Harmony's rhythm

[Dawe]

we saw in rhythm of war that it requires two people to combine even a small amount of two different types of investiture, and that the two people can't be trying to overpower each other, so how did sazed combine two shards by himself

[TheSurvivorofDeath]

Sazed took the actual power of the shard, rather than trying to combine portions of their power and opposing intents. He was connected enough to the intents of both Shards to take both powers. He embodied both intents and effectively made them one intent.

[alder24]

6 hours ago, Dawe said:

we saw in rhythm of war that it requires two people to combine even a small amount of two different types of investiture, and that the two people can't be trying to overpower each other, so how did sazed combine two shards by himself

Becoming a Vessel of a Shard or Shards is different than combining different types of investiture. For a Vessel, you need to have strong Connections to a Shard, or multiple Shards. Sazed had that Connection. He was a Feruchemist (invested art that came from both Ruin and Preservation), and as such he worked on Preserving knowledge of ancient and current times. He was even Preserving the knowledge about Steel Ministry and TRL's religion, as for him it was worth Preserving. However, despite the fact that as a Keeper he should avoid any conflict with the Ministry, he was actively involved in the rebellion to abolish TLR, which is an Ruinous action. Then, during the events of WoA, he became a warrior, he fought, killed and brought Ruin to Koloss army, which connected him strongly with Ruin. All his actions during Era 1 Connected him strongly with both Shards, and gave him understanding of their nature. He knew Ruin is necessary, as equally as Preservation. And, because of the knowledge preserved in Terris religion, he knew both of these powers can work in Harmony, they did create Scadrial and humanity after all. This was enough for Sazed to Ascend.

All of that is different from combining two types of Investiture, like Stormlight and Voidlight. Both of these are strongly Connected to existing Shards, they are part of Shard's power, and they are resonating with Shard's Rhythms. That's why they need to sing, starting from Shard's Rhythms, so they can slowly lead investiture into new Rhythms, and disconnect it just a bit from a Shard that they belong to.