| New moon | May 22, 768 | |
| Waxing crescent | from May 23, 768 to May 29, 768 | |
| Moon first quarter | May 30, 768 | |
| Growing moon | from May 31, 768 to Jun 6, 768 | |
| Full moon | Jun 7, 768 | |
| Waning moon | from Jun 8, 768 to Jun 12, 768 | |
| Moon third quarter | Jun 13, 768 | |
| Waning crescent | from Jun 14, 768 to Jun 19, 768 |
| New moon | Jun 20, 768 | |
| Waxing crescent | from Jun 21, 768 to Jun 27, 768 | |
| Moon first quarter | Jun 28, 768 | |
| Growing moon | from Jun 29, 768 to Jul 5, 768 | |
| Full moon | Jul 6, 768 | |
| Waning moon | from Jul 7, 768 to Jul 12, 768 | |
| Moon third quarter | Jul 13, 768 | |
| Waning crescent | from Jul 14, 768 to Jul 19, 768 |