Audible tones in noises can cause negative evaluations of indoor sound quality by increasing listeners' annoyance. Continuous exposure to noise with tones has the potential to affect stress, discomfort and work performance. Building mechanical systems are likely to generate audible tones due to rotating components such as fans and pumps. However, prior research has shown that current indoor noise criteria do not address tonality well and consequently correlate poorly with annoyance ratings. This study aims to increase understanding of how multiple dimensions of tonal noise, as created by heating, ventilation, and air-conditioning (HVAC) systems, can impact annoyance. These dimensions include tone frequency, tonal strength, harmonic structures, and time fluctuation characteristics. Subjective testing is conducted using both actual HVAC recordings and artificially synthesized signals, which exhibit various combinations of the dimensions above. Twenty participants are exposed individually to signals in a controlled test chamber. The participants are asked to judge how two sound stimuli presented in a pair are similar and which one is perceived to be more annoying than the other. The dominant perceptual dimensions are then determined through multidimensional scaling analysis.