superparticularadj.n.

Brit.

/ˌsuːpəpəˈtɪkjᵿlə/,

/ˌsjuːpəpəˈtɪkjᵿlə/, U.S.

/ˌsupərpə(r)ˈtɪkjələr/,

/ˈˌsupərpɑrˈtɪkjələr/

Forms: 1500s superparticulare, 1500s superperticular, 1500s– superparticular.

Origin: A borrowing from Latin. Etymon: Latin superparticularis.

Etymology: < post-classical Latin superparticularis (5th cent.) < classical Latin super- super- prefix + particulāris particular adj.

Mathematics. Now chiefly historical (in the context of early music).

A. adj.

1. Of a ratio: having a first term (the antecedent) with a value equal to the second term (the consequent) plus one (e.g. 3:2, 4:3, etc.), i.e. in which the antecedent contains the consequent once with one aliquot part remaining (e.g. 1½, 1⅓, 1¼ times).

ΘΚΠ

the world > relative properties > number > ratio or proportion > [adjective] > multiple > fractional or mixed

superparticular1557

superpartient1557

multiple superpartient1705

a1398 J. Trevisa tr. Bartholomaeus Anglicus De Proprietatibus Rerum (BL Add. 27944) (1975) II. xix. cxxv. 1363 Þe superparticularis nombre conteyneþ in comparisoun al þe lasse nombre and somwhat ouer, as þre conteyneþ tweyne and oon more.]

1557 R. Record Whetstone of Witte sig. Bii If the greater [number] containe the lesser, and any one parte of hym, that proportion is called Superparticulare.

1621 R. Burton Anat. Melancholy i. iii. i. iv. 250 T'is superparticular, sesquialtera, sesquitertia,..all those Geometricall proportions are too little to expresse it.

1776 J. Hawkins Gen. Hist. Music I. i. vi. 83 The sesquioctave tone, as being in a superparticular ratio, is incapable of an equal division.

1842 W. Smith Dict. Greek & Rom. Antiq. 624/2 Each of the four ratios..is superparticular; i.e., the two terms of each differ from one another by unity.

1913 P. Monroe Cycl. Educ. V. 108/1 For example, there were multiple ratios (na: a), superparticular ratios (n +1: n),..and so on.

2010 S. Hagel Anc. Greek Music v. 169 The quest for mathematical elegance, and more specifically, for the description of musical scales in superparticular ratios.

2. multiple superparticular adj. (of a ratio) having an antecedent which contains the consequent a number of times with one aliquot part remaining, e.g. 2½, 2⅓, 3½, 3⅓, etc.

ΚΠ

1570 H. Billingsley tr. Euclid Elements Geom. v. f.127^v Multiplex Superperticular is when the antecedent containeth the consequent more then once, and moreouer onely one parte of the same.]

1705 E. Scarburgh Eng. Euclide 180 (note) If..there remains..any Quotal part of the Consequent..then the proportion is called Multiple Superparticular.

1816 New Monthly Mag. Apr. 209/1 Multiple-superparticular ratio is when the greater contains the less many times, and some part of it besides.

1981 Amer. Jrnl. Philol. 102 407 The multiple superparticular ratio when reduced to its lowest terms is of the form (nx + 1):x, where x > 1 and n > 1.

B. n.

A superparticular ratio.

ΚΠ

1597 T. Morley Plaine & Easie Introd. Musicke Annot. sig. *4^v Proportions of multiplicitie might be..vsed..without great..offence: but those superparticulars and superpartients carry great difficultie.

1705 E. Scarburgh Eng. Euclide 180 (note) In all Superparticulars the Numerator is, or may ever be reduced to an Unite.

1816 T. Taylor Theoretic Arithm. ii. ii. 58 It is now requisite to investigate how many superparticulars every multiple has for its attendants.

1916 G. Johnson Arithm. Philos. Nicomachus Gerasa vii. 32 The first species of the multiple and the first species of the superparticular, yield the second multiple.

2011 A. Heeffer in B. S. Yadav Anc. Indian Leaps into Math. 135 A superparticular has the form ⁿ⁺¹/ _n and thus covers proportions such as the common sesquialter (3/2) and sesquiter (4/3) proportions.

This entry has been updated (OED Third Edition, June 2012; most recently modified version published online March 2022).

单词	superparticular
释义	superparticularadj.n. Brit. /ˌsuːpəpəˈtɪkjᵿlə/, /ˌsjuːpəpəˈtɪkjᵿlə/, U.S. /ˌsupərpə(r)ˈtɪkjələr/, /ˈˌsupərpɑrˈtɪkjələr/ Forms: 1500s superparticulare, 1500s superperticular, 1500s– superparticular. Origin: A borrowing from Latin. Etymon: Latin superparticularis. Etymology: < post-classical Latin superparticularis (5th cent.) < classical Latin super- super- prefix + particulāris particular adj. Mathematics. Now chiefly historical (in the context of early music). A. adj. 1. Of a ratio: having a first term (the antecedent) with a value equal to the second term (the consequent) plus one (e.g. 3:2, 4:3, etc.), i.e. in which the antecedent contains the consequent once with one aliquot part remaining (e.g. 1½, 1⅓, 1¼ times). ΘΚΠ the world > relative properties > number > ratio or proportion > [adjective] > multiple > fractional or mixed superparticular1557 superpartient1557 multiple superpartient1705 a1398 J. Trevisa tr. Bartholomaeus Anglicus De Proprietatibus Rerum (BL Add. 27944) (1975) II. xix. cxxv. 1363 Þe superparticularis nombre conteyneþ in comparisoun al þe lasse nombre and somwhat ouer, as þre conteyneþ tweyne and oon more.] 1557 R. Record Whetstone of Witte sig. Bii If the greater [number] containe the lesser, and any one parte of hym, that proportion is called Superparticulare. 1621 R. Burton Anat. Melancholy i. iii. i. iv. 250 T'is superparticular, sesquialtera, sesquitertia,..all those Geometricall proportions are too little to expresse it. 1776 J. Hawkins Gen. Hist. Music I. i. vi. 83 The sesquioctave tone, as being in a superparticular ratio, is incapable of an equal division. 1842 W. Smith Dict. Greek & Rom. Antiq. 624/2 Each of the four ratios..is superparticular; i.e., the two terms of each differ from one another by unity. 1913 P. Monroe Cycl. Educ. V. 108/1 For example, there were multiple ratios (na: a), superparticular ratios (n +1: n),..and so on. 2010 S. Hagel Anc. Greek Music v. 169 The quest for mathematical elegance, and more specifically, for the description of musical scales in superparticular ratios. 2. multiple superparticular adj. (of a ratio) having an antecedent which contains the consequent a number of times with one aliquot part remaining, e.g. 2½, 2⅓, 3½, 3⅓, etc. ΚΠ 1570 H. Billingsley tr. Euclid Elements Geom. v. f.127^v Multiplex Superperticular is when the antecedent containeth the consequent more then once, and moreouer onely one parte of the same.] 1705 E. Scarburgh Eng. Euclide 180 (note) If..there remains..any Quotal part of the Consequent..then the proportion is called Multiple Superparticular. 1816 New Monthly Mag. Apr. 209/1 Multiple-superparticular ratio is when the greater contains the less many times, and some part of it besides. 1981 Amer. Jrnl. Philol. 102 407 The multiple superparticular ratio when reduced to its lowest terms is of the form (nx + 1):x, where x > 1 and n > 1. B. n. A superparticular ratio. ΚΠ 1597 T. Morley Plaine & Easie Introd. Musicke Annot. sig. 4^v Proportions of multiplicitie might be..vsed..without great..offence: but those superparticulars and superpartients carry great difficultie. 1705 E. Scarburgh Eng. Euclide* 180 (note) In all Superparticulars the Numerator is, or may ever be reduced to an Unite. 1816 T. Taylor Theoretic Arithm. ii. ii. 58 It is now requisite to investigate how many superparticulars every multiple has for its attendants. 1916 G. Johnson Arithm. Philos. Nicomachus Gerasa vii. 32 The first species of the multiple and the first species of the superparticular, yield the second multiple. 2011 A. Heeffer in B. S. Yadav Anc. Indian Leaps into Math. 135 A superparticular has the form ⁿ⁺¹/ _n and thus covers proportions such as the common sesquialter (3/2) and sesquiter (4/3) proportions. This entry has been updated (OED Third Edition, June 2012; most recently modified version published online March 2022). < adj.n.1557
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