Why is the Pitum HaKetores said after Musaf?

Question

The Tur (O.C. 132) quotes from Siddur Rav Amram that one should say the Parsha of Ketores every day after davening, and the Rama there writes that his custom is to do so only on Shabbos and Yom Tov. However, every siddur that I've ever seen places it after Mussaf, not just after Shachris. Why is this so? Shouldn't the Ketores be said before Mussaf, since the incense was always brought before the Korban Musaf (Yoma 33a)?

Answer 1

Your question is asked word for word by the Mishnah Berurah on Orach Chayim 132, seif katan 14:

וצ"ע למה אנו אומרין אותה בשבת ויו"ט אחר מוסף והלא הקטורת קודמת למוספין לכו"ע והיא שייכא לקרבן תמיד

And he gives the Magen Avraham's answer as a possibility - that we want to finish our prayer with divrei Torah, before starting out with our day:

ואפשר דכונתנו ליפטר מתוך ד"ת

And he brings another kabbalah-based reason - to drive away the kelipot:

ובכתבים איתא שהטעם להבריח הקליפות

Answer 2

I don't think that the concern of placing Pitum Haktoret before or after Musaph is a factor, here. I think it is merely a factor that Pitum Haktoret always follows En Kelokeinu. The two are linked, and this article explains why.

The focus of the question, perhaps, is why En Kelokeinu is said after Musaph on Shabbat rather than before, as might be suggested in your question, and including the above logic.

This article cites Siddur Rash"i ch. 511 which states that in the piyut En K'elokeinu, we recite each of the words En, Mi and Nodeh 4 times which total 12. This is to compensate for the 12 blessings that are missing from the middle section of Shemoneh Esreh of Shabbat as compared to the weekday one. Thus, combining these 12 expressions with the 7 blessings including in the Shabbat Musaph Amidah, we reach 19 brachot.

You should read the rest of the article, as Rashi's mathematical claim and reasoning does not really work, and Sefer Hamanhig strongly objected to this thinking.