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superparticular
† ˌsuperparˈticular, a. (n.) 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. 1½, 11/3, 11/4 times), i.e. the ratio of any number to the next below it (3/2, 4/3, 5/4); a... Oxford English Dictionary
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Superpartient ratio
In mathematics, a superpartient ratio, also called superpartient number or epimeric ratio, is a rational number that is greater than one and is not superparticular Ratios of the form are also greater than one and fully reduced, but are called superparticular ratios and are not superpartient. wikipedia.org
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superpartient
† superˈpartient, a. (n.) Arith. Obs. [ad. late L. superpartientem, -ens, f. super- super- 14 + partiens, pr. pple. of partīrī to divide.] Applied to a ratio in which the antecedent contains the consequent once (or, multiple superpartient, any number of times) with any number (greater than one) of a... Oxford English Dictionary
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1.5
three halves, or sesquialterum) may refer to: 1.5 °C is the preferred limit of global warming signed in the Paris Agreement 1.5, an album by Big Data Superparticular wikipedia.org
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sesquialteral
sesquialteral, a. (sɛskwɪˈæltərəl) [f. L. sesquialter: see prec.] = sesquialter 1.1603 Holland Plutarch's Mor. 1358 The proportion..of Diapente, [is] Hemolios or Sesquialterall, that is to say, the whole and halfe as much more. 1692 Bentley Boyle Lect. viii. (1693) 10 As the six Primary Planets revo... Oxford English Dictionary
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Ragisma
In music and tuning, the ragisma is an interval with the ratio of 4375:4374, ≈0.396 cents (a superparticular ratio). wikipedia.org
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Sesquialtera
Sesquialtera ('one and a half') may refer to: Sesquialterum in mathematics, the ratio 3:2, a superparticular ratio Sesquialtera or the equivalent Greek wikipedia.org
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sescuple
sescuple, a. Now rare. (ˈsɛskjuːp(ə)l) [ad. L. sescuplus or sescuplex, var. sesquiplus, -plex, f. sesqui- sesqui- + -plus, -plex -fold.] = sesquialter a.1694 W. Wotton Anc. & Mod. Learn. (1697) 100, 9 is in a Sescuple Proportion to 6. 1774 Mitford Ess. Harmony Lang. 13 Rhythmus is either even, as in... Oxford English Dictionary
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Superparticular数
Superparticular数是以下形式的有理数： 其中n为正整数。 Superparticular数是由在其著作《算术简介》〈Introduction to Arithmetic〉中提出，应用在音乐理论及视觉和谐度的研究中。 比例英文名称及相关的音程 参考资料 外部连结 An Arithmetical Rubric：由Siemen Terpstra所著，有关Superparticular数在和声上的应用 Superparticular numbers：David Canright应用Superparticular数架构五声调式 wikipedia.org
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Syntonic comma
Mathematically, by Størmer's theorem, 81:80 is the closest superparticular ratio possible with regular numbers as numerator and denominator. Thus, although smaller intervals can be described within 5-limit tunings, they cannot be described as superparticular ratios. wikipedia.org
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Pythagorean interval
Fundamental intervals The fundamental intervals are the superparticular ratios 2/1, 3/2, and 4/3. 2/1 is the octave or diapason (Greek for "across all" This has the ratio 9/8, also known as epogdoon and it is the only other superparticular ratio of Pythagorean tuning, as shown by Størmer's theorem. wikipedia.org
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Størmer's theorem
Example To find the ten consecutive pairs of {2,3,5}-smooth numbers (in music theory, giving the superparticular ratios for just tuning) let P = {2,3,5 Størmer's theorem allows all possible superparticular ratios in a given limit to be found. wikipedia.org
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List of intervals in 5-limit just intonation
The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third). wikipedia.org
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Euler product
Leibniz formula for can be interpreted as a Dirichlet series using the (unique) Dirichlet character modulo 4, and converted to an Euler product of superparticular wikipedia.org
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Leibniz formula for π
It is: In this product, each term is a superparticular ratio, each numerator is an odd prime number, and each denominator is the nearest multiple of 4 wikipedia.org
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