a. (sb.) Arith. Obs. [ad. late L. superparticulāris: see SUPER- 14 and PARTICULAR.] Applied to a ratio in which the antecedent contains the consequent once with one aliquot part over (e.g., 11/2, 11/3, 11/4 times), i.e., the ratio of any number to the next below it (3/2, 4/3, 5/4); also (multiple superparticular) to one in which the antecedent contains the consequent any number of times with one aliquot part over (e.g., 21/2, 21/3, 31/2, 31/3.). Also sb., a superparticular ratio.
1557. Recorde, Whetst., B ij. If the greater [number] containe the lesser, and any one parte of hym, that proportion is called Superparticulare.
1570. Billingsley, Euclid, V. 127 b. Multiplex Superperticular is when the antecedent containeth the consequent more then once, and moreouer onely one parte of the same.
1597. Morley, Introd. Mus., Annot. Proportions of multiplicitie might be … vsed … without great … offence: but those superparticulars and superpartients carry great difficultie.
1621. Burton, Anat. Mel., I. iii. I. iv. ’Tis superparticular, sesquialtera, sesquitertia … all those geometrical proportions are too little to express it.
a. 1696. Scarburgh, Euclid (1705), 180. In all Superparticulars the Numerator is, or may ever be reduced to an Unite. Ibid. If … there remains … any Quotal part of the Consequent … then the proportion is called Multiple Superparticular.
1776. Sir J. Hawkins, Gen. Hist. Mus., I. vi. 83. The sesquioctave tone, as being in a superparticular ratio, is incapable of an equal division.
1842. Smith’s Dict. Gr. & Rom. Antiq., 624/2. Each of the four ratios … is superparticular: i. e., the two terms of each differ from one another by unity.
Hence † Superparticularity.
1597. Morley, Introd. Mus., Annot. Al soundes contained in habitude of multiplicitie, or superparticularity, were of the olde musicians esteemed consonantes.
