Yosef Karo, Translation:Shulchan Aruch — Orach Chaim 592…
“ Rem"a: Some say that there should be one set of tekiah-shevarim-teruah-tekiah for the kingship verses, and similar for the remembrance and shofar verses (Tur in the name of Rabbeinu Tam and Minhagim) , and this is the custom in these countries. The practice is to say "Hayom harat olam" after every series of blasts (Mahari"l) . Even on Shabbat, when there are no blasts, we say "Hayom harat olam" although not "Areshet" (Minhagim) . ”
