Haptic Experience (HX) is a proposed set of quality criteria useful to haptics, with prior evidence for a 5-factor model with vibrotactile feedback. We report on an ongoing process of scale development to measure HX, and explore whether these criteria hold when applied to more diverse devices, including vibrotactile, force feedback, surface haptics, and mid-air haptics. From an in-person user study with 430 participants, exploratory factor analysis (EFA), and confirmatory factor analysis (CFA), we extract an 11-item and 4-factor model (Realism, Harmony, Involvement, Expressivity) with only a partial overlap to the previous model. We compare this model to the previous vibrotactile model, finding that the new 4-factor model is more generalized and can guide attributes or applications of new haptic systems. Our findings suggest that HX may vary depending on the modalities used in an application, but these four factors are general constructs that might overlap with modality-specific concepts of HX. These factors can inform designers about the right quality criteria to use when designing or evaluating haptic experiences for multiple modalities.