When designing pie menus, there are both physical (articulatory) and mental (cognitive) factors that you should consider when choosing the number of items and their directions.
Gordon Kurtenbach and Bill Buxton did an experiment that varied the number of menu items and measured the selection time and error rate. They expected the selection time to be monotonically increasing as they added more items. To their surprise, that was almost true, except for the transition from seven to eight items. It was quicker to select from an eight item menu, then from a seven item menu!
That, I believe, was because of the effect of the cognitive bottleneck of associating the items with which direction to move, not the physical difficulty of moving in those directions. While the slices of the seven item menus were wider and had more area than the slices of the eight item menus, and Fitts' Law would predict that seven item menus were faster than eight item menus, Fitts' Law does not take into account the time it takes for users to map their intended command to the direction of that command, and how the mental framework in which users remember and relate the directions to each other affects selection time.
Eight item menus have all of their items in well known directions, each of which is associated with a very familiar concept, which come in nice pairs, and the pairs come in convenient orthogonal groups, like up/down, left/right, vertical/horizontal/diagonal, like compass directions.
Twelve item menus like a clock face also work well, especially for circular sets of items like hours, months, zodiac signs, etc. But the effect going from 11 to 12 is not as dramatic as from 7 to 8. But still the 12 item menu has a nice familiar aesthetically pleasing cognitive framework (including opposite and orthogonal pairs, first tier vertical/horizontal axes and second tier in-betweens) that you can often exploit, depending on the content.
Three item menus are still slightly faster than four item menus, because the effect of the proportional difference in target area overwhelms the difference in the number of items, and two of three triangular directions are well known concepts that are pretty easy to remember, compared to six of seven directions.
An eight item menu optimally exploits that effect, while a seven item is unfortunately sub-optimal with mostly difficult to remember directions. There's no word or concept in the English language for six out of seven of those directions -- they're all just kind of slanted differently, similar to but not quite like the well known compass directions, and there are no nice symmetries, opposite or orthogonal groupings to exploit, by arranging complementary items in opposite directions, independent pairs along orthogonal axes, etc.
So if you're designing a pie menu with seven items (or even eleven), it's better to just throw another item in to bring it up to eight (or twelve)! I gave an example in the DDJ article of a "seven days a week" menu with an additional "today" item thrown in at the bottom to bring it up to eight, with the weekend and today in the lower part of the menu, and Wednesday at the top. See, I don't even have to link to a picture or enumerate every item for you to easily visualize and remember it!
Gordon Kurtenbach and Bill Buxton did an experiment that varied the number of menu items and measured the selection time and error rate. They expected the selection time to be monotonically increasing as they added more items. To their surprise, that was almost true, except for the transition from seven to eight items. It was quicker to select from an eight item menu, then from a seven item menu!
That, I believe, was because of the effect of the cognitive bottleneck of associating the items with which direction to move, not the physical difficulty of moving in those directions. While the slices of the seven item menus were wider and had more area than the slices of the eight item menus, and Fitts' Law would predict that seven item menus were faster than eight item menus, Fitts' Law does not take into account the time it takes for users to map their intended command to the direction of that command, and how the mental framework in which users remember and relate the directions to each other affects selection time.
Eight item menus have all of their items in well known directions, each of which is associated with a very familiar concept, which come in nice pairs, and the pairs come in convenient orthogonal groups, like up/down, left/right, vertical/horizontal/diagonal, like compass directions.
Twelve item menus like a clock face also work well, especially for circular sets of items like hours, months, zodiac signs, etc. But the effect going from 11 to 12 is not as dramatic as from 7 to 8. But still the 12 item menu has a nice familiar aesthetically pleasing cognitive framework (including opposite and orthogonal pairs, first tier vertical/horizontal axes and second tier in-betweens) that you can often exploit, depending on the content.
Three item menus are still slightly faster than four item menus, because the effect of the proportional difference in target area overwhelms the difference in the number of items, and two of three triangular directions are well known concepts that are pretty easy to remember, compared to six of seven directions.
An eight item menu optimally exploits that effect, while a seven item is unfortunately sub-optimal with mostly difficult to remember directions. There's no word or concept in the English language for six out of seven of those directions -- they're all just kind of slanted differently, similar to but not quite like the well known compass directions, and there are no nice symmetries, opposite or orthogonal groupings to exploit, by arranging complementary items in opposite directions, independent pairs along orthogonal axes, etc.
So if you're designing a pie menu with seven items (or even eleven), it's better to just throw another item in to bring it up to eight (or twelve)! I gave an example in the DDJ article of a "seven days a week" menu with an additional "today" item thrown in at the bottom to bring it up to eight, with the weekend and today in the lower part of the menu, and Wednesday at the top. See, I don't even have to link to a picture or enumerate every item for you to easily visualize and remember it!