Distances in biological databases are known not to be ultrametric. Deviations from ultrametricity can however reveal useful features of biodata. In the present study we examine deviations from ultrametricity of the distances between known phage proteins quantified in two senses: (1) the failure of triangles to be isosceles and (2) failure of every point to be the center of any sphere in which it resides. The deviations from these two ultrametric properties undergo qualitative changes as a function of the distance. Below we describe these changes and how they can be observed. We further argue that the distances at which the qualitative changes take place reveal intrinsic scales in the dataset. Such scales are important for choosing threshold values of the distance in various algorithms and reveal natural chunking of the data that can be used to decide clade levels in phage phylogeny.