Before you start this quest, you must first complete your way through the star chart to Neptune, and then complete the The Second Dream
1)Select Octavia's Anthem from the library left of navigation to make it your active quest. This will also tell you if you are missing any requirements.
2) travel to a relay (town zone), like the one on Venus. Here you need to speak to Cephalon Suda, the leader of the Syndicate named after him. He's in the left middle part. Agree to help build the Mandachord. Cephalon will give you a quest to go to Neptune.
3) Find the Mandachord Body, Mandachord Fret, and Mandacord Bridge on a Corpus base in Sao, Neptune. These will be hidden, but are necessary to complete the mission. A blue light will try to guide you to each one, but I found it difficult to follow and imprecise. You may just have to look everywhere.
4) Build the Mandachord in the foundry. This will take 30 minutes.
5) Collect the first sound fragment in Stephano, Uranus. Fight through the mission to reach a pipe organ. Activate the organ and copy the symbols at the top into the Mandachord.
6) This step is just like 5, but on the moon and you need to fight Sentient Battalysts to reach the pipe organ. Copy the symbols again.
7) Again this is similar to 5, but after copying the pipe organ, you will need to travel to consoles and defend them from Sentients.
8) Visit Cephalon Simaris at a relay. You can fast-travel directly to him. He's on the second level. He will send you on a unique quest in the Datascape.
9) In this place you need to step on squares with a gold or red hologram above them, and avoid stepping on any others. You will also want to avoid a spinning beam or falling off. You'll need to complete three rounds of this, with weak enemies spawning in the later rounds. You won't be able to step on a note if an enemy is above it. This quest is frustrating, but hard to fail, so you may spend a lot of time here.
10) Speak with Suda, as in step 2 to complete the quest.
Here's a video someone made: