Auntie does not judge ... much. Here is a simple way to accomplish what you're looking for without having to work with additional software. In addition to this approach, there are a number of third-party apps that can also help. Auntie's sticking to iTunes for today.
Import the MIDI. Import your MIDI file into iTunes -- Either drag the file into iTunes or use File > Open.
Trim it. Once imported, you need to shorten the track so that iTunes won't complain about using it as a ringtone. Right-click the new track, and choose Get Info. In the Info pane, choose the Options tab. Edit the Stop Time to 30 seconds (0:30) and check the option. You can change the start time as well if you want to pick the optimal 30-second snippet in your larger Star Trek experience. Click OK. (If your MIDI is under 30 seconds in length, you won't need to do this.)
Convert the MIDI to AAC. After shortening the duration, convert the track to AAC format using the pop-up menu. Right-click, and then choose Create AAC Version.
Locate the files. Right-click the converted track. Choose Show in Finder. Leave that Finder window open, return to iTunes.
Clean up iTunes. Delete both copies of your track from iTunes. If you have iTunes set up to copy tracks, move the duplicate MIDI version to trash but make sure to Keep File for your AAC version.
Transform the AAC file into a Ringtone. In the Finder window, rename your track to use the m4r extension instead of the m4a extension (you'll have to confirm that you want to do this) and drag the newly renamed m4r file into iTunes. It will appear in the Ringtones section of your library.
Sync. Sync your iPhone, making sure to enable the Sync Ringtones option with your new ringtone selected.
Set your ringtone. On the iPhone, open Settings > Sounds > Ringtones. Select your Custom ringtone. This list appears below any Purchased items and above any Standard iOS ringtones.
You can now play your geeky ringtone to your heart's content and to the annoyance of everyone around you. Auntie hopes this helps you achieve the inner geekitude that you seek.