So https://www.bipm.org/en/bipm-services/timescales/tai.html says A practical scale of time for world-wide use has two essential elements: a realization of the unit of time and a continuous temporal reference. The reference used is International Atomic Time (TAI), a time scale calculated at the BIPM using data from some four hundred atomic clocks in over eighty national laboratories. In that context, what is a "time scale"? Does it assign an hour/minute/second value to each second? It then says TAI is a uniform and stable scale which does not, therefore, keep in step with the slightly irregular rotation of the Earth. For public and practical purposes it is necessary to have a scale that, in the long term, does. Such a scale is Coordinated Universal Time (UTC), which is identical with TAI except that from time to time a leap second is added to ensure that, when averaged over a year, the Sun crosses the Greenwich meridian at noon UTC to within 0.9 s. so UTC is also a "time scale". ITU-R Recommendation TF.460-6: http://www.itu.int/dms_pubrec/itu-r/rec/tf/R-REC-TF.460-6-200202-I!!PDF-E.pd... says A positive leap-second begins at 23h 59m 60s ... which suggests that *something* is assigning hour/minute/second values to seconds. It also says A positive or negative leap-second should be the last second of a UTC month ... suggesting that the clock is tied to a calendar in some fashion.