The following articles explain Rosh Chodesh and the correct lunar phase associated with it.  I found them extremely useful in my studies.   ~NeorahYah Germaine McGuffie~

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1.    ​http://www.bayithamashiyach.com/What_and_When_is_Rosh_Chodesh_Part_1.pdf. 
​2.    ​​​http://www.bayithamashiyach.com/What_and_When_is_Rosh_Chodesh_Part_2.pdf
3.    ​​​​http://www.bayithamashiyach.com/What_and_When_is_Rosh_Chodesh_Part_3.pdf