Who Is a Jew? According To Tanakh, Anyone Up To At Least A 16th Jewish

The Family of Manasseh (West)

¹⁴ The descendants of Manasseh: his Syrian concubine bore him Machir the father of Gilead, the father of Asriel.^{[e] 15} Machir took as his wife the sister of Huppim and Shuppim,^[f] whose name was Maachah. The name of Gilead’s grandson^[g]was Zelophehad,^[h] but Zelophehad begot only daughters. ¹⁶ (Maachah the wife of Machir bore a son, and she called his name Peresh. The name of his brother was Sheresh, and his sons were Ulam and Rakem. ¹⁷ The son of Ulam was Bedan.) These were the descendants of Gilead the son of Machir, the son of Manasseh.
¹⁸ His sister Hammoleketh bore Ishhod, Abiezer, and Mahlah.
¹⁹ And the sons of Shemida were Ahian, Shechem, Likhi, and Aniam.

We can see that the following applies:

1. Yitzchak (Fully Jewish, toshav l'habrit-- born of the covenant)
2. Ya'akov v'Esav (Rivkah is a Hebrew but a gentile.)
3. bnei-Yisra'el (Whose mothers are all gentile)
4. Y'hudah takes Tamar; Yosef takes Asenat, etc.. Bnei-Y'hudah v'bnei-Yosef, and those in similar situations (e.g., Shaul HaBen-Simon v'HaKena'anit)
5. Menashe took an Aramit as a wife and had Makhir, who was 1/16th Jewish.

Somewhere, though, I had gotten a 1/32nd or even 1/64th Jewish to be considered Jewish before. If any one of these is correct, please correct my 1/16th assumption.