I am not sure of your context? some seasonal data can be considered circular. Anyway there is a book by Professor Adrian Barnett
Barnett, Adrian G. & Dobson, Annette J. (2010)Analysing Seasonal Health Data. Statistics for Biology and Health. Springer, New York.
Daily data would be considered circular. Circadian rhythms in insects and many other animals.
Yearly cycles in oceans:
Ebert, T. A., J. C. Hernandez, and M. P. Russell. 2012. Ocean conditions and bottom-up modifications of gonad development in the sea urchin Strongelocentrotus purpuratus over space and time. Mar. Ecol. Prog. Ser. 467: 147-166.
Growing Degree days, phenology are some other key words.
All that said, I am not clear on the meaning of "strongly balanced." Even the machines that are supposed to do take repeated measurements at regular time intervals (like weather stations) often break down and leave gaps in the data.
Biological systems are so variable that a very rigid structure is often pointless. Say measuring my blood pressure at exactly 10:05 every day will be indistinguishable from measuring it sometime between 9:50 and 10:15 (roughly) because my physiological state changes slightly from day to day. Did I get 5 hours of sleep or 9? Did I eat _____ or ______? The answer to all these questions influences the outcome to some extent.
strongly balanced is the situation in which the treatment is preceded by itself and the experimental design is also repeated measurement or sometimes call cross-over
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