If your local building authority has a rafter spacing code you may not space rafters wider than required by code.
Porch roof rafter spacing.
The smallest beams for patio covers are typically 4 by 6.
For determination of roof rafter sizes reduction of roof spans shall be permitted where a roof rafter support brace is installed in accordance with section 804 3 2 2.
Chapter 4101 8 9 roof assemblies.
For example in the rafter span table below the highlighted cell in the 40 live load table indicates that 2 x 8 southern yellow pine joists that have a grade of 2 that are spaced 24 apart can have a maximum span of 10 feet 3 inches 10 3 if designing for a live load of 40 lbs ft 2.
However you can only use this pitch with built up roofing or specialized synthetic roofing.
An essential part of planning a patio roof or gazebo project is determining the number size and spacing of rafters beams and posts according to the loads they will carry.
A 4 by 10 can usually span up to 12 feet between posts.
The same concept holds true for roof trusses.
If your project had a rafter length of 8 or less a safe and strong method is to use 2x8 framed 16 on center.
In general the maximum span for a 4 by 6 beam is 6 feet between 4 by 4 posts.
Common spacing for trusses on this type of building is often between 2 and 4 feet but trusses built with advanced designs may allow spacing as great as 8 or 12 feet.
When a reference is made within this rule to a federal statutory provision an industry consensus standard or any other technical publication the specific date and title of the publication as well as the name and address of the promulgating agency are listed in rule 4101 8 44 01 of the administrative code.
The reduced roof rafter span shall be taken as the larger of the distances from the roof rafter support brace to the ridge or to the heel measured horizontally.
This table agrees that 10 12ft is the max span for typical grade lumber at typical spacings for a 5psf dead load.
The minimum pitch for a roof is 1 4 12 which translates to 1 4 inch rise to 12 inches of run.
Maximum rafter spans for a patio roof in areas with mild climates patio roofs are generally designed for loads of 30 psf pounds per square foot.
If this calculator from the american wood council is to be believed and if my assumptions about your materials and load are correct the max span is about 10ft for a pine 2x6.
So the space between rafters can be greater without reducing the maximum span.
Visit the roof framing page for more information on cutting roof rafters and visit the roof pitch calculator for determining rafter lengths based on rise and run.
As a general rule roofs that have a high human occupancy rate should be framed with rafters every 16 structures such as sheds or barns can be frames with rafters every 24 again make sure to consult local codes.