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Narada Purana (Jyotisha Selections) · by Vyasa
Chapter 6 · Calendar, Muhurta Elements
कालमानं मुहूर्ताङ्गानि च
चांद्रो दर्शावधिः सौरः संक्रांत्या सावनो दिनैः ।त्रिंशद्भिश्चंद्रभगणो मासो नाक्षत्रसंज्ञकः ॥ १२९ ॥
In the full Narada Purana (Purva Bhaga) this is chapter 56, verse 129.
The lunar month ends at the new moon. The solar month runs from one sankranti (the Sun's entry into a sign) to the next. The civil month is thirty days. The month of the Moon's one round of the stars is called the nakshatra (star) month.
Simple meaning: A month can be counted by the Moon, by the Sun, by thirty days, or by the Moon's round of the stars.
मधुश्च माधवः शुक्रः शुचिश्चाथ नभस्ततः ।
These are the first ten names of the twelve lunar months.
तपास्तपस्य क्रमशश्चैत्रादीनां समाह्वयाः ।
Tapas and Tapasya are the last two month names. The rest of the sentence runs into the next verse.
तन्नक्षत्राह्वयो मासः पौर्णमासी तदाह्वया ।
A month is named after the star its full moon sits in. Its two fortnights are the bright and the dark.