「スーパーパーティキュラー」の版間の差分

''superparticular''という単語はラテン語から来ていて、"1パーツ分だけ超過している"という意味になる。相当するギリシャ語由来の単語は''epimoric'' (希: επιμοριος, ''epimórios'') である。

== Definitions ==

In ancient Greece and until around the 19th century, superparticular ratios are defined as follows: "When one number contains the whole of another in itself, and some part of it besides, it is called superparticular."<ref>Taylor, Thomas (1816), ''[https://books.google.com.au/books?id=VuY3AAAAMAAJ Theoretic Arithmetic, in Three Books]'', p. 37</ref> In other words, a ratio is superparticular if, when expressed as an irreducible fraction, the denominator divides into the numerator once and leaves a remainder of 1.

In almost every case, this matches the modern definition of superparticular, i.e. ratios of the form <math>\frac{n + 1}{n}</math>, where <math>n</math> is a positive integer. In only one case does it deviate: that of [[2/1]]. According to traditional Greek arithmetic, 2/1 is not a superparticular ratio, but rather a ''multiple'': 1 divides into 2 twice, leaving a remainder of 0. Multiples and superparticulars are considered as distinct categories of numbers from that perspective. In musical terms, this would imply considering that 2/1 is not superparticular because it describes a [[Harmonic|multiple of the fundamental]], which other superparticular ratios do not.