In this work a new type of magnetic resonance (MR) imaging sequence is proposed that was designed with the focus on acoustic noise reduction during MR image acquisition. The newly developed Hilbert-Moore sequence samples k-space along the Hilbert-Moore space filling curve. The frequent, feigned stochastic gradient switching pattern leads to a smoother acoustic noise characteristic in comparison to standard imaging sequences like EPI with the hard pulsed sound emittance. The Hilbert-Moore sequence acoustic noise characteristic is more pleasant for the human hearing system due to its continuous structure. The distribution of the acoustic energy over the complete frequency spectrum of the human hearing system allows better damping of the acoustic noise by attenuators like earmuffs or earplugs. The design of the sequence and an appropriate reconstruction algorithm are presented as well as the evaluation of the generated acoustic noise.