The stability of coordinated rhythmic movement is primarily affected by the required mean relative phase. In general, symmetrical coordination is more stable than asymmetrical coordination; however, there are two ways to define relative phase and the associated symmetries. The first is in an egocentric frame of reference, with symmetry defined relative to the sagittal plane down the midline of the body. The second is in an allocentric frame of reference, with symmetry defined in terms of the relative direction of motion. Experiments designed to separate these constraints have shown that both egocentric and allocentric constraints contribute to overall coordination stability, with the former typically showing larger effects. However, separating these constraints has meant comparing movements made either in different planes of motion, or by limbs in different postures. In addition, allocentric information about the coordination is either in the form of the actual limb motion, or a transformed, Lissajous feedback display. These factors limit both the comparisons that can be made and the interpretations of these comparisons. The current study examined the effects of egocentric relative phase, allocentric relative phase, and allocentric feedback format on coordination stability in a single task. We found that while all three independently contributed to stability, the egocentric constraint dominated. This supports previous work. We examine the evidence underpinning theoretical explanations for the egocentric constraint, and describe how it may reflect the haptic perception of relative phase.