
We see from the Gemara there that on festivals, the Shir of the Korban Tamid is also different! How are we to reconcile our Gemara, which says that the Shir of the Korban Tamid does not change on the festival, with the Gemara in Rosh Hashanah? (MINCHAS CHINUCH #312)
(a) The MINCHAS CHINUCH explains that the Shir of the Tamid is changed only on a day that is sanctified and on which Melachah is forbidden, such as Rosh ha'Shanah, Shabbos, and Yom Tov. However, Chol ha'Mo'ed and Rosh Chodesh -- days on which Melachah is permitted -- the normal Shir of the Tamid is recited. Since the Beraisa is discussing Chol ha'Mo'ed, the special Shir that it is discussing must be the one of the Korban Musaf.
The TUREI EVEN (Rosh Hashanah 30b) says that on Rosh Chodesh there is no special Shir for the Tamid. He might have had in mind the same logic as the Minchas Chinuch.
(b) The Minchas Chinuch cites the RAMA MI'PANU (in Asarah Ma'amaros, Ma'amar "Em Kol Chai" 2:19), who says that the Shir of the Tamid changes only on Rosh Chodesh and Rosh ha'Shanah. The reason is the same reason that our Gemara (54b) gives to explain why the Shir of Musaf of Rosh Chodesh that falls on Shabbos is recited before the Shir of Shabbos. It is to publicize that Beis Din is certainly correct in their determination of the date of Rosh Chodesh. Likewise, on Rosh Chodesh the Shir of the Tamid is changed to show the people that the Beis Din is correct in their establishment of the day as Rosh Chodesh. On Rosh ha'Shanah, too, the Rabanan enacted that a special Shir be recited at the time of the Tamid, in order to publicize that Beis Din is correct in their establishment of the new month.
(This might be the intention of the RE'AH in Beitzah (4b) and the RAMBAM (Kidush ha'Chodesh 3:5) as well, who write that the same Kilkul described above (when the witnesses came late in the afternoon of Rosh ha'Shanah and the Levi'im said the wrong Shir) could occur on any Rosh Chodesh, "since every Rosh Chodesh has not only a Korban Musaf, but a special Shir," i.e., during the offering of the Tamid.)
(c) RAV Y. S. ELYASHEV says that perhaps Rosh ha'Shanah is unique out of all the festivals. Because of the day's special status as the Day of Judgement, the Rabanan established that a special Shir be recited at the time of the offering of the Tamid on Rosh ha'Shanah, a Shir which describes Matan Torah (Tehilim 29), in order to "mention the merit of the Shofar blasts of Matan Torah" (Rashi, Rosh ha'Shanah 30b, DH Kol). They did not establish a special Shir for the Korban Tamid of other festivals. (HE'AROS B'MASECHES SUKAH)
Although we find that Shabbos has a special Shir for the afternoon Tamid, as the Gemara says in Rosh Hashanah (30a), that Shir is recited because Shabbos is a separate day of the week, and in that capacity it deserves its own Shirim, for both the morning and the afternoon Tamid. True, a number of Rishonim write that no Shir at all was recited at the time of the afternoon Tamid, such as the TUR (OC 133) and ORCHOS CHAIM (cited by the BEIS YOSEF OC 133). However, this is clearly contradicted by the Gemara in Rosh Hashanah cited above, which states that on Shabbos and Rosh ha'Shanah a Shir was recited for the afternoon Tamid. The RAMBAM (Hilchos Temidim u'Musafim 6:9, 11) also writes that the same procedure was done for the afternoon Tamid as was done for the morning Tamid, implying that the same Shir was said for the afternoon Tamid. The SEDER OLAM (ch. 14), too, discusses a Shir that was said in the afternoon.
The DERISHAH and MAGEN AVRAHAM (OC 132:4) explain that the Tur agrees that there was a Shir in the afternoon; when the Tur says that there was no Shir, he means that it was not Me'akev, meaning that sometimes it would not be said -- such as when the Nesachim were brought after nightfall, because the Shir was said when the Nesachim were brought and the Shir could not be said at night, as TOSFOS (Rosh Hashanah 30b, DH v'Niskalkelu) says. (Alternatively the Tur may mean that a Shir is sung for the afternoon Tamid only on days during which Melachah is prohibited, but on Yom Tov or Shabbos a Shir is said.)