Narada Purana (Jyotisha Selections) · by Vyasa
Chapter 6 · Calendar, Muhurta Elements
कालमानं मुहूर्ताङ्गानि च
विनायकयमौ नागचंद्रौ स्कंदोऽर्कवासवौ ।महेन्द्रवासवौ नागदुर्गादंडधराह्वयः ॥ १३४ ॥
In the full Narada Purana (Purva Bhaga) this is chapter 56, verse 134.
Vinayaka and Yama, Naga and Chandra, Skanda, Arka and Vasava, Mahendra and Vasava, Naga, Durga, and the one called Dandadhara.
Simple meaning: This verse lists more gods who rule the moon days in order.
शिवविष्णूहरिरवीकामःसर्वःकलीततः ।
The list of moon-day gods goes on. The new moon day is ruled by the ancestors.
नंदाभद्राजयारिक्ता पूर्णाः स्युस्तिथयः पुनः ।
Five kinds of moon day go round three times. In the bright fortnight the three rounds are poor, middling, then good.
कृष्णपक्षे त्विष्टमध्यानिष्टदाः क्रमशस्तदा ।
In the dark fortnight the three rounds are good, middling, then bad. The 8th, 12th, 6th, 4th and 14th moon days follow.