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Genesis of the idea
I thought of this game years back, after watching the famous videos of VTF-INO double playing Ikaruga, like this one https://www.youtube.com/watch?v=ToBdzV7w5Pc. Those videos are impressive because Ikaruga wasn't designed to be played this way, and is already difficult enough for a player controlling a single ship. But it ocurred to me, what if there WAS a game where it's whole design was based on the presumption of double play? The difficulty would be adjusted accordingly, so that the average shmup player could play it and not just rare talents like VTF-INO. But more than that, it would open up a whole load of mechanics that could play on this idea of controlling two ships at once
Tektite Symphony

Tektite Symphony is a dual analog-stick controlled shmup where the player controls a single ship which he may split in two or recombine at will. A combined ship’s bullets deal twice the damage, however a single ship covers much less ground.

As the enemies move downward, a single ship will not be able to move fast enough to destroy all of the enemies here.

That's better!
Weapons
The weapon system is completely designed around the double play idea:


By sending blue's bullets to the red ship, the player can aim at enemies which pass between the two, like some kind of high energy garroting wire. But what happens to those bullets which red is absorbing?

Well every shmup needs its smart bomb. By moving the red ship at the moment of release, the blue bullets may also be directed in a concentrated 100-degree wide arc.
Each weapon will behave uniquely across the three firing states of Forward, Send, and Release.
Abilities
Tektite Symphony is not a bullet hell shooter. It's unrealistic to control two ships at once in a bullet hell game, unless you're VTF-INO of course. Instead, bullets in Tektite Symphony are fewer while moving at a slow pace, so the challenge is one of spacial awareness, and choosing the correct moment to split or combine ships.
Still, even allowing for this, the eye has difficulty tracking two objects at once, so we need to help the player further with some special abilities.
1. Focusing
2. Teleport
3. Pin
1. The Focus System
While a ship-half is close to danger, a spotlight will grow around the ship and the rest of the screen will darken according to the proximity of that danger.

This attracts the eye towards the danger area, allowing the player to take evasive action.
If both ship halves are close to danger, the ship in the more immediate danger will have a brighter spotlight.

In-game the gradual blend to darkness is a subtle effect, allowing it to aid the player without being obtrusive, though focusing can be disabled if the player wishes.
2. Teleport
At any moment, the player can teleport either ship to its other half.

This is obviously useful as an evasive technique, but also allows for strategic play, such as using a ship as a decoy. Imagine a situation where a turret in the middle of the screen fires a wall of bullets at any ship that approaches it, preventing passage. Blue as bait approaches on the left side and draws fire towards the bottom left corner of the screen. Meanwhile red has safe passage to pass the turret on the right. Blue, now trapped in the corner by the hail of bullets, ports to red at the last moment. Both ships advance safely.
In addition to situations like the above, the beginning player will find it useful to port on occasions where they become disoriented by controlling two ships simultaneously (this is especially liable to happen if the blue ship, controlled by the left analog, moves to the right half of the screen, and the red ship moves to the left, in effect cross wiring the analog sticks. By porting and becoming one ship, the player’s bearings are restored in an instant.
3. Pin

Pinning locks the movement of separated ships to one analog stick, as though the ships are connected by a rigid bar. There are times when the player will face symmetrical enemy formations, or environmental hazards, etc. Pinning ships removes the burden of controlling two ships, while still maintaining two points of attack.
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More updates to come. In the meantime i'll be glad to answer questions and so forth! Thanks for reading.