There are two different attributes of an ohel. It spreads tumat ha'met that is beneath it, and can act as a barrier, preventing tumah from spreading above the ohel. In the eighth perek we learnt about different cases, where the "ohel" has only one of these attributes. In the fourth Mishnah we learn about cases where the items prevent the tumah from passing through but does not spread tumah beneath it. That case is set of drawn parallel warp threads that are resting over an aruba -- a hole between two floors in a house.

The Bartenura explains that since it is not a woven fabric, it cannot spread the tumah beneath it. However, since the gaps between the threads are less than a tephach that tumah cannot pass through it.

The Tifferet Yisrael explains that the ruling in the Mishnah is only when the source of tumah is inside the house and not beneath the aruba. Since the gaps between the strings are less than a tephach the tumah cannot escape through those holes. If however, the tumah was directly under the spaces between the threads, then the tumah would pass through to the upper floor. The Tifferet Yisrael's proof is from the later Mishnah (10:2) where tumat ha'met is located directly beneath an aruba that is less than a tephach. The Mishnah rules that the house remains tahor and anything above the tumah would be tameh.

The Mishnah Achrona however provides a different explanation that implies that the law would be the same, even if the tumah was directly beneath the threads. He also explains that this Mishnah is the basis for those that maintains that levud can be applied for the laws of tumah. If you recall, levud is the principle in the laws of mechitzot, that any gap that is less than three tephachim, is considered filled. The Mishnah Achrona cites the Rama (YD 371:1) who explains that for tumah, levud is not applied when it results in a stringency. This implies that when it would result in a leniency it could be applied. That explains our Mishnah where these threads do not spread tumah -- applying levud instead in that case would result in a stringency. Nevertheless, tumah does not pass through it, since levud is applied resulting in this leniency.

The case the Rama discuses involves two separate roofs, next to one another, separated by a gap of less than a tephach. The Rama explains that levud is not applied, and if tumat ha'met is underneath one, the contents under the other remain tahor.

The Taz however asks that the Mishnah teaches that tumah can pass from room to room in a space that is the size of a tephach. Since it is less than three tephachim, we should apply levud preventing the tumah from passing through. The Sidrei Taharot explains that for tumah, the region for "levud" to apply is less than a tephach. That region is equivalent to the three tephachim when considering the laws of mechitzot. It is a different levud. He cites the Rashba (Ritva Sukkah 17a) who provides this explanation.¹

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¹ How can we relate to the Mishnah brought by the Tifferet Yisrael as a proof for his explanation. Reading that Mishnah carefully the Mishnah only states that the house would remain tahor; but does not mention the law regarding tumah above the hole.

See also the Chazon Ish (Ohalot 10:1) who argues that from the language of the Mishnah, it cannot be discussing where the tumah is under the ceiling of the house. Nevertheless, he agrees with the Tifferet Yisrael that if it were under the gaps the tumah make tameh anything above it. Instead, the Mishnah is referring to where the tumah is directly beneath the strings themselves.