The chainring interface determines how it can be installed onto a crankset. The crankset is generally the determining factor of what chainring interface to use since they are typically far more expensive to replace.
The most common interface consists of 3-5 chainring bolts which can be a variety of distances apart. This is where the term BCD comes in, it stands for Bolt Center Diameter. Imagine a circle that goes through the center of each bolt hole; the diameter of that imaginary circle is know as the BCD which can be seen in the provided image.
Another common system is that of Direct Mount chainrings which mount directly to the crankset without the use of chainring bolts. This system makes it easier and faster to swap chainrings in addition to allowing for smaller chainrings to be used. A chainring cannot be any smaller than the BCD since the chainring teeth would be inside the chainring's mounting interface. Direct Mount chainrings get around this problem because there is no hole pattern to obstruct the teeth.
For example: a crankset with a 4 bolt - 104 bcd interface cannot accept a chainring with less than 30 teeth since the teeth would directly obstruct where the bolts needs to go.
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