Odd-limit
An odd-limit is a set of intervals defined by a maximum allowable number in the numerator or denominator once all factors of two are removed. It may be considered as a set of consonant intervals, generalizing the 12edo concept of consonance and dissonance. The 5-limit, for instance, includes 8/5, 6/5, and 3/2, but not 7/5 as that contains 7 (an odd number higher than 5); it does not contain 14/5 either because 14 reduces to 7.
The 3-odd-limit contains the perfect consonances - the unison, fourth, fifth, and octave. (Though note that the fourth may be considered a dissonance in some functional contexts, leading down to the major third). The 5-odd-limit expands the range to include imperfect consonances, which are intervals that alongside 1, 2, 3, and 4, may also have numerators and denominators of 5, 6, and 8. These are 5/4, 6/5, 8/5, and 5/3 - the 5-limit major and minor thirds and sixths, approximated in 12edo. The diatonic intervals corresponding to these categories were considered dissonances historically, due to using the complex Pythagorean tunings instead of meantone-related ones.
The 7- and 9-odd limit contain more exotic septimal consonances; expanding to the 9-odd-limit also implies considering 10/9 and 9/8 consonant. These may be called secondary consonances. Note that this includes a tritone, 7/5. These may be considered "secondary" consonances.
More info is on each individual odd-limit page.
