# superparticular

(*not comparable*)

- 1621, Robert Burton,
*The Anatomy of Melancholy*, I.iii.1.4:- 'Tis superparticular,
*sesquialtera*,*sesquitertia*[...]; all those geometric proportions are too little to express it.

- 'Tis superparticular,
- (mathematics, music) Pertaining to a ratio of any whole number to the next below it (i.e. , etc.).

It seems that the meaning of the term superparticular has narrowed over time. According to the definition of Thomas Taylor, e.g. 144 is superparticular (sesquitertian, to be specific) in relation to 108, because it contains exactly the number 108 and a third part (36) of it. Similarly, 144 is also superparticular in relation to 96, 120, 126, 128, 132, 135, 136, 138, 140, 141, 142 and 143. Current sources limit the meaning to whole numbers that are larger than another number by 1. The definitions are not contradictory, since *n + 1* always consists of *n* plus one nth part of *n*. If defined in the latter way, 144 is superparticular only in relation to 143.

From Late Latin *superparticulāris*.