Abacusynth is a synthesizer inspired by an abacus, the ancient counting tool used all around the world. Just like an abacus is used to learn the fundamentals of math, the Abacusynth can be used to explore the building blocks of audio synthesis.
"Oh, you foolish filly... Prince Blueblood is Royalty. You're just a commoner... that's something no desperate bid to trap him is going to change. I think you've overstayed your welcome. I won't let you ruin his life. Go home."
No, no he doesn't. Madame Cinch made sure of that. Made sure that Ditzy wouldn't want to tell him either, putting all those doubts in her head - Ditzy thinks that it might be best to let sleeping Diamond Dogs lie and just raise Dinky herself.
And if you can believe it Cinch genuinely thinks she did the right thing.
Cinch had three charges in her care once, Celestia entrusted her with the day-to-day care of Prince Blueblood, the new Princess Cadence and her student Sunset Shimmer - running a kingdom is difficult enough alone without three young ponies to look after - so when Celestia is absent (often) that means Cinch was in charge of these three ponies. And while the matron of the castle was always rigid about rules and wanted her three charges to uphold her reputation and to build their own budding reputations high, she cared about them very much. You'd have to, spending your time with the same three young ponies for so long, guiding and teaching them to be their best...
By the time Ditzy came into the picture, Cinch was down to two charges. She refused to fail them the way she failed...
Well, with one down, there were two left and she cared so much she wouldn't let anyone ruin them, especially not themselves. Surely they would come to realize Cinch was only helping.