The Tosefta
Curious as is the order of subjects followed in this treatise, in which several mishnaic sources have been combined, the Tosefta follows it, adding comments that form the basis of the Gemara in both Talmuds. The contents of the Mishnah with the corresponding sections of the Tosefta are as follows:
General calendar for the year, i.1-4 = Tosef. i.1-13. Regulations concerning the months' witnesses, i.5-ii.1 (connecting with i.4) = Tosef. i.15-ii.1 (abbreviated). Historical matter regarding fire-signals and messengers and their reception on the Sabbath, ii.2-6 = Tosef. ii.2 (abbreviated). The continuation of the laws of ii.1 concerning witnesses (ii.7, 8), and the questioning of witnesses, and the sanctification of the months are entirely lacking in the Tosefta. Historical data concerning Gamaliel and the dispute with Joshua, ii.8-9 = Tosef. ii.3 (a mere final sentence). Continuation of the laws of ii.7 concerning witnesses, iii.1 = Tosef. iii.1, 2. Regulations regarding the shofar and its use, iii.2-5 = Tosef. iii.3-6a. Haggadic sentence on devotion = Tosef. iii.6b. Final remarks on the shofar and on its obligations, iii.6-end = Tosef. iv.1. Ordinances of Johanan ben Zakkai concerning Rosh ha-Shanah and the Sabbath, and other matters = Tosef. iv.2. Order of worship, iv.5-end = Tosef. iv.4-end.
Mishnah ii.7 seems to have been transposed according to Tosef. iv.3, but it belongs there according to its contents.
In quoting many of Gamliel's ordinances the Mishnah emphasizes the authority of the patriarchal house by recounting the dispute between the patriarch and his deputy Joshua and showing how the latter was forced to yield. The Tosefta omits the ordinances of Gamliel and of Johanan ben Zakkai, and the dispute of the two leaders of the school-house, nor does it mention anything of the power of any tannaitic dignitary; the Tosefta is here a product of the time of the Amoraim. The dignity of the nasi is not emphasized, because acumen and scholarship prevailed in the schoolhouse, and there was no desire to let old precedences (see Eduyot) come to the fore again. Even the Mishnah contains some additions from the time of the Amoraim (see, for example, iv.2, where a gap must be filled from the Tosefta).
Read more about this topic: Rosh Hashanah (tractate)