I'm worldbuilding an alternate earth which has less gravity and the high oxygen levels of the late carboniferous. Thus, resulting in very large invertebrate life. In one scene, the main character is pursued by a giant spider. But, as I was writing the scene, I realized that I don't know what sounds a spider of that size would produce. Let's assume that the spider in this world are almost identical to the American Loxosceles reclusa in every way save for size. Realistically, what sounds would such a creature produce that would be audible to humans?
There would be a mechanical clicking or clacking sound as it moves. (I'm extrapolating that it becomes a loud clacking sound based on size.)
The largest spider in the world makes a clicking sound as it moves through the jungle undergrowth. Link
Further, this species makes a strange noise as a warning to other organisms to stay away called stridulation. Youtube
The mechanics of the sound are sort of like how a cricket performs its chirp. Presumably, your giant spider might make any sort of sound that uses a similar mechanism.
No sound at all
The majority of spiders alive today are some form of ambush or trap predators. Making sound kind of spoils the surprise that the spider was planning.
For a giant spider that is actively pursuing a tasty main character, I would expect the spider to be eerily silent. I would not expect any vocalizations from the spider at all while it is hunting. The goal of the spider isn't to scare, or warn its prey, the goal is to capture the prey with the least effort required.
It is rare for spiders to work in groups or packs (yes, social spiders exist, but it is rare). It is not likely that spiders will want to warn other spiders of nearby threats. There probably aren't too many predators that try to take down a horse-sized spider which a spider would want to scare off using its voice. Overall, there are few reasons for a spider to want to vocalize ever.
Any time the delicious main character is not looking at the spider, it is difficult to tell exactly where the spider even is. And looking at a pursuer while trying to run away means you're not looking where you are running towards... making it all the more likely for the juicy main character to stumble or crash into a tree.
The reason you don't know what sounds a spider would produce are mostly because it is in the interest of spiders to not produce any sounds.
Whatever you want
One of the limiting factors on the size of spiders and other arachnids is their relatively simple, primitive respiratory system. However, increasing the atmospheric percentage of oxygen from today's 21% to the late Carboniferous 35% will only allow a modest increase in the size of a spider. So a bird eating spider might be able to chow down on sparrows rather than hummingbirds, but it's not going to be eating emus or humans.
The bigger limiting factor on land-based arachnid size is the size constraint on exoskeletal creatures in Earth's gravity. (Except where the weight is supported by water, which is why very large crustaceans are possible.) The effects of the square cube law literally do not support large arachnids. Increasing the percentage of oxygen in the atmosphere will not change this constraint at all.
So you can make a giant spider's vocalisations sound any way you want them to, because they need a completely reworked, more efficient respiratory system (which can incorporate any sound-producing characteristics you like) and magic to overcome physical size limits. With a rebuild that complete the sounds produced could be anything from ultrasonic bat-like sounds used for sonar to pig-like squeals to Celene Dion, whatever you think is most frightening.
Expanding on this answer:
Arachnids have at least some variability in breathing apparatus. Most arachnid species use book lungs:
However harvestmen use trachea (not the same as human trachea, but holes in the side of the body that extend inwards creating surface area) that are thought to derive from book lungs. This is likely an adaptation for their small size, as mites also have the same structure.
It's also thought that lower oxygen levels were not the cause of the extinction of large land invertebrates, but the evolution of vertebrate predators which could out-compete and prey on even with invertebrates larger than these vertebrates. Which is to say that higher levels of oxygen don't lead to significantly larger invertebrates, but a lack of vertebrate predators might. We can even see this with the massive coconut crab, whose large adult form spends the vast majority of time on land, can weigh up to 10 pounds, and be about 1 meter in diameter. The coconut crab likely is larger than the largest spider ever in history despite lower oxygen levels today, and said spider did not look like modern spindly arachnids, and would have been incapable of chasing a rat down, let alone a full grown human.
Such a planet would also not be able to have that much less gravity than earth, as at a certain point the escape velocity of essential molecules is so low that your atmosphere disappears (mars is such a planet, so no going below 1/3 gravity) so unless you're being chased inside a pressurized habitat, these spiders won't have a chance to live on the planet at all, though even on mars it would take millions of years for the atmosphere to disappear.
Spiders are known for making clicking noises. Nesting spiders often lie in wait for hours and days at a time waiting for unfortunate victims. They are tuned to the vibrations of the environment and any slight disturbance to their web will provoke a reaction. This attunement to vibrations is based on their hair - which form "elaborate arrays of sensors".
Spiders have no need for complex vocal cords and air breathing, although they do require oxygen. Combined with a reworked breathing system, I imagine spider breathing and communication would sound like a series of fast rhythmic clicks and hisses.
The only sound I have found that a spider makes is a purr so I think the best sound is a purr mixed with a roar, hope this helps.