The common tone theorem describes that scales possessing the deep scale property share a different number of common tones for every different transposition of the scale, suggesting an explanation for the use and usefulness of the diatonic collection. (ibid, p.42)
Winograd, Terry. "An Analysis of the Properties of 'Deep Scales' in a T-Tone System", unpublished.
Gamer, Carlton (1967). "Deep Scales and Difference Sets in Equal-Tempered Systems", American Society of University Composers: Proceedings of the Second Annual Conference: 113-22 and "Some Combinational Resources of Equal-Tempered Systems", Journal of Music Theory 11: 32-59.
Browne, Richmond (1981). "Tonal Implications of the Diatonic Set" In Theory Only 5, no. 6-7: 6-10.