Why did I get Tartar build up a month after getting dental scaling?

I'm learning to play the Clarinet since two weeks so I want my teeth all white and shiny. I got dental scaling done like a month back yet I got some plaque build up on my lower teeth even though I brushed my teeth twice a day with Himalaya toothpaste so I ditched it for Colgate Anti Tartar toothpaste today. Will it work?