Tusculum
A Latin city of the Alban Hills, home of Cato's family, whose calendar gave July 36 days and where Jupiter was worshiped as the god Maius.
Today: near Frascati, Lazio, Italy
How the Romans fixed the year
Censorinus, On the Birthday 20–22 (238 CE), in the edition of Friedrich Hultsch (Leipzig, 1867) · 238 CE
apud Albanos Martius est sex et triginta, Maius viginti duum, Sextilis duodeviginti, September sedecim: Tusculanorum Quintilis dies habet XXXVI, October XXXII, idem October apud Aricinos XXXVIIII.
Among the Albans, March has 36 days, May 22, Sextilis 18 and September 16. At Tusculum, Quintilis has 36 days and October 32, and at Aricia October has 39.
Where the months got their names
Macrobius, Saturnalia 1.12–14 (early fifth century CE), in the edition of Franz Eyssenhardt (Leipzig, 1893) · early fifth century CE; the dialogue is set in the 380s
sunt qui hunc mensem ad nostros fastos a Tusculanis transisse commemorent, apud quos nunc quoque uocatur deus Maius, qui est Iuppiter, a magnitudine scilicet ac maiestate dictus.
Some say this month came into our calendar from the people of Tusculum. There Jupiter is still called the god Maius, a name that comes, of course, from his greatness (magnitudo) and majesty (maiestas).