The Moon, Its Phases, Influences And The Different Parts Of The Lunar Month
The original question was: does the New Moon influence lasts to the First Quarter, First Quarter to the Full Moon etc - or just on that day?
And here is my answer.
As you probably know, the Moon's phases are technically the specific angles, measured in ecliptical longitude, between the Sun and the Moon as seen from the Earth. Say, New Moon is the moment when the angle between the Sun and the Moon is 0 degrees, Full Moon - 180 degrees, First Quarter - 90 degrees, measured from the Sun, Last Quarter - 270 degrees, measured from the Sun.
This means that there is a specific moment in time when the phase is precise and its influence is most pronounced. The influence can be noticed for some time before it culminates, as well as for some time after the culmination. How long this period of time is - a difficult question. It depends on many factors. If we are speaking about the influence on humans, some humans are more sensitive to the Moon than the others. Also when the Moon is in perigee, its influence will be stronger.
But if I have to give an estimate of the period of time when the influence of the phase is there, I would say 24 hours before and after the moment of the phase. From this point of view, one could say that two days after the New Moon we should not be saying that the New Moon is still in action.
However, there are certain considerations that are associated by the tradition not with the phases themselves but with the periods of time between the phases. Say, there is a waxing Moon (from the New Moon to the Full Moon) and a waning Moon (from the Full Moon to the New Moon) and there are things to be done when the Moon is waxing and other things to be done when the Moon is waning. Likewise, there are certain considerations associated with the first week (or the first quarter of the lunar month, the period between the New Moon and the First Quarter phase), the second week (the second quarter of the month, the period between the First Quarter and the Full Moon) and so on.
You have probably already noticed the ambiguity in terms: there is a lunar phase named First Quarter and there is the first quarter (or the first week) of the lunar month. They are different. The former is a specific moment in time (like 27 August 2009, 12:42 PM BST) while the latter is a period of time - from the moment of the New Moon phase to the moment of the First Quarter phase. There is also an ambiguity between the Last Quarter phase (the precise moment when the Moon is 270 degrees ahead of the Sun) and the last quarter (or the last week) of the lunar month, which is a period of time between the Last Quarter phase and the New Moon phase.
Certain considerations refer to the exact moment, the phase, like there is a higher probability of bleeding and complications during a surgery around the moment of the Full Moon. Other considerations refer to the periods of time, like such and such plants are recommended to plant during the first week of the lunar month. The bottom line is that when you hear or read a reference to the first quarter, you need to clarify whether that is the First Quarter of the Moon (the phase) or the first quarter of the lunar month (the week).
I hope this makes sense to you.