It depends on what you call a "High Grade" or a "Higher Degree". A man can be a Master mason for a mere 4 weeks under UGLE to become a Companion in Royal Arch although thankfully it usually takes a bit longer in practical terms.
As regards the likes of KTs, R&SM and many of the others it is necessary to be in Royal Arch so this would mean a further period and some also require an applicant to have been an MM for a period of so many years in any event. KTPs require one to be a KT and to have been through the Chair of a Craft Lodge which usually takes at least 7 years.
Unfortunatley I agree with Steve, there is so many different criteria for joining the diffeent Orders. I tend to think of most other degrees as side orders and the higher degrees the more esoteric ones! As that would inclue The SRIA then you could join the SRIA one day after you were Raised. Other Orders like KTP require you to have gone through the Chais and be a member of Royal Arch and KT so that would mean at least 6 or 7 years!
There is nothing more easy than to come to the gate of truth; there is nothing more difficult than to enter it. This applies to most of the wise of this world.