There are three main types of lunar calendars: lunar-sidereal, the pure lunar and the lunisolar.
As you can see from the table below, there are many lunar calendars with different cycles.
|Chinese New Year's Eve||8th Feb||28th Jan|
|Vietnam: Tet Eve||8th Feb||28th Jan|
|Korea: Seollal Eve||8th Feb||28th Jan|
|Mongolia: Bituun Eve||8th Feb||28th Jan|
|Tibet: Losar Eve||8th Feb||28th Jan|
|Bali: Hari Raya Nyepi Tahrun Baru Saka||9th Mar||28th Mar|
|Hindu: Ugadi and Gudi Patwa||8th Apr||28th Mar|
|Punjabi New Year||13th Apr||13th Apr|
|Sikh New Year||13th Apr||13th Apr|
|Tamil New Year||13th Apr||14th Apr|
|Thailand: Songkran||13th Apr||13th Apr|
|Nepali New Year||13th Apr||14th Apr|
|Parsi New Year||17th Aug||17th Aug|
|Moslem: Al Hijra||2nd Oct||22nd Sep|
|Israel: Rosh Hashana||2nd Oct||20th Sep|
|Diwali||30th Oct||19th Oct|
|Gujurat New Year||31st Oct||20th Oct|
Check Moon Time app nearer to one of these new year start dates and observe the moon phase leading up to that day. You will find that some new years begin with a full moon whereas others begin with a new moon or even a half moon.