The meaning of the lunar phase terms in bronze inscriptions is a difficult problem in Western Zhou chronology. Scholars have attempted to discover their meanings by various means, including philological and textual analysis and by dating the inscriptions to specific historical contexts and to the reigns of particular kings. But because there are a number of uncertainties about the early texts, the reigns to which bronze vessels belong, as well as the lengths of reign of the Western Zhou kings, several different interpretations of lunar phases still persist. The present article presents a method which avoids the questions of historical date and reign length, and instead investigates the possible range of meaning of each lunar phase term by means of the relational constraints imposed by the calendar dates themselves. Seven groups of materials were selected, each having two or more lunar phases and calendar dates so their separation in days could be calculated. Within each group of inscriptions arithmetic constraints then make it possible to establish the range of days to which the lunar phase term could possibly refer. The results obtained from the seven groups are all consistent: jishengba and jisiba ought to refer to the waxing and waning halves of the month, respectively. Chuji refers to certain days at the beginning of the month, probably the first occurrence of the auspicious heavenly stems (gan 干).