There is much mis or contradicting information on the internet and even amongst reputable lumber dealers and manufacturers regarding what constitutes quarter and rift sawn lumber.

Part of the reason why is that there are several different industry recognized organizations that provide information about quarter and rift sawn lumber. In the US, these include the USDA Forestry Products Lab (FPL), the National Hardwood Lumber Association (NHLA), the National Hardwood Flooring Manufacturers Association (NHFMA), and the Architectural Woodworking Institute (AWI). In Canada, the Architectural Woodwork Manufacturers Association of Canada (AWMAC) and Woodwork Institute (WI) are recognized as the primary lumber standards body.

All of these organizations agree that quartersawn lumber is determined by the angle that the annular growth rings intersect the face of the board. Unfortunately, they don't all agree on exactly what that angle is. Some define it as between 60 - 90 degrees, others define it as between 75 - 90 degrees, and still others define it as 45 - 90 degrees. 

In Bruce Hoadley's book "Understanding Wood", he defines quartersawn lumber as that where the growth rings form angles of anywhere from 45 degrees to 90 degrees with the surface, with "rift grain" indicating surfaces intermediate between 45 degrees to 90 degrees. Hoadley also refers to rift sawn lumber as "bastard grain" too. Unfortunately, Hoadley does not provide references to any FLP, NHLA or AWI standards in his book.

The current industry recognized definition of quarter and rift sawn lumber recognized by architects and professional cabinet shops nationwide is published jointly by the AWI in the US and by the AWMAC and WI in Canada. AWI defines quartersawn lumber as having annual growth ring orientation between 60 - 90 degrees relative to the face of the board. AWI defines rift sawn lumber as measured by annular growth ring orientation between 30 - 60 degrees to the face of the board, with 45 degrees being "optimum" (page 449, Appendix B, section 3 Lumber of the 2009 1st edition of Architectural Woodwork Standards with drawing from same posted above). 

Currently, most of the lumber manufacturing industry adheres to the AWI standard regarding rift and quarter sawn lumber; however there are still some variances so it is good to ask questions and verify that the definition that you are using is the same definition as the lumber seller.

Lumber which is not quarter and rift sawn is referred to "Plain sawn" or "flat sawn". Flat sawn lumber is noted for having cathedral grain appearance on the face of the boards.

There are several different milling techniques that produce quartersawn lumber. Perfectly quartersawn lumber requires that the pith of the log be centered in two planes when milling, in order to achieve an edge grain that has minimal if any slope of grain relative to the face of the board. When you look at a quartersawn oak board that has high ray fleck on one end of the board and much lower fleck on the opposite end, this is the result of either a crook in the log, a log that may have had an off center pith due to nature, or the fact that the log was only centered in one plane when milling. Two of the three of these variances is beyond the millers control, but typically higher grade of quartersawn boards will have minimal slope of grain when viewed from the edge.