What are the connotations of "Shabason"?
Ramban: It is a day of rest from work.
Ramban (citing Shabbos, 24b): It is an Asei, and someone who performs Melachah on it, transgresses a Lo Sa'aseh and an Asei, 1 and whoever desists from performing Melachah on it has fulfilled an Asei.
Ramban, Moshav Zekenim (citing the Mechilta): It is an Asei to desist even from activities that are neither Avos Melachos nor Toldos, such as transporting Keilim from one place to another. 2
Ramban: Even though the Torah does not write "Shabbason" in connection with Pesach and Shavu'os, we learn one Yom-Tov from the other with a Hekesh in Pasuk 4 (See R. Cheval's footnotes). And it also extends to Shabbos.
See Ramban who elaborates. And this applies to Yom-Tov, but not to Chol ha'Mo'ed, though the Chachamim decreed even the Sh'vus of Amirah le'Nochri on Chol ha'Mo'ed as well.
Ramban: Even those that are connected with a Mitzvah, such as declaring Hekdesh and separating T'rumos and Ma'asros.
Why does the Torah refer to "Zichron Teru'ah"?
Rashi #2 (on the Sidur): It is the name of the Yom-Tov - which explains why we refer to it as 'Yom ha'Zikaron'. +3. Ramban #1 and Rashbam: Because it is via the blowing of the Shofar that we will be remembered by Hashem for the good (on the day of judgment). 3
Ramban #2: Refer to 23:24:5:2*.
Moshav Zekenim: When Rosh Hashanah is on Shabbos, we do not blow; this is a decree 6 lest one carry a Shofar in Reshus ha'Rabim. It is merely a day of Zikaron, i.e. reciting Pesukim of Malchuyos, Zichronos and of Shofros. In Bamidbar (29:1), it says "Yom Teru'ah", i.e. when it is not on Shabbos, and we blow. Also R. Amram says so.
And Malchuyos - Ramban (See R. Chavel's footnotes DH 'd'Ha Vadai Hu Safek') who points out that this is in fact, not min ha'Torah, but an Asmachta.
See also Ba'al ha'Turim.
Moshav Zekenim says that the verse teaches a mid'Rabanan law. This implies like the Ritva (Rosh Hashanah 16a, before DH uv'Mah) says, that 'an Asmachta is to arouse Chachamim to enact, but Hashem did not make it obligatory, and left it to Chachamim's discretion. This is unlike those who say (like the Rambam's introduction to the Mishnah, just before DH v'Elu) that the Torah did not intend for this, just Chachamim found a 'Siman' to support their decree. This is heretical!' (PF)
What is the significance of the blowing? Why is Rosh Chodesh Tishri included in the Mikra'ei Kodesh?
Ramban: Refer to 23:24:2:3. Based on the fact that it occurs at the beginning of the same month as Yom Kipur, it is evident that it is the day on which Hashem judges the nations of the world, followed by ten days of Teshuvah 1 and a Day of Atonement.
Seforno: Refer to 23:24:2:4.
Ramban: Which in turn, is evident from the fact that the Midas ha'Din (Teru'ah) is tempered with Rachamim (Teki'ah).
Why does the Torah mention specifically "Teru'ah"?
Ramban #1 (according to Kabalah): Because the Teru'ah (which represents Midas ha'Din) stood for our fathers and for us. 1
Ramban: However, a Teru'ah is never blown on its own; it is always flanked by a Teki'ah (Midas Rachamim), one before and one after (in order to contain the Midas ha'Din) - See for example, Rashi in Bamidbar 10:5 and R. Chavel's footnotes DH 'Tiske'u ve'Lo Sari'u'. See also Ramban (DH 'v'Al Derech ha'Emes'). Refer to 23:24:3:1*.
How do we know to blow a Shofar and not a trumpet?
Ramban #1: Since the Torah did not yet mention , and Stam Teru'ah refers to a Shofar, like it says "Shofar Teru'ah" (25:9). Moshav Zekenim - a Hekesh equates Rosh Hashanah to Yovel.
Ramban #2 (according to Kabalah): Because "Shofar" hints at Midas ha'Rachamim, like "Yom". 1
Consequently, when the Torah writes "Yom Teru'ah", it is as if it wrote 'Shofar Teru'ah', a combination of Rachamim and Din. In the same vein, 'Zikaron' hints at Midas Rachamim, in which case "Zichron Teru'ah" too, refers to a combination of Din and Rachamim (R. Chavel's footnotes).
What is the corollary between Rosh Hashanah and Yom Kipur?
Ramban: Rosh Hashanah is Din (Tempered with Rachamim); whereas Yom Kipur is Rachamim, tempered with Din.
Why are women exempt from Shofar? We should say that since the Lav of Melachah applies to them, also the Aseh of Shofar, just like we say that whoever is forbidden Chametz has a Mitzvah to eat Matzah!
Moshav Zekenim #1: Perhaps we say 'whoever is forbidden
Moshav Zekenim: Similarly, wearing Sha'atnez and wearing Tzitzis [are similar, so one might have thought that one who is exempt from one is exempt from the other]. We need a verse to obligate women in Kivud Av v'Em. We do not say that since they are obligated in Shabbos, they are obligated in fearing parents (both are in 19:3. Honoring parents is written right after Shabbos - Shemos 20:11-12. - PF).
How many 'notes' must one hear?
Moshav Zekenim: One must hear three Teru'os, for it says "Shofar Teru'ah", "Yom Teru'ah" and "Zichron Teru'ah." There is always a Teki'ah before and after each Teru'ah, so in all, one must hear nine 'notes'. 1
Since we are unsure whether the Torah's Teru'ah is what we call Teru'ah (nine sounds of duration Mashehu) or Shevarim (three sounds, each the duration of three sounds of Mashehu, or both of these, for each Teru'ah we blow three times (four notes, for one time is Teru'ah and Shevarim) with three Teki'os before and three after. 10 notes in all (Rosh Hashanah 34a). We do so three times (30 notes) before Musaf to fulfill the Torah Mitzvah according to all opinions, and again during Musaf (to confound the Satan - Rosh Hashanah 16a). The custom is to hear another 40 after Musaf, to make a total of 100. (PF)